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| <a href="online__sv_8sql__in.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/* ----------------------------------------------------------------------- */</span><span class="comment">/** </span></div> |
| <div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"> * @file online_sv.sql_in</span></div> |
| <div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> * @brief SQL functions for support vector machines</span></div> |
| <div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> * @sa For an introduction to Support vector machines (SVMs) and related kernel</span></div> |
| <div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> * methods, see the module description \ref grp_kernmach.</span></div> |
| <div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> */</span><span class="comment">/* ------------------------------------------------------------------------*/</span></div> |
| <div class="line"><a name="l00010"></a><span class="lineno"> 10</span> </div> |
| <div class="line"><a name="l00011"></a><span class="lineno"> 11</span> m4_include(`SQLCommon.m4<span class="stringliteral">')</span></div> |
| <div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment">@addtogroup grp_kernmach</span></div> |
| <div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">@about</span></div> |
| <div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment">Support vector machines (SVMs) and related kernel methods have been one of </span></div> |
| <div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment">the most popular and well-studied machine learning techniques of the </span></div> |
| <div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment">past 15 years, with an amazing number of innovations and applications.</span></div> |
| <div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment">In a nutshell, an SVM model \f$f(x)\f$ takes the form of</span></div> |
| <div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment">\f[</span></div> |
| <div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment"> f(x) = \sum_i \alpha_i k(x_i,x),</span></div> |
| <div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment">\f]</span></div> |
| <div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment">where each \f$ \alpha_i \f$ is a real number, each \f$ \boldsymbol x_i \f$ is a</span></div> |
| <div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment">data point from the training set (called a support vector), and</span></div> |
| <div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment">\f$ k(\cdot, \cdot) \f$ is a kernel function that measures how "similar" two</span></div> |
| <div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment">objects are. In regression, \f$ f(\boldsymbol x) \f$ is the regression function</span></div> |
| <div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment">we seek. In classification, \f$ f(\boldsymbol x) \f$ serves as</span></div> |
| <div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">the decision boundary; so for example in binary classification, the predictor </span></div> |
| <div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">can output class 1 for object \f$x\f$ if \f$ f(\boldsymbol x) \geq 0 \f$, and class</span></div> |
| <div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">2 otherwise.</span></div> |
| <div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">In the case when the kernel function \f$ k(\cdot, \cdot) \f$ is the standard</span></div> |
| <div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">inner product on vectors, \f$ f(\boldsymbol x) \f$ is just an alternative way of</span></div> |
| <div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment">writing a linear function</span></div> |
| <div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment">\f[</span></div> |
| <div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment"> f'(\boldsymbol x) = \langle \boldsymbol w, \boldsymbol x \rangle,</span></div> |
| <div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">\f]</span></div> |
| <div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">where \f$ \boldsymbol w \f$ is a weight vector having the same dimension as</span></div> |
| <div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment">\f$ \boldsymbol x \f$. One of the key points of SVMs is that we can use more</span></div> |
| <div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">fancy kernel functions to efficiently learn linear models in high-dimensional</span></div> |
| <div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment">feature spaces, since \f$ k(\boldsymbol x_i, \boldsymbol x_j) \f$ can be</span></div> |
| <div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="comment">understood as an efficient way of computing an inner product in the feature</span></div> |
| <div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment">space:</span></div> |
| <div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">\f[</span></div> |
| <div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment"> k(\boldsymbol x_i, \boldsymbol x_j)</span></div> |
| <div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment"> = \langle \phi(\boldsymbol x_i), \phi(\boldsymbol x_j) \rangle,</span></div> |
| <div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment">\f]</span></div> |
| <div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">where \f$ \phi(\boldsymbol x) \f$ projects \f$ \boldsymbol x \f$ into a</span></div> |
| <div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment">(possibly infinite-dimensional) feature space.</span></div> |
| <div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment">There are many algorithms for learning kernel machines. This module</span></div> |
| <div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment">implements the class of online learning with kernels algorithms</span></div> |
| <div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment">described in Kivinen et al. [1]. It also includes the Stochastic</span></div> |
| <div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment">Gradient Descent (SGD) method [3] for learning linear SVMs with the Hinge</span></div> |
| <div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment">loss \f$l(z) = \max(0, 1-z)\f$. See also the book Scholkopf and Smola [2] for much more</span></div> |
| <div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment">details.</span></div> |
| <div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment">The SGD implementation is based on L&eacute;on Bottou's SGD package</span></div> |
| <div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="comment">(http://leon.bottou.org/projects/sgd). The methods introduced in [1]</span></div> |
| <div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="comment">are implemented according to their original descriptions, except that</span></div> |
| <div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment">we only update the support vector model when we make a significant</span></div> |
| <div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment">error. The original algorithms in [1] update the support vector model at</span></div> |
| <div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment">every step, even when no error was made, in the name of</span></div> |
| <div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment">regularisation. For practical purposes, and this is verified</span></div> |
| <div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="comment">empirically to a certain degree, updating only when necessary is both</span></div> |
| <div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment">faster and better from a learning-theoretic point of view, at least in</span></div> |
| <div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment">the i.i.d. setting.</span></div> |
| <div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment">Methods for classification, regression and novelty detection are </span></div> |
| <div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment">available. Multiple instances of the algorithms can be executed </span></div> |
| <div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="comment">in parallel on different subsets of the training data. The resultant</span></div> |
| <div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="comment">support vector models can then be combined using standard techniques</span></div> |
| <div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="comment">like averaging or majority voting.</span></div> |
| <div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="comment">Training data points are accessed via a table or a view. The support</span></div> |
| <div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment">vector models can also be stored in tables for fast execution.</span></div> |
| <div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="comment">@input</span></div> |
| <div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="comment">For classification and regression, the training table/view is expected to be of the following form (the array size of <em>ind</em> must not be greater than 102,400.):\n</span></div> |
| <div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="comment"><pre>{TABLE|VIEW} <em>input_table</em> (</span></div> |
| <div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="comment"> ...</span></div> |
| <div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="comment"> <em>id</em> INT,</span></div> |
| <div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="comment"> <em>ind</em> FLOAT8[],</span></div> |
| <div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="comment"> <em>label</em> FLOAT8,</span></div> |
| <div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="comment"> ...</span></div> |
| <div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="comment">)</pre></span></div> |
| <div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="comment">For novelty detection, the label field is not required.</span></div> |
| <div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="comment">@usage</span></div> |
| <div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="comment">- Regression learning is achieved through the following function:</span></div> |
| <div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="comment"> <pre>SELECT \ref svm_regression(</span></div> |
| <div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="comment"> '<em>input_table</em>', '<em>model_table</em>', <em>parallel</em>, '<em>kernel_func</em>', </span></div> |
| <div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="comment"> <em>verbose DEFAULT false</em>, <em>eta DEFAULT 0.1</em>, <em>nu DEFAULT 0.005</em>, <em>slambda DEFAULT 0.05</em></span></div> |
| <div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="comment"> );</pre> </span></div> |
| <div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="comment">- Classification learning is achieved through the following two</span></div> |
| <div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="comment"> functions:</span></div> |
| <div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="comment"> -# Learn linear SVM(s) using SGD [3]:</span></div> |
| <div class="line"><a name="l00103"></a><span class="lineno"> 103</span> <span class="comment"> <pre>SELECT \ref lsvm_classification(</span></div> |
| <div class="line"><a name="l00104"></a><span class="lineno"> 104</span> <span class="comment"> '<em>input_table</em>', '<em>model_table</em>', <em>parallel</em>, </span></div> |
| <div class="line"><a name="l00105"></a><span class="lineno"> 105</span> <span class="comment"> <em>verbose DEFAULT false</em>, <em>eta DEFAULT 0.1</em>, <em>reg DEFAULT 0.001</em></span></div> |
| <div class="line"><a name="l00106"></a><span class="lineno"> 106</span> <span class="comment"> );</pre> </span></div> |
| <div class="line"><a name="l00107"></a><span class="lineno"> 107</span> <span class="comment"> -# Learn linear or non-linear SVM(s) using the method described in [1]:</span></div> |
| <div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="comment"> <pre>SELECT \ref svm_classification(</span></div> |
| <div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="comment"> '<em>input_table</em>', '<em>model_table</em>', <em>parallel</em>, '<em>kernel_func</em>', </span></div> |
| <div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="comment"> <em>verbose DEFAULT false</em>, <em>eta DEFAULT 0.1</em>, <em>nu DEFAULT 0.005</em></span></div> |
| <div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="comment"> );</pre> </span></div> |
| <div class="line"><a name="l00112"></a><span class="lineno"> 112</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00113"></a><span class="lineno"> 113</span> <span class="comment">- Novelty detection is achieved through the following function:</span></div> |
| <div class="line"><a name="l00114"></a><span class="lineno"> 114</span> <span class="comment"> <pre>SELECT \ref svm_novelty_detection(</span></div> |
| <div class="line"><a name="l00115"></a><span class="lineno"> 115</span> <span class="comment"> '<em>input_table</em>', '<em>model_table</em>', <em>parallel</em>, '<em>kernel_func</em>', </span></div> |
| <div class="line"><a name="l00116"></a><span class="lineno"> 116</span> <span class="comment"> <em>verbose DEFAULT false</em>, <em>eta DEFAULT 0.1</em>, <em>nu DEFAULT 0.005</em></span></div> |
| <div class="line"><a name="l00117"></a><span class="lineno"> 117</span> <span class="comment"> );</pre></span></div> |
| <div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="comment"> Assuming the model_table parameter takes on value 'model', each learning function will produce two tables </span></div> |
| <div class="line"><a name="l00119"></a><span class="lineno"> 119</span> <span class="comment"> as output: 'model' and 'model_param'.</span></div> |
| <div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="comment"> The first contains the support vectors of the model(s) learned.</span></div> |
| <div class="line"><a name="l00121"></a><span class="lineno"> 121</span> <span class="comment"> The second contains the parameters of the model(s) learned, which includes information like the kernel function</span></div> |
| <div class="line"><a name="l00122"></a><span class="lineno"> 122</span> <span class="comment"> used and the value of the intercept, if there is one.</span></div> |
| <div class="line"><a name="l00123"></a><span class="lineno"> 123</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00124"></a><span class="lineno"> 124</span> <span class="comment">- To make predictions on a single data point x using a single model</span></div> |
| <div class="line"><a name="l00125"></a><span class="lineno"> 125</span> <span class="comment"> learned previously, we use the function</span></div> |
| <div class="line"><a name="l00126"></a><span class="lineno"> 126</span> <span class="comment"> <pre>SELECT \ref</span></div> |
| <div class="line"><a name="l00127"></a><span class="lineno"> 127</span> <span class="comment"> svm_predict('<em>model_table</em>',<em>x</em>);</pre></span></div> |
| <div class="line"><a name="l00128"></a><span class="lineno"> 128</span> <span class="comment"> If the model is produced by the lsvm_classification() function, use</span></div> |
| <div class="line"><a name="l00129"></a><span class="lineno"> 129</span> <span class="comment"> the following prediction function instead</span></div> |
| <div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="comment"> <pre>SELECT \ref</span></div> |
| <div class="line"><a name="l00131"></a><span class="lineno"> 131</span> <span class="comment"> lsvm_predict('<em>model_table</em>',<em>x</em>);</pre></span></div> |
| <div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00133"></a><span class="lineno"> 133</span> <span class="comment">- To make predictions on new data points using multiple models</span></div> |
| <div class="line"><a name="l00134"></a><span class="lineno"> 134</span> <span class="comment"> learned in parallel, we use the function</span></div> |
| <div class="line"><a name="l00135"></a><span class="lineno"> 135</span> <span class="comment"> <pre>SELECT \ref</span></div> |
| <div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="comment"> svm_predict_combo('<em>model_table</em>',<em>x</em>);</pre></span></div> |
| <div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="comment"> If the models are produced by the lsvm_classification() function, use</span></div> |
| <div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="comment"> the following prediction function instead</span></div> |
| <div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="comment"> <pre>SELECT \ref</span></div> |
| <div class="line"><a name="l00140"></a><span class="lineno"> 140</span> <span class="comment"> lsvm_predict_combo('<em>model_table</em>',<em>x</em>);</pre></span></div> |
| <div class="line"><a name="l00141"></a><span class="lineno"> 141</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00143"></a><span class="lineno"> 143</span> <span class="comment">- Note that, at the moment, we cannot use MADLIB_SCHEMA.svm_predict() and MADLIB_SCHEMA.svm_predict_combo()</span></div> |
| <div class="line"><a name="l00144"></a><span class="lineno"> 144</span> <span class="comment"> on multiple data points. For example, something like the following will fail:</span></div> |
| <div class="line"><a name="l00145"></a><span class="lineno"> 145</span> <span class="comment"> <pre>SELECT \ref svm_predict('<em>model_table</em>',<em>x</em>) FROM data_table;</pre></span></div> |
| <div class="line"><a name="l00146"></a><span class="lineno"> 146</span> <span class="comment"> Instead, to make predictions on new data points stored in a table using</span></div> |
| <div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="comment"> previously learned models, we use the function:</span></div> |
| <div class="line"><a name="l00148"></a><span class="lineno"> 148</span> <span class="comment"> <pre>SELECT \ref svm_predict_batch('<em>input_table</em>', '<em>data_col</em>', '<em>id_col</em>', '<em>model_table</em>', '<em>output_table</em>', <em>parallel</em>);</pre></span></div> |
| <div class="line"><a name="l00149"></a><span class="lineno"> 149</span> <span class="comment"> The output_table is created during the function call; an existing table with </span></div> |
| <div class="line"><a name="l00150"></a><span class="lineno"> 150</span> <span class="comment"> the same name will be dropped.</span></div> |
| <div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="comment"> If the parallel parameter is true, then each data point in the input table will have multiple </span></div> |
| <div class="line"><a name="l00152"></a><span class="lineno"> 152</span> <span class="comment"> predicted values corresponding to the number of models learned in</span></div> |
| <div class="line"><a name="l00153"></a><span class="lineno"> 153</span> <span class="comment"> parallel.\n\n</span></div> |
| <div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="comment"> Similarly, use the following function for batch prediction if the</span></div> |
| <div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="comment"> model(s) is produced by the lsvm_classification() function:</span></div> |
| <div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="comment"> <pre>SELECT \ref lsvm_predict_batch('<em>input_table</em>', '<em>data_col</em>', '<em>id_col</em>', '<em>model_table</em>','<em>output_table</em>', <em>parallel</em>);</pre></span></div> |
| <div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="comment"> </span></div> |
| <div class="line"><a name="l00158"></a><span class="lineno"> 158</span> <span class="comment"> </span></div> |
| <div class="line"><a name="l00159"></a><span class="lineno"> 159</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00160"></a><span class="lineno"> 160</span> <span class="comment">@implementation</span></div> |
| <div class="line"><a name="l00161"></a><span class="lineno"> 161</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="comment">Currently, three kernel functions have been implemented: dot product (\ref svm_dot), polynomial (\ref svm_polynomial) and Gaussian (\ref svm_gaussian) kernels. To use the dot product kernel function,</span></div> |
| <div class="line"><a name="l00163"></a><span class="lineno"> 163</span> <span class="comment">simply use '<tt><em>MADLIB_SCHEMA.svm_dot</em></tt>' as the <tt>kernel_func</tt> argument, which accepts any function that takes in two float[] and returns a float. To use the polynomial or Gaussian kernels,</span></div> |
| <div class="line"><a name="l00164"></a><span class="lineno"> 164</span> <span class="comment">a wrapper function is needed since these kernels require additional input parameters (see online_sv.sql_in for input parameters).</span></div> |
| <div class="line"><a name="l00165"></a><span class="lineno"> 165</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00166"></a><span class="lineno"> 166</span> <span class="comment">For example, to use the polynomial kernel with degree 2, first create a wrapper function:</span></div> |
| <div class="line"><a name="l00167"></a><span class="lineno"> 167</span> <span class="comment"><pre>CREATE OR REPLACE FUNCTION mykernel(FLOAT[],FLOAT[]) RETURNS FLOAT AS $$</span></div> |
| <div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <span class="comment"> SELECT \ref svm_polynomial($1,$2,2)</span></div> |
| <div class="line"><a name="l00169"></a><span class="lineno"> 169</span> <span class="comment">$$ language sql;</pre></span></div> |
| <div class="line"><a name="l00170"></a><span class="lineno"> 170</span> <span class="comment">Then call the SVM learning functions with <tt>mykernel</tt> as the argument to <tt>kernel_func</tt>.</span></div> |
| <div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="comment"><pre>SELECT \ref svm_regression('my_schema.my_train_data', 'mymodel', false, 'mykernel');</pre></span></div> |
| <div class="line"><a name="l00172"></a><span class="lineno"> 172</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="comment">To drop all tables pertaining to the model, we can use</span></div> |
| <div class="line"><a name="l00174"></a><span class="lineno"> 174</span> <span class="comment"><pre>SELECT \ref svm_drop_model('model_table');</pre></span></div> |
| <div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00176"></a><span class="lineno"> 176</span> <span class="comment">@examp</span></div> |
| <div class="line"><a name="l00177"></a><span class="lineno"> 177</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00178"></a><span class="lineno"> 178</span> <span class="comment">As a general first step, we need to prepare and populate an input </span></div> |
| <div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="comment">table/view with the following structure:</span></div> |
| <div class="line"><a name="l00180"></a><span class="lineno"> 180</span> <span class="comment">\code </span></div> |
| <div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="comment">TABLE/VIEW my_schema.my_input_table </span></div> |
| <div class="line"><a name="l00182"></a><span class="lineno"> 182</span> <span class="comment">( </span></div> |
| <div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="comment"> id INT, -- point ID</span></div> |
| <div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="comment"> ind FLOAT8[], -- data point</span></div> |
| <div class="line"><a name="l00185"></a><span class="lineno"> 185</span> <span class="comment"> label FLOAT8 -- label of data point</span></div> |
| <div class="line"><a name="l00186"></a><span class="lineno"> 186</span> <span class="comment">);</span></div> |
| <div class="line"><a name="l00187"></a><span class="lineno"> 187</span> <span class="comment">\endcode </span></div> |
| <div class="line"><a name="l00188"></a><span class="lineno"> 188</span> <span class="comment"> Note: The label field is not required for novelty detection.</span></div> |
| <div class="line"><a name="l00189"></a><span class="lineno"> 189</span> <span class="comment"> </span></div> |
| <div class="line"><a name="l00190"></a><span class="lineno"> 190</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00191"></a><span class="lineno"> 191</span> <span class="comment"><strong>Example usage for regression</strong>:</span></div> |
| <div class="line"><a name="l00192"></a><span class="lineno"> 192</span> <span class="comment"> -# We can randomly generate 1000 5-dimensional data labelled by the simple target function </span></div> |
| <div class="line"><a name="l00193"></a><span class="lineno"> 193</span> <span class="comment">\code</span></div> |
| <div class="line"><a name="l00194"></a><span class="lineno"> 194</span> <span class="comment">t(x) = if x[5] = 10 then 50 else if x[5] = -10 then 50 else 0;</span></div> |
| <div class="line"><a name="l00195"></a><span class="lineno"> 195</span> <span class="comment">\endcode</span></div> |
| <div class="line"><a name="l00196"></a><span class="lineno"> 196</span> <span class="comment">and store that in the my_schema.my_train_data table as follows:</span></div> |
| <div class="line"><a name="l00197"></a><span class="lineno"> 197</span> <span class="comment">\code</span></div> |
| <div class="line"><a name="l00198"></a><span class="lineno"> 198</span> <span class="comment">sql> select MADLIB_SCHEMA.svm_generate_reg_data('my_schema.my_train_data', 1000, 5);</span></div> |
| <div class="line"><a name="l00199"></a><span class="lineno"> 199</span> <span class="comment">\endcode</span></div> |
| <div class="line"><a name="l00200"></a><span class="lineno"> 200</span> <span class="comment"> -# We can now learn a regression model and store the resultant model</span></div> |
| <div class="line"><a name="l00201"></a><span class="lineno"> 201</span> <span class="comment"> under the name 'myexp'.</span></div> |
| <div class="line"><a name="l00202"></a><span class="lineno"> 202</span> <span class="comment">\code</span></div> |
| <div class="line"><a name="l00203"></a><span class="lineno"> 203</span> <span class="comment">sql> select MADLIB_SCHEMA.svm_regression('my_schema.my_train_data', 'myexp', false, 'MADLIB_SCHEMA.svm_dot');</span></div> |
| <div class="line"><a name="l00204"></a><span class="lineno"> 204</span> <span class="comment">\endcode</span></div> |
| <div class="line"><a name="l00205"></a><span class="lineno"> 205</span> <span class="comment"> -# We can now start using it to predict the labels of new data points </span></div> |
| <div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="comment"> like as follows:</span></div> |
| <div class="line"><a name="l00207"></a><span class="lineno"> 207</span> <span class="comment">\code</span></div> |
| <div class="line"><a name="l00208"></a><span class="lineno"> 208</span> <span class="comment">sql> select MADLIB_SCHEMA.svm_predict('myexp', '{1,2,4,20,10}');</span></div> |
| <div class="line"><a name="l00209"></a><span class="lineno"> 209</span> <span class="comment">sql> select MADLIB_SCHEMA.svm_predict('myexp', '{1,2,4,20,-10}');</span></div> |
| <div class="line"><a name="l00210"></a><span class="lineno"> 210</span> <span class="comment">\endcode</span></div> |
| <div class="line"><a name="l00211"></a><span class="lineno"> 211</span> <span class="comment"> -# To learn multiple support vector models, we replace the learning step above by </span></div> |
| <div class="line"><a name="l00212"></a><span class="lineno"> 212</span> <span class="comment">\code</span></div> |
| <div class="line"><a name="l00213"></a><span class="lineno"> 213</span> <span class="comment">sql> select MADLIB_SCHEMA.svm_regression('my_schema.my_train_data', 'myexp', true, 'MADLIB_SCHEMA.svm_dot');</span></div> |
| <div class="line"><a name="l00214"></a><span class="lineno"> 214</span> <span class="comment">\endcode</span></div> |
| <div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="comment">The resultant models can be used for prediction as follows:</span></div> |
| <div class="line"><a name="l00216"></a><span class="lineno"> 216</span> <span class="comment">\code</span></div> |
| <div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="comment">sql> select * from MADLIB_SCHEMA.svm_predict_combo('myexp', '{1,2,4,20,10}');</span></div> |
| <div class="line"><a name="l00218"></a><span class="lineno"> 218</span> <span class="comment">\endcode</span></div> |
| <div class="line"><a name="l00219"></a><span class="lineno"> 219</span> <span class="comment"> -# We can also predict the labels of all the data points stored in a table.</span></div> |
| <div class="line"><a name="l00220"></a><span class="lineno"> 220</span> <span class="comment"> For example, we can execute the following:</span></div> |
| <div class="line"><a name="l00221"></a><span class="lineno"> 221</span> <span class="comment">\code</span></div> |
| <div class="line"><a name="l00222"></a><span class="lineno"> 222</span> <span class="comment">sql> create table MADLIB_SCHEMA.svm_reg_test ( id int, ind float8[] );</span></div> |
| <div class="line"><a name="l00223"></a><span class="lineno"> 223</span> <span class="comment">sql> insert into MADLIB_SCHEMA.svm_reg_test (select id, ind from my_schema.my_train_data limit 20);</span></div> |
| <div class="line"><a name="l00224"></a><span class="lineno"> 224</span> <span class="comment">sql> select MADLIB_SCHEMA.svm_predict_batch('MADLIB_SCHEMA.svm_reg_test', 'ind', 'id', 'myexp', 'MADLIB_SCHEMA.svm_reg_output1', false); </span></div> |
| <div class="line"><a name="l00225"></a><span class="lineno"> 225</span> <span class="comment">sql> select * from MADLIB_SCHEMA.svm_reg_output1;</span></div> |
| <div class="line"><a name="l00226"></a><span class="lineno"> 226</span> <span class="comment">sql> select MADLIB_SCHEMA.svm_predict_batch('MADLIB_SCHEMA.svm_reg_test', 'ind', 'id, 'myexp', 'MADLIB_SCHEMA.svm_reg_output2', true);</span></div> |
| <div class="line"><a name="l00227"></a><span class="lineno"> 227</span> <span class="comment">sql> select * from MADLIB_SCHEMA.svm_reg_output2;</span></div> |
| <div class="line"><a name="l00228"></a><span class="lineno"> 228</span> <span class="comment">\endcode </span></div> |
| <div class="line"><a name="l00229"></a><span class="lineno"> 229</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00230"></a><span class="lineno"> 230</span> <span class="comment"><strong>Example usage for classification:</strong></span></div> |
| <div class="line"><a name="l00231"></a><span class="lineno"> 231</span> <span class="comment">-# We can randomly generate 2000 5-dimensional data labelled by the simple</span></div> |
| <div class="line"><a name="l00232"></a><span class="lineno"> 232</span> <span class="comment">target function </span></div> |
| <div class="line"><a name="l00233"></a><span class="lineno"> 233</span> <span class="comment">\code</span></div> |
| <div class="line"><a name="l00234"></a><span class="lineno"> 234</span> <span class="comment">t(x) = if x[1] > 0 and x[2] < 0 then 1 else -1;</span></div> |
| <div class="line"><a name="l00235"></a><span class="lineno"> 235</span> <span class="comment">\endcode</span></div> |
| <div class="line"><a name="l00236"></a><span class="lineno"> 236</span> <span class="comment">and store that in the my_schema.my_train_data table as follows:</span></div> |
| <div class="line"><a name="l00237"></a><span class="lineno"> 237</span> <span class="comment">\code </span></div> |
| <div class="line"><a name="l00238"></a><span class="lineno"> 238</span> <span class="comment">sql> select MADLIB_SCHEMA.svm_generate_cls_data('my_schema.my_train_data', 2000, 5);</span></div> |
| <div class="line"><a name="l00239"></a><span class="lineno"> 239</span> <span class="comment">\endcode</span></div> |
| <div class="line"><a name="l00240"></a><span class="lineno"> 240</span> <span class="comment">-# We can now learn a classification model and store the resultant model</span></div> |
| <div class="line"><a name="l00241"></a><span class="lineno"> 241</span> <span class="comment">under the name 'myexpc'.</span></div> |
| <div class="line"><a name="l00242"></a><span class="lineno"> 242</span> <span class="comment">\code</span></div> |
| <div class="line"><a name="l00243"></a><span class="lineno"> 243</span> <span class="comment">sql> select MADLIB_SCHEMA.svm_classification('my_schema.my_train_data', 'myexpc', false, 'MADLIB_SCHEMA.svm_dot');</span></div> |
| <div class="line"><a name="l00244"></a><span class="lineno"> 244</span> <span class="comment">\endcode</span></div> |
| <div class="line"><a name="l00245"></a><span class="lineno"> 245</span> <span class="comment">-# We can now start using it to predict the labels of new data points </span></div> |
| <div class="line"><a name="l00246"></a><span class="lineno"> 246</span> <span class="comment">like as follows:</span></div> |
| <div class="line"><a name="l00247"></a><span class="lineno"> 247</span> <span class="comment">\code</span></div> |
| <div class="line"><a name="l00248"></a><span class="lineno"> 248</span> <span class="comment">sql> select MADLIB_SCHEMA.svm_predict('myexpc', '{10,-2,4,20,10}');</span></div> |
| <div class="line"><a name="l00249"></a><span class="lineno"> 249</span> <span class="comment">\endcode </span></div> |
| <div class="line"><a name="l00250"></a><span class="lineno"> 250</span> <span class="comment">-# To learn multiple support vector models, replace the model-building and prediction steps above by </span></div> |
| <div class="line"><a name="l00251"></a><span class="lineno"> 251</span> <span class="comment">\code</span></div> |
| <div class="line"><a name="l00252"></a><span class="lineno"> 252</span> <span class="comment">sql> select MADLIB_SCHEMA.svm_classification('my_schema.my_train_data', 'myexpc', true, 'MADLIB_SCHEMA.svm_dot');</span></div> |
| <div class="line"><a name="l00253"></a><span class="lineno"> 253</span> <span class="comment">sql> select * from MADLIB_SCHEMA.svm_predict_combo('myexpc', '{10,-2,4,20,10}');</span></div> |
| <div class="line"><a name="l00254"></a><span class="lineno"> 254</span> <span class="comment">\endcode</span></div> |
| <div class="line"><a name="l00255"></a><span class="lineno"> 255</span> <span class="comment">-# To learn a linear support vector model using SGD, replace the model-building and prediction steps above by </span></div> |
| <div class="line"><a name="l00256"></a><span class="lineno"> 256</span> <span class="comment">\code</span></div> |
| <div class="line"><a name="l00257"></a><span class="lineno"> 257</span> <span class="comment">sql> select MADLIB_SCHEMA.lsvm_classification('my_schema.my_train_data', 'myexpc', false);</span></div> |
| <div class="line"><a name="l00258"></a><span class="lineno"> 258</span> <span class="comment">sql> select MADLIB_SCHEMA.lsvm_predict('myexpc', '{10,-2,4,20,10}');</span></div> |
| <div class="line"><a name="l00259"></a><span class="lineno"> 259</span> <span class="comment">\endcode</span></div> |
| <div class="line"><a name="l00260"></a><span class="lineno"> 260</span> <span class="comment">-# To learn multiple linear support vector models using SGD, replace the model-building and prediction steps above by </span></div> |
| <div class="line"><a name="l00261"></a><span class="lineno"> 261</span> <span class="comment">\code</span></div> |
| <div class="line"><a name="l00262"></a><span class="lineno"> 262</span> <span class="comment">sql> select MADLIB_SCHEMA.lsvm_classification('my_schema.my_train_data', 'myexpc', true);</span></div> |
| <div class="line"><a name="l00263"></a><span class="lineno"> 263</span> <span class="comment">sql> select MADLIB_SCHEMA.lsvm_predict_combo('myexpc', '{10,-2,4,20,10}');</span></div> |
| <div class="line"><a name="l00264"></a><span class="lineno"> 264</span> <span class="comment">\endcode</span></div> |
| <div class="line"><a name="l00265"></a><span class="lineno"> 265</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00266"></a><span class="lineno"> 266</span> <span class="comment"><strong>Example usage for novelty detection:</strong></span></div> |
| <div class="line"><a name="l00267"></a><span class="lineno"> 267</span> <span class="comment">-# We can randomly generate 100 2-dimensional data (the normal cases)</span></div> |
| <div class="line"><a name="l00268"></a><span class="lineno"> 268</span> <span class="comment">and store that in the my_schema.my_train_data table as follows:</span></div> |
| <div class="line"><a name="l00269"></a><span class="lineno"> 269</span> <span class="comment">\code</span></div> |
| <div class="line"><a name="l00270"></a><span class="lineno"> 270</span> <span class="comment">sql> select MADLIB_SCHEMA.svm_generate_nd_data('my_schema.my_train_data', 100, 2);</span></div> |
| <div class="line"><a name="l00271"></a><span class="lineno"> 271</span> <span class="comment">\endcode</span></div> |
| <div class="line"><a name="l00272"></a><span class="lineno"> 272</span> <span class="comment">-# Learning and predicting using a single novelty detection model can be done as follows:</span></div> |
| <div class="line"><a name="l00273"></a><span class="lineno"> 273</span> <span class="comment">\code</span></div> |
| <div class="line"><a name="l00274"></a><span class="lineno"> 274</span> <span class="comment">sql> select MADLIB_SCHEMA.svm_novelty_detection('my_schema.my_train_data', 'myexpnd', false, 'MADLIB_SCHEMA.svm_dot');</span></div> |
| <div class="line"><a name="l00275"></a><span class="lineno"> 275</span> <span class="comment">sql> select MADLIB_SCHEMA.svm_predict('myexpnd', '{10,-10}'); </span></div> |
| <div class="line"><a name="l00276"></a><span class="lineno"> 276</span> <span class="comment">sql> select MADLIB_SCHEMA.svm_predict('myexpnd', '{-1,-1}'); </span></div> |
| <div class="line"><a name="l00277"></a><span class="lineno"> 277</span> <span class="comment">\endcode</span></div> |
| <div class="line"><a name="l00278"></a><span class="lineno"> 278</span> <span class="comment">-# Learning and predicting using multiple models can be done as follows:</span></div> |
| <div class="line"><a name="l00279"></a><span class="lineno"> 279</span> <span class="comment">\code</span></div> |
| <div class="line"><a name="l00280"></a><span class="lineno"> 280</span> <span class="comment">sql> select MADLIB_SCHEMA.svm_novelty_detection('my_schema.my_train_data', 'myexpnd', true, 'MADLIB_SCHEMA.svm_dot');</span></div> |
| <div class="line"><a name="l00281"></a><span class="lineno"> 281</span> <span class="comment">sql> select * from MADLIB_SCHEMA.svm_predict_combo('myexpnd', '{10,-10}'); </span></div> |
| <div class="line"><a name="l00282"></a><span class="lineno"> 282</span> <span class="comment">sql> select * from MADLIB_SCHEMA.svm_predict_combo('myexpnd', '{-1,-1}'); </span></div> |
| <div class="line"><a name="l00283"></a><span class="lineno"> 283</span> <span class="comment">\endcode</span></div> |
| <div class="line"><a name="l00284"></a><span class="lineno"> 284</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00285"></a><span class="lineno"> 285</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00286"></a><span class="lineno"> 286</span> <span class="comment">@literature</span></div> |
| <div class="line"><a name="l00287"></a><span class="lineno"> 287</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00288"></a><span class="lineno"> 288</span> <span class="comment">[1] Jyrki Kivinen, Alexander J. Smola, and Robert C. Williamson: <em>Online</span></div> |
| <div class="line"><a name="l00289"></a><span class="lineno"> 289</span> <span class="comment"> Learning with Kernels</em>, IEEE Transactions on Signal Processing, 52(8),</span></div> |
| <div class="line"><a name="l00290"></a><span class="lineno"> 290</span> <span class="comment"> 2165-2176, 2004.</span></div> |
| <div class="line"><a name="l00291"></a><span class="lineno"> 291</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00292"></a><span class="lineno"> 292</span> <span class="comment">[2] Bernhard Scholkopf and Alexander J. Smola: <em>Learning with Kernels:</span></div> |
| <div class="line"><a name="l00293"></a><span class="lineno"> 293</span> <span class="comment"> Support Vector Machines, Regularization, Optimization, and Beyond</em>, </span></div> |
| <div class="line"><a name="l00294"></a><span class="lineno"> 294</span> <span class="comment"> MIT Press, 2002.</span></div> |
| <div class="line"><a name="l00295"></a><span class="lineno"> 295</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00296"></a><span class="lineno"> 296</span> <span class="comment">[3] L&eacute;on Bottou: <em>Large-Scale Machine Learning with Stochastic</span></div> |
| <div class="line"><a name="l00297"></a><span class="lineno"> 297</span> <span class="comment">Gradient Descent</em>, Proceedings of the 19th International</span></div> |
| <div class="line"><a name="l00298"></a><span class="lineno"> 298</span> <span class="comment">Conference on Computational Statistics, Springer, 2010.</span></div> |
| <div class="line"><a name="l00299"></a><span class="lineno"> 299</span> <span class="comment"> </span></div> |
| <div class="line"><a name="l00300"></a><span class="lineno"> 300</span> <span class="comment">@sa File online_sv.sql_in documenting the SQL functions.</span></div> |
| <div class="line"><a name="l00301"></a><span class="lineno"> 301</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00302"></a><span class="lineno"> 302</span> <span class="comment">@internal</span></div> |
| <div class="line"><a name="l00303"></a><span class="lineno"> 303</span> <span class="comment">@sa namespace online_sv (documenting the implementation in Python)</span></div> |
| <div class="line"><a name="l00304"></a><span class="lineno"> 304</span> <span class="comment">@endinternal</span></div> |
| <div class="line"><a name="l00305"></a><span class="lineno"> 305</span> <span class="comment"> </span></div> |
| <div class="line"><a name="l00306"></a><span class="lineno"> 306</span> <span class="comment">*/</span></div> |
| <div class="line"><a name="l00307"></a><span class="lineno"> 307</span> </div> |
| <div class="line"><a name="l00308"></a><span class="lineno"> 308</span> </div> |
| <div class="line"><a name="l00309"></a><span class="lineno"> 309</span> </div> |
| <div class="line"><a name="l00310"></a><span class="lineno"> 310</span> -- The following is the structure to record the results of a learning process.</div> |
| <div class="line"><a name="l00311"></a><span class="lineno"> 311</span> -- We work with arrays of float8 for now; we'll extend the code to work with sparse vectors next.</div> |
| <div class="line"><a name="l00312"></a><span class="lineno"> 312</span> --</div> |
| <div class="line"><a name="l00313"></a><span class="lineno"> 313</span> CREATE TYPE MADLIB_SCHEMA.svm_model_rec AS (</div> |
| <div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  inds <span class="keywordtype">int</span>, -- number of individuals processed </div> |
| <div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  cum_err float8, -- cumulative error</div> |
| <div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  epsilon float8, -- the size of the epsilon tube around the hyperplane, adaptively adjusted by algorithm</div> |
| <div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  rho float8, -- classification margin</div> |
| <div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  b float8, -- classifier offset</div> |
| <div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  nsvs <span class="keywordtype">int</span>, -- number of support vectors</div> |
| <div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  ind_dim <span class="keywordtype">int</span>, -- the dimension of the individuals</div> |
| <div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  weights float8[], -- the weight of the support vectors</div> |
| <div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  individuals float8[], -- the array of support vectors, represented as a 1-D array</div> |
| <div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  kernel_oid oid -- OID of kernel <span class="keyword">function</span></div> |
| <div class="line"><a name="l00324"></a><span class="lineno"> 324</span> );</div> |
| <div class="line"><a name="l00325"></a><span class="lineno"> 325</span> </div> |
| <div class="line"><a name="l00326"></a><span class="lineno"> 326</span> -- The following is the structure to record the results of the linear SVM sgd algorithm</div> |
| <div class="line"><a name="l00327"></a><span class="lineno"> 327</span> --</div> |
| <div class="line"><a name="l00328"></a><span class="lineno"> 328</span> CREATE TYPE MADLIB_SCHEMA.lsvm_sgd_model_rec AS (</div> |
| <div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  weights float8[], -- the weight vector</div> |
| <div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  wdiv float8, -- scaling factor <span class="keywordflow">for</span> the weights</div> |
| <div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  wbias float8, -- offset/bias of the linear model</div> |
| <div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  ind_dim <span class="keywordtype">int</span>, -- the dimension of the individuals</div> |
| <div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  inds <span class="keywordtype">int</span>, -- number of individuals processed </div> |
| <div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  cum_err <span class="keywordtype">int</span> -- cumulative error</div> |
| <div class="line"><a name="l00335"></a><span class="lineno"> 335</span> );</div> |
| <div class="line"><a name="l00336"></a><span class="lineno"> 336</span> </div> |
| <div class="line"><a name="l00337"></a><span class="lineno"> 337</span> </div> |
| <div class="line"><a name="l00338"></a><span class="lineno"> 338</span> -- The following is the <span class="keywordflow">return</span> type of a regression learning process</div> |
| <div class="line"><a name="l00339"></a><span class="lineno"> 339</span> --</div> |
| <div class="line"><a name="l00340"></a><span class="lineno"> 340</span> CREATE TYPE MADLIB_SCHEMA.svm_reg_result AS (</div> |
| <div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  model_table text, -- table where the model is stored</div> |
| <div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  model_name text, -- model name</div> |
| <div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  inds <span class="keywordtype">int</span>, -- number of individuals processed </div> |
| <div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  cum_err float8, -- cumulative error</div> |
| <div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  epsilon float8, -- the size of the epsilon tube around the hyperplane, adaptively adjusted by algorithm</div> |
| <div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  b float8, -- classifier offset</div> |
| <div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  nsvs <span class="keywordtype">int</span> -- number of support vectors</div> |
| <div class="line"><a name="l00348"></a><span class="lineno"> 348</span> );</div> |
| <div class="line"><a name="l00349"></a><span class="lineno"> 349</span> </div> |
| <div class="line"><a name="l00350"></a><span class="lineno"> 350</span> -- The following is the <span class="keywordflow">return</span> type of a classification learning process</div> |
| <div class="line"><a name="l00351"></a><span class="lineno"> 351</span> --</div> |
| <div class="line"><a name="l00352"></a><span class="lineno"> 352</span> CREATE TYPE MADLIB_SCHEMA.svm_cls_result AS (</div> |
| <div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  model_table text, -- table where the model is stored</div> |
| <div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  model_name text, -- model name</div> |
| <div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  inds <span class="keywordtype">int</span>, -- number of individuals processed </div> |
| <div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  cum_err float8, -- cumulative error</div> |
| <div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  rho float8, -- classification margin</div> |
| <div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  b float8, -- classifier offset</div> |
| <div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  nsvs <span class="keywordtype">int</span> -- number of support vectors</div> |
| <div class="line"><a name="l00360"></a><span class="lineno"> 360</span> );</div> |
| <div class="line"><a name="l00361"></a><span class="lineno"> 361</span> </div> |
| <div class="line"><a name="l00362"></a><span class="lineno"> 362</span> -- The following is the <span class="keywordflow">return</span> type of a linear classifier learning process</div> |
| <div class="line"><a name="l00363"></a><span class="lineno"> 363</span> --</div> |
| <div class="line"><a name="l00364"></a><span class="lineno"> 364</span> CREATE TYPE MADLIB_SCHEMA.lsvm_sgd_result AS (</div> |
| <div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  model_table text, -- table where the model is stored</div> |
| <div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  model_name text, -- model name</div> |
| <div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  inds <span class="keywordtype">int</span>, -- number of individuals processed </div> |
| <div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  ind_dim <span class="keywordtype">int</span>, -- the dimension of the individuals</div> |
| <div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  cum_err float8, -- cumulative error</div> |
| <div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  wdiv float8, -- scaling factor <span class="keywordflow">for</span> the weights</div> |
| <div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  wbias float8 -- classifier offset</div> |
| <div class="line"><a name="l00372"></a><span class="lineno"> 372</span> );</div> |
| <div class="line"><a name="l00373"></a><span class="lineno"> 373</span> </div> |
| <div class="line"><a name="l00374"></a><span class="lineno"> 374</span> -- The following is the <span class="keywordflow">return</span> type of a novelty detection learning process</div> |
| <div class="line"><a name="l00375"></a><span class="lineno"> 375</span> --</div> |
| <div class="line"><a name="l00376"></a><span class="lineno"> 376</span> CREATE TYPE MADLIB_SCHEMA.svm_nd_result AS (</div> |
| <div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  model_table text, -- table where the model is stored</div> |
| <div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  model_name text, -- model name</div> |
| <div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  inds <span class="keywordtype">int</span>, -- number of individuals processed </div> |
| <div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  rho float8, -- classification margin</div> |
| <div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  nsvs <span class="keywordtype">int</span> -- number of support vectors</div> |
| <div class="line"><a name="l00382"></a><span class="lineno"> 382</span> );</div> |
| <div class="line"><a name="l00383"></a><span class="lineno"> 383</span> </div> |
| <div class="line"><a name="l00384"></a><span class="lineno"> 384</span> -- The type <span class="keywordflow">for</span> representing support vectors</div> |
| <div class="line"><a name="l00385"></a><span class="lineno"> 385</span> --</div> |
| <div class="line"><a name="l00386"></a><span class="lineno"> 386</span> CREATE TYPE MADLIB_SCHEMA.svm_support_vector AS ( <span class="keywordtype">id</span> text, weight float8, sv float8[] );</div> |
| <div class="line"><a name="l00387"></a><span class="lineno"> 387</span> </div> |
| <div class="line"><a name="l00388"></a><span class="lineno"> 388</span> </div> |
| <div class="line"><a name="l00389"></a><span class="lineno"> 389</span> </div> |
| <div class="line"><a name="l00390"></a><span class="lineno"> 390</span> -- Kernel functions are a generalisation of inner products. </div> |
| <div class="line"><a name="l00391"></a><span class="lineno"> 391</span> -- They provide the means by which we can extend linear machines to work in non-linear transformed feature spaces.</div> |
| <div class="line"><a name="l00392"></a><span class="lineno"> 392</span> -- Here are a few standard kernels: dot product, polynomial kernel, Gaussian kernel.</div> |
| <div class="line"><a name="l00393"></a><span class="lineno"> 393</span> --<span class="comment"></span></div> |
| <div class="line"><a name="l00394"></a><span class="lineno"> 394</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00395"></a><span class="lineno"> 395</span> <span class="comment"> * @brief Dot product kernel function</span></div> |
| <div class="line"><a name="l00396"></a><span class="lineno"> 396</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00397"></a><span class="lineno"> 397</span> <span class="comment"> * @param x The data point \f$ \boldsymbol x \f$</span></div> |
| <div class="line"><a name="l00398"></a><span class="lineno"> 398</span> <span class="comment"> * @param y The data point \f$ \boldsymbol y \f$</span></div> |
| <div class="line"><a name="l00399"></a><span class="lineno"> 399</span> <span class="comment"> * @return Returns dot product of the two data points.</span></div> |
| <div class="line"><a name="l00400"></a><span class="lineno"> 400</span> <span class="comment"> * </span></div> |
| <div class="line"><a name="l00401"></a><span class="lineno"> 401</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00402"></a><span class="lineno"> 402</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.svm_dot(x float8[], y float8[]) RETURNS float8 </div> |
| <div class="line"><a name="l00403"></a><span class="lineno"> 403</span> AS <span class="stringliteral">'MODULE_PATHNAME'</span>, <span class="stringliteral">'svm_dot'</span> LANGUAGE C IMMUTABLE STRICT;</div> |
| <div class="line"><a name="l00404"></a><span class="lineno"> 404</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00405"></a><span class="lineno"> 405</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00406"></a><span class="lineno"> 406</span> <span class="comment"> * @brief Polynomial kernel function</span></div> |
| <div class="line"><a name="l00407"></a><span class="lineno"> 407</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00408"></a><span class="lineno"> 408</span> <span class="comment"> * @param x The data point \f$ \boldsymbol x \f$</span></div> |
| <div class="line"><a name="l00409"></a><span class="lineno"> 409</span> <span class="comment"> * @param y The data point \f$ \boldsymbol y \f$</span></div> |
| <div class="line"><a name="l00410"></a><span class="lineno"> 410</span> <span class="comment"> * @param degree The degree \f$ d \f$</span></div> |
| <div class="line"><a name="l00411"></a><span class="lineno"> 411</span> <span class="comment"> * @return Returns \f$ K(\boldsymbol x,\boldsymbol y)=(\boldsymbol x \cdot \boldsymbol y)^d \f$</span></div> |
| <div class="line"><a name="l00412"></a><span class="lineno"> 412</span> <span class="comment"> * </span></div> |
| <div class="line"><a name="l00413"></a><span class="lineno"> 413</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00414"></a><span class="lineno"> 414</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.svm_polynomial(x float8[], y float8[], degree float8) RETURNS float8 </div> |
| <div class="line"><a name="l00415"></a><span class="lineno"> 415</span> AS <span class="stringliteral">'MODULE_PATHNAME'</span>, <span class="stringliteral">'svm_polynomial'</span> LANGUAGE C IMMUTABLE STRICT;</div> |
| <div class="line"><a name="l00416"></a><span class="lineno"> 416</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00417"></a><span class="lineno"> 417</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00418"></a><span class="lineno"> 418</span> <span class="comment"> * @brief Gaussian kernel function</span></div> |
| <div class="line"><a name="l00419"></a><span class="lineno"> 419</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00420"></a><span class="lineno"> 420</span> <span class="comment"> * @param x The data point \f$ \boldsymbol x \f$</span></div> |
| <div class="line"><a name="l00421"></a><span class="lineno"> 421</span> <span class="comment"> * @param y The data point \f$ \boldsymbol y \f$</span></div> |
| <div class="line"><a name="l00422"></a><span class="lineno"> 422</span> <span class="comment"> * @param gamma The spread \f$ \gamma \f$</span></div> |
| <div class="line"><a name="l00423"></a><span class="lineno"> 423</span> <span class="comment"> * @return Returns \f$ K(\boldsymbol x,\boldsymbol y)=exp(-\gamma || \boldsymbol x \cdot \boldsymbol y ||^2 ) \f$</span></div> |
| <div class="line"><a name="l00424"></a><span class="lineno"><a class="code" href="online__sv_8sql__in.html#acc2d778a8eb48ab775ff9c1dff4a3141"> 424</a></span> <span class="comment"> * </span></div> |
| <div class="line"><a name="l00425"></a><span class="lineno"> 425</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00426"></a><span class="lineno"> 426</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.svm_gaussian(x float8[], y float8[], gamma float8) RETURNS float8 </div> |
| <div class="line"><a name="l00427"></a><span class="lineno"> 427</span> AS <span class="stringliteral">'MODULE_PATHNAME'</span>, <span class="stringliteral">'svm_gaussian'</span> LANGUAGE C IMMUTABLE STRICT; </div> |
| <div class="line"><a name="l00428"></a><span class="lineno"> 428</span> </div> |
| <div class="line"><a name="l00429"></a><span class="lineno"> 429</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.svm_predict_sub(<span class="keywordtype">int</span>,<span class="keywordtype">int</span>,float8[],float8[],float8[],text) RETURNS float8</div> |
| <div class="line"><a name="l00430"></a><span class="lineno"> 430</span> AS <span class="stringliteral">'MODULE_PATHNAME'</span>, <span class="stringliteral">'svm_predict_sub'</span> LANGUAGE C IMMUTABLE STRICT;</div> |
| <div class="line"><a name="l00431"></a><span class="lineno"> 431</span> </div> |
| <div class="line"><a name="l00432"></a><span class="lineno"> 432</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.svm_predict(svs MADLIB_SCHEMA.svm_model_rec, ind float8[], kernel text) </div> |
| <div class="line"><a name="l00433"></a><span class="lineno"> 433</span> RETURNS float8 AS $$</div> |
| <div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  SELECT MADLIB_SCHEMA.svm_predict_sub($1.nsvs, $1.ind_dim, $1.weights, $1.individuals, $2, $3);</div> |
| <div class="line"><a name="l00435"></a><span class="lineno"> 435</span> $$ LANGUAGE SQL;</div> |
| <div class="line"><a name="l00436"></a><span class="lineno"><a class="code" href="online__sv_8sql__in.html#a1ac76fdf9623e0a4db47665f2a80be90"> 436</a></span> </div> |
| <div class="line"><a name="l00437"></a><span class="lineno"> 437</span> -- This is the main online support vector regression learning algorithm. </div> |
| <div class="line"><a name="l00438"></a><span class="lineno"> 438</span> -- The <span class="keyword">function</span> updates the support vector model as it processes each <span class="keyword">new</span> training example.</div> |
| <div class="line"><a name="l00439"></a><span class="lineno"> 439</span> -- This <span class="keyword">function</span> is wrapped in an aggregate <span class="keyword">function</span> to process all the training examples stored in a table. </div> |
| <div class="line"><a name="l00440"></a><span class="lineno"> 440</span> --</div> |
| <div class="line"><a name="l00441"></a><span class="lineno"> 441</span> CREATE OR REPLACE FUNCTION </div> |
| <div class="line"><a name="l00442"></a><span class="lineno"> 442</span> MADLIB_SCHEMA.svm_reg_update(svs MADLIB_SCHEMA.svm_model_rec, ind FLOAT8[], label FLOAT8, kernel TEXT, eta FLOAT8, nu FLOAT8, slambda FLOAT8)</div> |
| <div class="line"><a name="l00443"></a><span class="lineno"> 443</span> RETURNS MADLIB_SCHEMA.svm_model_rec AS <span class="stringliteral">'MODULE_PATHNAME'</span>, <span class="stringliteral">'svm_reg_update'</span> LANGUAGE C STRICT; </div> |
| <div class="line"><a name="l00444"></a><span class="lineno"> 444</span> </div> |
| <div class="line"><a name="l00445"></a><span class="lineno"> 445</span> CREATE AGGREGATE MADLIB_SCHEMA.svm_reg_agg(float8[], float8, text, float8, float8, float8) (</div> |
| <div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  sfunc = MADLIB_SCHEMA.svm_reg_update,</div> |
| <div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  stype = MADLIB_SCHEMA.svm_model_rec,</div> |
| <div class="line"><a name="l00448"></a><span class="lineno"><a class="code" href="online__sv_8sql__in.html#a9f2a96e1a241ecc66386a78b110777d3"> 448</a></span>  initcond = <span class="stringliteral">'(0,0,0,0,0,0,0,{},{},0)'</span></div> |
| <div class="line"><a name="l00449"></a><span class="lineno"> 449</span> );</div> |
| <div class="line"><a name="l00450"></a><span class="lineno"> 450</span> </div> |
| <div class="line"><a name="l00451"></a><span class="lineno"> 451</span> -- This is the main online support vector classification learning algorithm. </div> |
| <div class="line"><a name="l00452"></a><span class="lineno"> 452</span> -- The <span class="keyword">function</span> updates the support vector model as it processes each <span class="keyword">new</span> training example.</div> |
| <div class="line"><a name="l00453"></a><span class="lineno"> 453</span> -- This <span class="keyword">function</span> is wrapped in an aggregate <span class="keyword">function</span> to process all the training examples stored in a table. </div> |
| <div class="line"><a name="l00454"></a><span class="lineno"> 454</span> --</div> |
| <div class="line"><a name="l00455"></a><span class="lineno"> 455</span> CREATE OR REPLACE FUNCTION </div> |
| <div class="line"><a name="l00456"></a><span class="lineno"> 456</span> MADLIB_SCHEMA.svm_cls_update(svs MADLIB_SCHEMA.svm_model_rec, ind FLOAT8[], label FLOAT8, kernel TEXT, eta FLOAT8, nu FLOAT8)</div> |
| <div class="line"><a name="l00457"></a><span class="lineno"> 457</span> RETURNS MADLIB_SCHEMA.svm_model_rec AS <span class="stringliteral">'MODULE_PATHNAME'</span>, <span class="stringliteral">'svm_cls_update'</span> LANGUAGE C STRICT; </div> |
| <div class="line"><a name="l00458"></a><span class="lineno"> 458</span> </div> |
| <div class="line"><a name="l00459"></a><span class="lineno"> 459</span> CREATE AGGREGATE MADLIB_SCHEMA.svm_cls_agg(float8[], float8, text, float8, float8) (</div> |
| <div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  sfunc = MADLIB_SCHEMA.svm_cls_update,</div> |
| <div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  stype = MADLIB_SCHEMA.svm_model_rec,</div> |
| <div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  initcond = <span class="stringliteral">'(0,0,0,0,0,0,0,{},{},0)'</span></div> |
| <div class="line"><a name="l00463"></a><span class="lineno"> 463</span> );</div> |
| <div class="line"><a name="l00464"></a><span class="lineno"> 464</span> </div> |
| <div class="line"><a name="l00465"></a><span class="lineno"> 465</span> -- This is the main online support vector novelty detection algorithm. </div> |
| <div class="line"><a name="l00466"></a><span class="lineno"> 466</span> -- The <span class="keyword">function</span> updates the support vector model as it processes each <span class="keyword">new</span> training example.</div> |
| <div class="line"><a name="l00467"></a><span class="lineno"> 467</span> -- In contrast to classification and regression, the training data points have no labels.</div> |
| <div class="line"><a name="l00468"></a><span class="lineno"> 468</span> -- This <span class="keyword">function</span> is wrapped in an aggregate <span class="keyword">function</span> to process all the training examples stored in a table. </div> |
| <div class="line"><a name="l00469"></a><span class="lineno"> 469</span> --</div> |
| <div class="line"><a name="l00470"></a><span class="lineno"> 470</span> CREATE OR REPLACE FUNCTION </div> |
| <div class="line"><a name="l00471"></a><span class="lineno"> 471</span> MADLIB_SCHEMA.svm_nd_update(svs MADLIB_SCHEMA.svm_model_rec, ind FLOAT8[], kernel TEXT, eta FLOAT8, nu FLOAT8)</div> |
| <div class="line"><a name="l00472"></a><span class="lineno"> 472</span> RETURNS MADLIB_SCHEMA.svm_model_rec AS <span class="stringliteral">'MODULE_PATHNAME'</span>, <span class="stringliteral">'svm_nd_update'</span> LANGUAGE C STRICT; </div> |
| <div class="line"><a name="l00473"></a><span class="lineno"> 473</span> </div> |
| <div class="line"><a name="l00474"></a><span class="lineno"> 474</span> CREATE AGGREGATE MADLIB_SCHEMA.svm_nd_agg(float8[], text, float8, float8) (</div> |
| <div class="line"><a name="l00475"></a><span class="lineno"> 475</span>  sfunc = MADLIB_SCHEMA.svm_nd_update,</div> |
| <div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  stype = MADLIB_SCHEMA.svm_model_rec,</div> |
| <div class="line"><a name="l00477"></a><span class="lineno"> 477</span>  initcond = <span class="stringliteral">'(0,0,0,0,0,0,0,{},{},0)'</span></div> |
| <div class="line"><a name="l00478"></a><span class="lineno"> 478</span> );</div> |
| <div class="line"><a name="l00479"></a><span class="lineno"> 479</span> </div> |
| <div class="line"><a name="l00480"></a><span class="lineno"> 480</span> -- This is the SGD algorithm <span class="keywordflow">for</span> linear SVMs. </div> |
| <div class="line"><a name="l00481"></a><span class="lineno"> 481</span> -- The <span class="keyword">function</span> updates the support vector model as it processes each <span class="keyword">new</span> training example.</div> |
| <div class="line"><a name="l00482"></a><span class="lineno"> 482</span> -- This <span class="keyword">function</span> is wrapped in an aggregate <span class="keyword">function</span> to process all the training examples stored in a table. </div> |
| <div class="line"><a name="l00483"></a><span class="lineno"> 483</span> --</div> |
| <div class="line"><a name="l00484"></a><span class="lineno"> 484</span> CREATE OR REPLACE FUNCTION </div> |
| <div class="line"><a name="l00485"></a><span class="lineno"> 485</span> MADLIB_SCHEMA.lsvm_sgd_update(svs MADLIB_SCHEMA.lsvm_sgd_model_rec, ind FLOAT8[], label FLOAT8, eta FLOAT8, reg FLOAT8)</div> |
| <div class="line"><a name="l00486"></a><span class="lineno"> 486</span> RETURNS MADLIB_SCHEMA.lsvm_sgd_model_rec AS <span class="stringliteral">'MODULE_PATHNAME'</span>, <span class="stringliteral">'lsvm_sgd_update'</span> LANGUAGE C STRICT; </div> |
| <div class="line"><a name="l00487"></a><span class="lineno"> 487</span> </div> |
| <div class="line"><a name="l00488"></a><span class="lineno"> 488</span> CREATE AGGREGATE MADLIB_SCHEMA.lsvm_sgd_agg(float8[], float8, float8, float8) (</div> |
| <div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  sfunc = MADLIB_SCHEMA.lsvm_sgd_update,</div> |
| <div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  stype = MADLIB_SCHEMA.lsvm_sgd_model_rec,</div> |
| <div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  initcond = <span class="stringliteral">'({},1,0,0,0,0)'</span></div> |
| <div class="line"><a name="l00492"></a><span class="lineno"> 492</span> );</div> |
| <div class="line"><a name="l00493"></a><span class="lineno"> 493</span> </div> |
| <div class="line"><a name="l00494"></a><span class="lineno"> 494</span> </div> |
| <div class="line"><a name="l00495"></a><span class="lineno"> 495</span> -- This <span class="keyword">function</span> stores a MADLIB_SCHEMA.svm_model_rec stored in model_temp_table into the model_table.</div> |
| <div class="line"><a name="l00496"></a><span class="lineno"> 496</span> --</div> |
| <div class="line"><a name="l00497"></a><span class="lineno"> 497</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.svm_store_model(model_temp_table TEXT, model_name TEXT, model_table TEXT) RETURNS VOID AS $$</div> |
| <div class="line"><a name="l00498"></a><span class="lineno"> 498</span> </div> |
| <div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  sql = <span class="stringliteral">"SELECT COUNT(*) FROM "</span> + model_temp_table + <span class="stringliteral">" WHERE id = \'"</span> + model_name + <span class="stringliteral">"\'"</span>;</div> |
| <div class="line"><a name="l00500"></a><span class="lineno"> 500</span>  temp = plpy.execute(sql);</div> |
| <div class="line"><a name="l00501"></a><span class="lineno"> 501</span>  <span class="keywordflow">if</span> (temp[0][<span class="stringliteral">'count'</span>] == 0):</div> |
| <div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  plpy.error(<span class="stringliteral">"No support vector model with name "</span> + model_name + <span class="stringliteral">" found."</span>);</div> |
| <div class="line"><a name="l00503"></a><span class="lineno"> 503</span> </div> |
| <div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  sql = <span class="stringliteral">"SELECT (model).ind_dim, (model).nsvs"</span> \</div> |
| <div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  + <span class="stringliteral">" FROM "</span> + model_temp_table + <span class="stringliteral">" WHERE id = '"</span> + model_name + <span class="stringliteral">"'"</span>;</div> |
| <div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  rv = plpy.execute(sql);</div> |
| <div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  myind_dim = rv[0][<span class="stringliteral">'ind_dim'</span>];</div> |
| <div class="line"><a name="l00508"></a><span class="lineno"> 508</span>  mynsvs = rv[0][<span class="stringliteral">'nsvs'</span>];</div> |
| <div class="line"><a name="l00509"></a><span class="lineno"> 509</span> </div> |
| <div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  <span class="keywordflow">if</span> (mynsvs == 0):</div> |
| <div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  plpy.error(<span class="stringliteral">"The specified model has no support vectors and therefore not processed"</span>);</div> |
| <div class="line"><a name="l00512"></a><span class="lineno"> 512</span> </div> |
| <div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  idx = 0; </div> |
| <div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  <span class="keywordflow">for</span> i in range(1,mynsvs+1):</div> |
| <div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  idx = myind_dim * (i-1);</div> |
| <div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  sql = <span class="stringliteral">"INSERT INTO "</span> + model_table \</div> |
| <div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  + <span class="stringliteral">" SELECT \'"</span> + model_name + <span class="stringliteral">"\', (model).weights["</span> + str(i) + <span class="stringliteral">"], "</span> \</div> |
| <div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  + <span class="stringliteral">" (model).individuals[("</span> + str(idx+1) + <span class="stringliteral">"):("</span> + str(idx) + <span class="stringliteral">"+"</span> + str(myind_dim) + <span class="stringliteral">")] "</span> \</div> |
| <div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  + <span class="stringliteral">" FROM "</span> + model_temp_table + <span class="stringliteral">" WHERE id = \'"</span> + model_name + <span class="stringliteral">"\' LIMIT 1"</span>;</div> |
| <div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  plpy.execute(sql); </div> |
| <div class="line"><a name="l00521"></a><span class="lineno"> 521</span> </div> |
| <div class="line"><a name="l00522"></a><span class="lineno"> 522</span> $$ LANGUAGE plpythonu;</div> |
| <div class="line"><a name="l00523"></a><span class="lineno"> 523</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00524"></a><span class="lineno"> 524</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00525"></a><span class="lineno"> 525</span> <span class="comment"> * @brief Drops all tables pertaining to a model</span></div> |
| <div class="line"><a name="l00526"></a><span class="lineno"> 526</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00527"></a><span class="lineno"> 527</span> <span class="comment"> * @param model_table The table to be dropped.</span></div> |
| <div class="line"><a name="l00528"></a><span class="lineno"> 528</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00529"></a><span class="lineno"> 529</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.svm_drop_model(model_table TEXT) RETURNS VOID AS $$</div> |
| <div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  plpy.execute(<span class="stringliteral">"drop table if exists "</span> + model_table)</div> |
| <div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  plpy.execute(<span class="stringliteral">"drop table if exists "</span> + model_table + <span class="stringliteral">"_param"</span>)</div> |
| <div class="line"><a name="l00532"></a><span class="lineno"> 532</span> $$ LANGUAGE plpythonu;</div> |
| <div class="line"><a name="l00533"></a><span class="lineno"> 533</span> </div> |
| <div class="line"><a name="l00534"></a><span class="lineno"> 534</span> CREATE TYPE MADLIB_SCHEMA.svm_model_pr AS ( model text, prediction float8 );</div> |
| <div class="line"><a name="l00535"></a><span class="lineno"> 535</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00536"></a><span class="lineno"> 536</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00537"></a><span class="lineno"> 537</span> <span class="comment"> * @brief Evaluates a support-vector model on a given data point</span></div> |
| <div class="line"><a name="l00538"></a><span class="lineno"> 538</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00539"></a><span class="lineno"> 539</span> <span class="comment"> * @param model_table The table storing the learned model \f$ f \f$ to be used</span></div> |
| <div class="line"><a name="l00540"></a><span class="lineno"> 540</span> <span class="comment"> * @param ind The data point \f$ \boldsymbol x \f$</span></div> |
| <div class="line"><a name="l00541"></a><span class="lineno"> 541</span> <span class="comment"> * @return This function returns \f$ f(\boldsymbol x) \f$</span></div> |
| <div class="line"><a name="l00542"></a><span class="lineno"> 542</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00543"></a><span class="lineno"> 543</span> CREATE OR REPLACE FUNCTION </div> |
| <div class="line"><a name="l00544"></a><span class="lineno"> 544</span> MADLIB_SCHEMA.svm_predict(model_table text, ind float8[]) RETURNS FLOAT8 AS $$</div> |
| <div class="line"><a name="l00545"></a><span class="lineno"> 545</span> </div> |
| <div class="line"><a name="l00546"></a><span class="lineno"> 546</span>  PythonFunctionBodyOnly(`kernel_machines<span class="stringliteral">', `online_sv'</span>)</div> |
| <div class="line"><a name="l00547"></a><span class="lineno"> 547</span>  </div> |
| <div class="line"><a name="l00548"></a><span class="lineno"> 548</span>  <span class="preprocessor"># schema_madlib comes from PythonFunctionBodyOnly</span></div> |
| <div class="line"><a name="l00549"></a><span class="lineno"> 549</span> <span class="preprocessor"></span> <span class="keywordflow">return</span> online_sv.svm_predict(model_table, ind);</div> |
| <div class="line"><a name="l00550"></a><span class="lineno"> 550</span> </div> |
| <div class="line"><a name="l00551"></a><span class="lineno"><a class="code" href="online__sv_8sql__in.html#ab54d33f13c0e00faa358e3e3f17c10fb"> 551</a></span> $$ LANGUAGE plpythonu;</div> |
| <div class="line"><a name="l00552"></a><span class="lineno"> 552</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00553"></a><span class="lineno"> 553</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00554"></a><span class="lineno"> 554</span> <span class="comment"> * @brief Evaluates multiple support-vector models on a data point</span></div> |
| <div class="line"><a name="l00555"></a><span class="lineno"> 555</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00556"></a><span class="lineno"> 556</span> <span class="comment"> * @param model_table The table storing the learned models to be used.</span></div> |
| <div class="line"><a name="l00557"></a><span class="lineno"> 557</span> <span class="comment"> * @param ind The data point \f$ \boldsymbol x \f$</span></div> |
| <div class="line"><a name="l00558"></a><span class="lineno"> 558</span> <span class="comment"> * @return This function returns a table, a row for each model.</span></div> |
| <div class="line"><a name="l00559"></a><span class="lineno"> 559</span> <span class="comment"> * Moreover, the last row contains the average value, over all models.</span></div> |
| <div class="line"><a name="l00560"></a><span class="lineno"> 560</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00561"></a><span class="lineno"> 561</span> <span class="comment"> * The different models are assumed to be named <tt><em>model_table</em>1</tt>,</span></div> |
| <div class="line"><a name="l00562"></a><span class="lineno"> 562</span> <span class="comment"> * <tt><em>model_table</em>2</tt>, ....</span></div> |
| <div class="line"><a name="l00563"></a><span class="lineno"> 563</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00564"></a><span class="lineno"> 564</span> CREATE OR REPLACE FUNCTION</div> |
| <div class="line"><a name="l00565"></a><span class="lineno"><a class="code" href="online__sv_8sql__in.html#a9916305653d464b23ef0fbd78867a654"> 565</a></span> MADLIB_SCHEMA.svm_predict_combo(model_table text, ind float8[]) RETURNS SETOF MADLIB_SCHEMA.svm_model_pr AS $$</div> |
| <div class="line"><a name="l00566"></a><span class="lineno"> 566</span> </div> |
| <div class="line"><a name="l00567"></a><span class="lineno"> 567</span>  PythonFunctionBodyOnly(`kernel_machines<span class="stringliteral">', `online_sv'</span>)</div> |
| <div class="line"><a name="l00568"></a><span class="lineno"> 568</span>  </div> |
| <div class="line"><a name="l00569"></a><span class="lineno"> 569</span>  <span class="preprocessor"># schema_madlib comes from PythonFunctionBodyOnly</span></div> |
| <div class="line"><a name="l00570"></a><span class="lineno"> 570</span> <span class="preprocessor"></span> <span class="keywordflow">return</span> online_sv.svm_predict_combo( schema_madlib, model_table, ind);</div> |
| <div class="line"><a name="l00571"></a><span class="lineno"> 571</span> </div> |
| <div class="line"><a name="l00572"></a><span class="lineno"> 572</span> $$ LANGUAGE plpythonu;</div> |
| <div class="line"><a name="l00573"></a><span class="lineno"> 573</span> </div> |
| <div class="line"><a name="l00574"></a><span class="lineno"> 574</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00575"></a><span class="lineno"> 575</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00576"></a><span class="lineno"> 576</span> <span class="comment"> * @brief This is the support vector regression function</span></div> |
| <div class="line"><a name="l00577"></a><span class="lineno"> 577</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00578"></a><span class="lineno"> 578</span> <span class="comment"> * @param input_table The name of the table/view with the training data</span></div> |
| <div class="line"><a name="l00579"></a><span class="lineno"> 579</span> <span class="comment"> * @param model_table The name of the table under which we want to store the learned model</span></div> |
| <div class="line"><a name="l00580"></a><span class="lineno"> 580</span> <span class="comment"> * @param parallel A flag indicating whether the system should learn multiple models in parallel</span></div> |
| <div class="line"><a name="l00581"></a><span class="lineno"> 581</span> <span class="comment"> * @param kernel_func Kernel function</span></div> |
| <div class="line"><a name="l00582"></a><span class="lineno"> 582</span> <span class="comment"> * @return A summary of the learning process</span></div> |
| <div class="line"><a name="l00583"></a><span class="lineno"> 583</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00584"></a><span class="lineno"> 584</span> <span class="comment"> * @internal </span></div> |
| <div class="line"><a name="l00585"></a><span class="lineno"> 585</span> <span class="comment"> * @sa This function is a wrapper for online_sv::svm_regression().</span></div> |
| <div class="line"><a name="l00586"></a><span class="lineno"><a class="code" href="online__sv_8sql__in.html#a883ff4ca340d19a11204b461dd388276"> 586</a></span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00587"></a><span class="lineno"> 587</span> CREATE OR REPLACE FUNCTION </div> |
| <div class="line"><a name="l00588"></a><span class="lineno"> 588</span> MADLIB_SCHEMA.svm_regression(input_table text, model_table text, parallel <span class="keywordtype">bool</span>, kernel_func text)</div> |
| <div class="line"><a name="l00589"></a><span class="lineno"> 589</span> RETURNS SETOF MADLIB_SCHEMA.svm_reg_result</div> |
| <div class="line"><a name="l00590"></a><span class="lineno"> 590</span> AS $$</div> |
| <div class="line"><a name="l00591"></a><span class="lineno"> 591</span> </div> |
| <div class="line"><a name="l00592"></a><span class="lineno"> 592</span>  PythonFunctionBodyOnly(`kernel_machines<span class="stringliteral">', `online_sv'</span>)</div> |
| <div class="line"><a name="l00593"></a><span class="lineno"> 593</span>  </div> |
| <div class="line"><a name="l00594"></a><span class="lineno"> 594</span>  <span class="preprocessor"># schema_madlib comes from PythonFunctionBodyOnly</span></div> |
| <div class="line"><a name="l00595"></a><span class="lineno"> 595</span> <span class="preprocessor"></span> <span class="keywordflow">return</span> online_sv.svm_regression( schema_madlib, input_table, model_table, parallel, kernel_func); </div> |
| <div class="line"><a name="l00596"></a><span class="lineno"> 596</span> </div> |
| <div class="line"><a name="l00597"></a><span class="lineno"> 597</span> $$ LANGUAGE <span class="stringliteral">'plpythonu'</span>;</div> |
| <div class="line"><a name="l00598"></a><span class="lineno"> 598</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00599"></a><span class="lineno"> 599</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00600"></a><span class="lineno"> 600</span> <span class="comment"> * @brief This is the support vector regression function</span></div> |
| <div class="line"><a name="l00601"></a><span class="lineno"> 601</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00602"></a><span class="lineno"> 602</span> <span class="comment"> * @param input_table The name of the table/view with the training data</span></div> |
| <div class="line"><a name="l00603"></a><span class="lineno"> 603</span> <span class="comment"> * @param model_table The name of the table under which we want to store the learned model</span></div> |
| <div class="line"><a name="l00604"></a><span class="lineno"> 604</span> <span class="comment"> * @param parallel A flag indicating whether the system should learn multiple models in parallel</span></div> |
| <div class="line"><a name="l00605"></a><span class="lineno"> 605</span> <span class="comment"> * @param kernel_func Kernel function</span></div> |
| <div class="line"><a name="l00606"></a><span class="lineno"> 606</span> <span class="comment"> * @param verbose Verbosity of reporting</span></div> |
| <div class="line"><a name="l00607"></a><span class="lineno"> 607</span> <span class="comment"> * @param eta Learning rate in (0,1] </span></div> |
| <div class="line"><a name="l00608"></a><span class="lineno"> 608</span> <span class="comment"> * @param nu Compression parameter in (0,1] associated with the fraction of training data that will become support vectors </span></div> |
| <div class="line"><a name="l00609"></a><span class="lineno"><a class="code" href="online__sv_8sql__in.html#acaf1f4aa3eec5710de5c03e368a4b106"> 609</a></span> <span class="comment"> * @param slambda Regularisation parameter</span></div> |
| <div class="line"><a name="l00610"></a><span class="lineno"> 610</span> <span class="comment"> * @return A summary of the learning process</span></div> |
| <div class="line"><a name="l00611"></a><span class="lineno"> 611</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00612"></a><span class="lineno"> 612</span> <span class="comment"> * @internal </span></div> |
| <div class="line"><a name="l00613"></a><span class="lineno"> 613</span> <span class="comment"> * @sa This function is a wrapper for online_sv::svm_regression().</span></div> |
| <div class="line"><a name="l00614"></a><span class="lineno"> 614</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00615"></a><span class="lineno"> 615</span> CREATE OR REPLACE FUNCTION </div> |
| <div class="line"><a name="l00616"></a><span class="lineno"> 616</span> MADLIB_SCHEMA.svm_regression(input_table text, model_table text, parallel <span class="keywordtype">bool</span>, kernel_func text, verbose <span class="keywordtype">bool</span>, eta float8, nu float8, slambda float8)</div> |
| <div class="line"><a name="l00617"></a><span class="lineno"> 617</span> RETURNS SETOF MADLIB_SCHEMA.svm_reg_result</div> |
| <div class="line"><a name="l00618"></a><span class="lineno"> 618</span> AS $$</div> |
| <div class="line"><a name="l00619"></a><span class="lineno"> 619</span> </div> |
| <div class="line"><a name="l00620"></a><span class="lineno"> 620</span>  PythonFunctionBodyOnly(`kernel_machines<span class="stringliteral">', `online_sv'</span>)</div> |
| <div class="line"><a name="l00621"></a><span class="lineno"> 621</span>  </div> |
| <div class="line"><a name="l00622"></a><span class="lineno"> 622</span>  <span class="preprocessor"># schema_madlib comes from PythonFunctionBodyOnly</span></div> |
| <div class="line"><a name="l00623"></a><span class="lineno"> 623</span> <span class="preprocessor"></span> <span class="keywordflow">return</span> online_sv.svm_regression( schema_madlib, input_table, model_table, parallel, kernel_func, verbose, eta, nu, slambda);</div> |
| <div class="line"><a name="l00624"></a><span class="lineno"> 624</span> </div> |
| <div class="line"><a name="l00625"></a><span class="lineno"> 625</span> $$ LANGUAGE <span class="stringliteral">'plpythonu'</span>;</div> |
| <div class="line"><a name="l00626"></a><span class="lineno"> 626</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00627"></a><span class="lineno"> 627</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00628"></a><span class="lineno"> 628</span> <span class="comment"> * @brief This is the support vector classification function</span></div> |
| <div class="line"><a name="l00629"></a><span class="lineno"> 629</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00630"></a><span class="lineno"> 630</span> <span class="comment"> * @param input_table The name of the table/view with the training data</span></div> |
| <div class="line"><a name="l00631"></a><span class="lineno"> 631</span> <span class="comment"> * @param model_table The name of the table under which we want to store the learned model</span></div> |
| <div class="line"><a name="l00632"></a><span class="lineno"> 632</span> <span class="comment"> * @param parallel A flag indicating whether the system should learn multiple models in parallel</span></div> |
| <div class="line"><a name="l00633"></a><span class="lineno"> 633</span> <span class="comment"> * @param kernel_func Kernel function</span></div> |
| <div class="line"><a name="l00634"></a><span class="lineno"> 634</span> <span class="comment"> * @return A summary of the learning process</span></div> |
| <div class="line"><a name="l00635"></a><span class="lineno"> 635</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00636"></a><span class="lineno"> 636</span> <span class="comment"> * @internal </span></div> |
| <div class="line"><a name="l00637"></a><span class="lineno"><a class="code" href="online__sv_8sql__in.html#ac5cb9c20d6620b155ac872576a056f2a"> 637</a></span> <span class="comment"> * @sa This function is a wrapper for online_sv::svm_classification().</span></div> |
| <div class="line"><a name="l00638"></a><span class="lineno"> 638</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00639"></a><span class="lineno"> 639</span> CREATE OR REPLACE FUNCTION </div> |
| <div class="line"><a name="l00640"></a><span class="lineno"> 640</span> MADLIB_SCHEMA.svm_classification(input_table text, model_table text, parallel <span class="keywordtype">bool</span>, kernel_func text)</div> |
| <div class="line"><a name="l00641"></a><span class="lineno"> 641</span> RETURNS SETOF MADLIB_SCHEMA.svm_cls_result</div> |
| <div class="line"><a name="l00642"></a><span class="lineno"> 642</span> AS $$</div> |
| <div class="line"><a name="l00643"></a><span class="lineno"> 643</span> </div> |
| <div class="line"><a name="l00644"></a><span class="lineno"> 644</span>  PythonFunctionBodyOnly(`kernel_machines<span class="stringliteral">', `online_sv'</span>)</div> |
| <div class="line"><a name="l00645"></a><span class="lineno"> 645</span>  </div> |
| <div class="line"><a name="l00646"></a><span class="lineno"> 646</span>  <span class="preprocessor"># schema_madlib comes from PythonFunctionBodyOnly</span></div> |
| <div class="line"><a name="l00647"></a><span class="lineno"> 647</span> <span class="preprocessor"></span> <span class="keywordflow">return</span> online_sv.svm_classification( schema_madlib, input_table, model_table, parallel, kernel_func);</div> |
| <div class="line"><a name="l00648"></a><span class="lineno"> 648</span>  </div> |
| <div class="line"><a name="l00649"></a><span class="lineno"> 649</span> $$ LANGUAGE <span class="stringliteral">'plpythonu'</span>;</div> |
| <div class="line"><a name="l00650"></a><span class="lineno"> 650</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00651"></a><span class="lineno"> 651</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00652"></a><span class="lineno"> 652</span> <span class="comment"> * @brief This is the support vector classification function</span></div> |
| <div class="line"><a name="l00653"></a><span class="lineno"> 653</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00654"></a><span class="lineno"> 654</span> <span class="comment"> * @param input_table The name of the table/view with the training data</span></div> |
| <div class="line"><a name="l00655"></a><span class="lineno"> 655</span> <span class="comment"> * @param model_table The name of the table under which we want to store the learned model</span></div> |
| <div class="line"><a name="l00656"></a><span class="lineno"> 656</span> <span class="comment"> * @param parallel A flag indicating whether the system should learn multiple models in parallel</span></div> |
| <div class="line"><a name="l00657"></a><span class="lineno"> 657</span> <span class="comment"> * @param kernel_func Kernel function</span></div> |
| <div class="line"><a name="l00658"></a><span class="lineno"> 658</span> <span class="comment"> * @param verbose Verbosity of reporting</span></div> |
| <div class="line"><a name="l00659"></a><span class="lineno"> 659</span> <span class="comment"> * @param eta Learning rate in (0,1]</span></div> |
| <div class="line"><a name="l00660"></a><span class="lineno"> 660</span> <span class="comment"> * @param nu Compression parameter in (0,1] associated with the fraction of training data that will become support vectors</span></div> |
| <div class="line"><a name="l00661"></a><span class="lineno"><a class="code" href="online__sv_8sql__in.html#a20a2c8a905be6e922885e23e9dab0a4c"> 661</a></span> <span class="comment"> * @return A summary of the learning process</span></div> |
| <div class="line"><a name="l00662"></a><span class="lineno"> 662</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00663"></a><span class="lineno"> 663</span> <span class="comment"> * @internal </span></div> |
| <div class="line"><a name="l00664"></a><span class="lineno"> 664</span> <span class="comment"> * @sa This function is a wrapper for online_sv::svm_classification().</span></div> |
| <div class="line"><a name="l00665"></a><span class="lineno"> 665</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00666"></a><span class="lineno"> 666</span> CREATE OR REPLACE FUNCTION </div> |
| <div class="line"><a name="l00667"></a><span class="lineno"> 667</span> MADLIB_SCHEMA.svm_classification(input_table text, model_table text, parallel <span class="keywordtype">bool</span>, kernel_func text, verbose <span class="keywordtype">bool</span>, eta float8, nu float8)</div> |
| <div class="line"><a name="l00668"></a><span class="lineno"> 668</span> RETURNS SETOF MADLIB_SCHEMA.svm_cls_result</div> |
| <div class="line"><a name="l00669"></a><span class="lineno"> 669</span> AS $$</div> |
| <div class="line"><a name="l00670"></a><span class="lineno"> 670</span> </div> |
| <div class="line"><a name="l00671"></a><span class="lineno"> 671</span>  PythonFunctionBodyOnly(`kernel_machines<span class="stringliteral">', `online_sv'</span>)</div> |
| <div class="line"><a name="l00672"></a><span class="lineno"> 672</span>  </div> |
| <div class="line"><a name="l00673"></a><span class="lineno"> 673</span>  <span class="preprocessor"># schema_madlib comes from PythonFunctionBodyOnly</span></div> |
| <div class="line"><a name="l00674"></a><span class="lineno"> 674</span> <span class="preprocessor"></span> <span class="keywordflow">return</span> online_sv.svm_classification( schema_madlib, input_table, model_table, parallel, kernel_func, verbose, eta, nu);</div> |
| <div class="line"><a name="l00675"></a><span class="lineno"> 675</span> </div> |
| <div class="line"><a name="l00676"></a><span class="lineno"> 676</span> $$ LANGUAGE <span class="stringliteral">'plpythonu'</span>;</div> |
| <div class="line"><a name="l00677"></a><span class="lineno"> 677</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00678"></a><span class="lineno"> 678</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00679"></a><span class="lineno"> 679</span> <span class="comment"> * @brief This is the support vector novelty detection function.</span></div> |
| <div class="line"><a name="l00680"></a><span class="lineno"> 680</span> <span class="comment"> * </span></div> |
| <div class="line"><a name="l00681"></a><span class="lineno"> 681</span> <span class="comment"> * @param input_table The name of the table/view with the training data</span></div> |
| <div class="line"><a name="l00682"></a><span class="lineno"> 682</span> <span class="comment"> * @param model_table The name of the table under which we want to store the learned model</span></div> |
| <div class="line"><a name="l00683"></a><span class="lineno"> 683</span> <span class="comment"> * @param parallel A flag indicating whether the system should learn multiple models in parallel</span></div> |
| <div class="line"><a name="l00684"></a><span class="lineno"> 684</span> <span class="comment"> * @param kernel_func Kernel function</span></div> |
| <div class="line"><a name="l00685"></a><span class="lineno"> 685</span> <span class="comment"> * @return A summary of the learning process</span></div> |
| <div class="line"><a name="l00686"></a><span class="lineno"> 686</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00687"></a><span class="lineno"> 687</span> <span class="comment"> * @internal </span></div> |
| <div class="line"><a name="l00688"></a><span class="lineno"><a class="code" href="online__sv_8sql__in.html#ad90b6bf3b807f22d37b0e2b1893262f0"> 688</a></span> <span class="comment"> * @sa This function is a wrapper for online_sv::svm_novelty_detection().</span></div> |
| <div class="line"><a name="l00689"></a><span class="lineno"> 689</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00690"></a><span class="lineno"> 690</span> CREATE OR REPLACE FUNCTION </div> |
| <div class="line"><a name="l00691"></a><span class="lineno"> 691</span> MADLIB_SCHEMA.svm_novelty_detection(input_table text, model_table text, parallel <span class="keywordtype">bool</span>, kernel_func text)</div> |
| <div class="line"><a name="l00692"></a><span class="lineno"> 692</span> RETURNS SETOF MADLIB_SCHEMA.svm_nd_result</div> |
| <div class="line"><a name="l00693"></a><span class="lineno"> 693</span> AS $$</div> |
| <div class="line"><a name="l00694"></a><span class="lineno"> 694</span> </div> |
| <div class="line"><a name="l00695"></a><span class="lineno"> 695</span>  PythonFunctionBodyOnly(`kernel_machines<span class="stringliteral">', `online_sv'</span>)</div> |
| <div class="line"><a name="l00696"></a><span class="lineno"> 696</span>  </div> |
| <div class="line"><a name="l00697"></a><span class="lineno"> 697</span>  <span class="preprocessor"># schema_madlib comes from PythonFunctionBodyOnly</span></div> |
| <div class="line"><a name="l00698"></a><span class="lineno"> 698</span> <span class="preprocessor"></span> <span class="keywordflow">return</span> online_sv.svm_novelty_detection( schema_madlib, input_table, model_table, parallel, kernel_func);</div> |
| <div class="line"><a name="l00699"></a><span class="lineno"> 699</span> </div> |
| <div class="line"><a name="l00700"></a><span class="lineno"> 700</span> $$ LANGUAGE <span class="stringliteral">'plpythonu'</span>;</div> |
| <div class="line"><a name="l00701"></a><span class="lineno"> 701</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00702"></a><span class="lineno"> 702</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00703"></a><span class="lineno"> 703</span> <span class="comment"> * @brief This is the support vector novelty detection function.</span></div> |
| <div class="line"><a name="l00704"></a><span class="lineno"> 704</span> <span class="comment"> * </span></div> |
| <div class="line"><a name="l00705"></a><span class="lineno"> 705</span> <span class="comment"> * @param input_table The name of the table/view with the training data</span></div> |
| <div class="line"><a name="l00706"></a><span class="lineno"> 706</span> <span class="comment"> * @param model_table The name of the table under which we want to store the learned model</span></div> |
| <div class="line"><a name="l00707"></a><span class="lineno"> 707</span> <span class="comment"> * @param parallel A flag indicating whether the system should learn multiple models in parallel</span></div> |
| <div class="line"><a name="l00708"></a><span class="lineno"> 708</span> <span class="comment"> * @param kernel_func Kernel function</span></div> |
| <div class="line"><a name="l00709"></a><span class="lineno"> 709</span> <span class="comment"> * @param verbose Verbosity of reporting</span></div> |
| <div class="line"><a name="l00710"></a><span class="lineno"> 710</span> <span class="comment"> * @param eta Learning rate in (0,1]</span></div> |
| <div class="line"><a name="l00711"></a><span class="lineno"> 711</span> <span class="comment"> * @param nu Compression parameter in (0,1] associated with the fraction of training data that will become support vectors</span></div> |
| <div class="line"><a name="l00712"></a><span class="lineno"><a class="code" href="online__sv_8sql__in.html#a3448ea62ab57fe4cf177f5fa6b5db7d3"> 712</a></span> <span class="comment"> * @return A summary of the learning process</span></div> |
| <div class="line"><a name="l00713"></a><span class="lineno"> 713</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00714"></a><span class="lineno"> 714</span> <span class="comment"> * @internal </span></div> |
| <div class="line"><a name="l00715"></a><span class="lineno"> 715</span> <span class="comment"> * @sa This function is a wrapper for online_sv::svm_novelty_detection().</span></div> |
| <div class="line"><a name="l00716"></a><span class="lineno"> 716</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00717"></a><span class="lineno"> 717</span> CREATE OR REPLACE FUNCTION </div> |
| <div class="line"><a name="l00718"></a><span class="lineno"> 718</span> MADLIB_SCHEMA.svm_novelty_detection(input_table text, model_table text, parallel <span class="keywordtype">bool</span>, kernel_func text, verbose <span class="keywordtype">bool</span>, eta float8, nu float8)</div> |
| <div class="line"><a name="l00719"></a><span class="lineno"> 719</span> RETURNS SETOF MADLIB_SCHEMA.svm_nd_result</div> |
| <div class="line"><a name="l00720"></a><span class="lineno"> 720</span> AS $$</div> |
| <div class="line"><a name="l00721"></a><span class="lineno"> 721</span> </div> |
| <div class="line"><a name="l00722"></a><span class="lineno"> 722</span>  PythonFunctionBodyOnly(`kernel_machines<span class="stringliteral">', `online_sv'</span>)</div> |
| <div class="line"><a name="l00723"></a><span class="lineno"> 723</span>  </div> |
| <div class="line"><a name="l00724"></a><span class="lineno"> 724</span>  <span class="preprocessor"># schema_madlib comes from PythonFunctionBodyOnly</span></div> |
| <div class="line"><a name="l00725"></a><span class="lineno"> 725</span> <span class="preprocessor"></span> <span class="keywordflow">return</span> online_sv.svm_novelty_detection( schema_madlib, input_table, model_table, parallel, kernel_func, verbose, eta, nu);</div> |
| <div class="line"><a name="l00726"></a><span class="lineno"> 726</span> </div> |
| <div class="line"><a name="l00727"></a><span class="lineno"> 727</span> $$ LANGUAGE <span class="stringliteral">'plpythonu'</span>;</div> |
| <div class="line"><a name="l00728"></a><span class="lineno"> 728</span> </div> |
| <div class="line"><a name="l00729"></a><span class="lineno"> 729</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00730"></a><span class="lineno"> 730</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00731"></a><span class="lineno"> 731</span> <span class="comment"> * @brief Scores the data points stored in a table using a learned support-vector model</span></div> |
| <div class="line"><a name="l00732"></a><span class="lineno"> 732</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00733"></a><span class="lineno"> 733</span> <span class="comment"> * @param input_table Name of table/view containing the data points to be scored</span></div> |
| <div class="line"><a name="l00734"></a><span class="lineno"> 734</span> <span class="comment"> * @param data_col Name of column in input_table containing the data points</span></div> |
| <div class="line"><a name="l00735"></a><span class="lineno"> 735</span> <span class="comment"> * @param id_col Name of column in input_table containing the integer identifier of data points</span></div> |
| <div class="line"><a name="l00736"></a><span class="lineno"> 736</span> <span class="comment"> * @param model_table Name of table where the learned model to be used is stored</span></div> |
| <div class="line"><a name="l00737"></a><span class="lineno"> 737</span> <span class="comment"> * @param output_table Name of table to store the results </span></div> |
| <div class="line"><a name="l00738"></a><span class="lineno"> 738</span> <span class="comment"> * @param parallel A flag indicating whether the model to be used was learned in parallel</span></div> |
| <div class="line"><a name="l00739"></a><span class="lineno"><a class="code" href="online__sv_8sql__in.html#a5bae5335b51e448cd7fb9cb7a54b0bfa"> 739</a></span> <span class="comment"> * @return Textual summary of the algorithm run</span></div> |
| <div class="line"><a name="l00740"></a><span class="lineno"> 740</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00741"></a><span class="lineno"> 741</span> <span class="comment"> * @internal </span></div> |
| <div class="line"><a name="l00742"></a><span class="lineno"> 742</span> <span class="comment"> * @sa This function is a wrapper for online_sv::svm_predict_batch().</span></div> |
| <div class="line"><a name="l00743"></a><span class="lineno"> 743</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00744"></a><span class="lineno"> 744</span> CREATE OR REPLACE FUNCTION</div> |
| <div class="line"><a name="l00745"></a><span class="lineno"> 745</span> MADLIB_SCHEMA.svm_predict_batch(input_table text, data_col text, id_col text, model_table text, output_table text, parallel <span class="keywordtype">bool</span>)</div> |
| <div class="line"><a name="l00746"></a><span class="lineno"> 746</span> RETURNS TEXT</div> |
| <div class="line"><a name="l00747"></a><span class="lineno"> 747</span> AS $$</div> |
| <div class="line"><a name="l00748"></a><span class="lineno"> 748</span> </div> |
| <div class="line"><a name="l00749"></a><span class="lineno"> 749</span>  PythonFunctionBodyOnly(`kernel_machines<span class="stringliteral">', `online_sv'</span>)</div> |
| <div class="line"><a name="l00750"></a><span class="lineno"> 750</span>  </div> |
| <div class="line"><a name="l00751"></a><span class="lineno"> 751</span>  <span class="preprocessor"># schema_madlib comes from PythonFunctionBodyOnly</span></div> |
| <div class="line"><a name="l00752"></a><span class="lineno"> 752</span> <span class="preprocessor"></span> <span class="keywordflow">return</span> online_sv.svm_predict_batch( input_table, data_col, id_col, model_table, output_table, parallel);</div> |
| <div class="line"><a name="l00753"></a><span class="lineno"> 753</span>  </div> |
| <div class="line"><a name="l00754"></a><span class="lineno"> 754</span> $$ LANGUAGE <span class="stringliteral">'plpythonu'</span>;</div> |
| <div class="line"><a name="l00755"></a><span class="lineno"> 755</span> </div> |
| <div class="line"><a name="l00756"></a><span class="lineno"> 756</span> -- Generate artificial training data </div> |
| <div class="line"><a name="l00757"></a><span class="lineno"> 757</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__svm_random_ind(d INT) RETURNS float8[] AS $$</div> |
| <div class="line"><a name="l00758"></a><span class="lineno"> 758</span> DECLARE</div> |
| <div class="line"><a name="l00759"></a><span class="lineno"> 759</span>  ret float8[];</div> |
| <div class="line"><a name="l00760"></a><span class="lineno"> 760</span> BEGIN</div> |
| <div class="line"><a name="l00761"></a><span class="lineno"> 761</span>  FOR i IN 1..(d-1) LOOP</div> |
| <div class="line"><a name="l00762"></a><span class="lineno"> 762</span>  ret[i] = RANDOM() * 40 - 20;</div> |
| <div class="line"><a name="l00763"></a><span class="lineno"> 763</span>  END LOOP;</div> |
| <div class="line"><a name="l00764"></a><span class="lineno"> 764</span>  IF (RANDOM() > 0.5) THEN</div> |
| <div class="line"><a name="l00765"></a><span class="lineno"> 765</span>  ret[d] = 10;</div> |
| <div class="line"><a name="l00766"></a><span class="lineno"><a class="code" href="online__sv_8sql__in.html#a91ac71354e9dec74e25339bf168c2e5b"> 766</a></span>  ELSE </div> |
| <div class="line"><a name="l00767"></a><span class="lineno"> 767</span>  ret[d] = -10;</div> |
| <div class="line"><a name="l00768"></a><span class="lineno"> 768</span>  END IF;</div> |
| <div class="line"><a name="l00769"></a><span class="lineno"> 769</span>  RETURN ret;</div> |
| <div class="line"><a name="l00770"></a><span class="lineno"> 770</span> END</div> |
| <div class="line"><a name="l00771"></a><span class="lineno"> 771</span> $$ LANGUAGE plpgsql;</div> |
| <div class="line"><a name="l00772"></a><span class="lineno"> 772</span> </div> |
| <div class="line"><a name="l00773"></a><span class="lineno"> 773</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__svm_random_ind2(d INT) RETURNS float8[] AS $$</div> |
| <div class="line"><a name="l00774"></a><span class="lineno"> 774</span> DECLARE</div> |
| <div class="line"><a name="l00775"></a><span class="lineno"> 775</span>  ret float8[];</div> |
| <div class="line"><a name="l00776"></a><span class="lineno"> 776</span> BEGIN</div> |
| <div class="line"><a name="l00777"></a><span class="lineno"> 777</span>  FOR i IN 1..d LOOP</div> |
| <div class="line"><a name="l00778"></a><span class="lineno"> 778</span>  ret[i] = RANDOM() * 5 + 10;</div> |
| <div class="line"><a name="l00779"></a><span class="lineno"> 779</span>  IF (RANDOM() > 0.5) THEN ret[i] = -ret[i]; END IF;</div> |
| <div class="line"><a name="l00780"></a><span class="lineno"> 780</span>  END LOOP;</div> |
| <div class="line"><a name="l00781"></a><span class="lineno"> 781</span>  RETURN ret;</div> |
| <div class="line"><a name="l00782"></a><span class="lineno"> 782</span> END</div> |
| <div class="line"><a name="l00783"></a><span class="lineno"> 783</span> $$ LANGUAGE plpgsql;</div> |
| <div class="line"><a name="l00784"></a><span class="lineno"> 784</span> </div> |
| <div class="line"><a name="l00785"></a><span class="lineno"> 785</span> </div> |
| <div class="line"><a name="l00786"></a><span class="lineno"> 786</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.svm_generate_reg_data(output_table text, num <span class="keywordtype">int</span>, dim <span class="keywordtype">int</span>) RETURNS VOID AS $$</div> |
| <div class="line"><a name="l00787"></a><span class="lineno"> 787</span>  plpy.execute("drop table if exists " + output_table)</div> |
| <div class="line"><a name="l00788"></a><span class="lineno"> 788</span>  plpy.execute("create table " + output_table + " ( <span class="keywordtype">id</span> <span class="keywordtype">int</span>, ind float8[], label float8 ) m4_ifdef(`__GREENPLUM__', `distributed by (<span class="keywordtype">id</span>)')")</div> |
| <div class="line"><a name="l00789"></a><span class="lineno"> 789</span>  plpy.execute("INSERT INTO " + output_table + " SELECT a.val, MADLIB_SCHEMA.__svm_random_ind(" + str(dim) + "), 0 FROM (SELECT generate_series(1," + str(num) + ") AS val) AS a")</div> |
| <div class="line"><a name="l00790"></a><span class="lineno"> 790</span>  plpy.execute("UPDATE " + output_table + " SET label = MADLIB_SCHEMA.__svm_target_reg_func(ind)")</div> |
| <div class="line"><a name="l00791"></a><span class="lineno"> 791</span> $$ LANGUAGE 'plpythonu';</div> |
| <div class="line"><a name="l00792"></a><span class="lineno"> 792</span> </div> |
| <div class="line"><a name="l00793"></a><span class="lineno"> 793</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__svm_target_reg_func(ind float8[]) RETURNS float8 AS $$</div> |
| <div class="line"><a name="l00794"></a><span class="lineno"> 794</span> DECLARE</div> |
| <div class="line"><a name="l00795"></a><span class="lineno"> 795</span>  dim <span class="keywordtype">int</span>;</div> |
| <div class="line"><a name="l00796"></a><span class="lineno"> 796</span> BEGIN</div> |
| <div class="line"><a name="l00797"></a><span class="lineno"> 797</span>  dim = array_upper(ind,1);</div> |
| <div class="line"><a name="l00798"></a><span class="lineno"> 798</span>  IF (ind[dim] = 10) THEN RETURN 50; END IF;</div> |
| <div class="line"><a name="l00799"></a><span class="lineno"> 799</span>  RETURN -50;</div> |
| <div class="line"><a name="l00800"></a><span class="lineno"> 800</span> END</div> |
| <div class="line"><a name="l00801"></a><span class="lineno"> 801</span> $$ LANGUAGE plpgsql;</div> |
| <div class="line"><a name="l00802"></a><span class="lineno"> 802</span> </div> |
| <div class="line"><a name="l00803"></a><span class="lineno"> 803</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.svm_generate_cls_data(output_table text, num <span class="keywordtype">int</span>, dim <span class="keywordtype">int</span>) RETURNS VOID AS $$</div> |
| <div class="line"><a name="l00804"></a><span class="lineno"> 804</span>  plpy.execute("drop table if exists " + output_table);</div> |
| <div class="line"><a name="l00805"></a><span class="lineno"> 805</span>  plpy.execute("create table " + output_table + " ( <span class="keywordtype">id</span> <span class="keywordtype">int</span>, ind float8[], label float8 ) m4_ifdef(`__GREENPLUM__', `distributed by (<span class="keywordtype">id</span>)')")</div> |
| <div class="line"><a name="l00806"></a><span class="lineno"> 806</span>  plpy.execute("INSERT INTO " + output_table + " SELECT a.val, MADLIB_SCHEMA.__svm_random_ind(" + str(dim) + "), 0 FROM (SELECT generate_series(1," + str(num) + ") AS val) AS a")</div> |
| <div class="line"><a name="l00807"></a><span class="lineno"> 807</span>  plpy.execute("UPDATE " + output_table + " SET label = MADLIB_SCHEMA.__svm_target_cl_func(ind)")</div> |
| <div class="line"><a name="l00808"></a><span class="lineno"> 808</span> $$ LANGUAGE 'plpythonu';</div> |
| <div class="line"><a name="l00809"></a><span class="lineno"> 809</span> </div> |
| <div class="line"><a name="l00810"></a><span class="lineno"> 810</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__svm_target_cl_func(ind float8[]) RETURNS float8 AS $$</div> |
| <div class="line"><a name="l00811"></a><span class="lineno"> 811</span> BEGIN</div> |
| <div class="line"><a name="l00812"></a><span class="lineno"> 812</span>  IF (ind[1] > 0 AND ind[2] < 0) THEN RETURN 1; END IF;</div> |
| <div class="line"><a name="l00813"></a><span class="lineno"> 813</span>  RETURN -1;</div> |
| <div class="line"><a name="l00814"></a><span class="lineno"> 814</span> END</div> |
| <div class="line"><a name="l00815"></a><span class="lineno"> 815</span> $$ LANGUAGE plpgsql;</div> |
| <div class="line"><a name="l00816"></a><span class="lineno"> 816</span> </div> |
| <div class="line"><a name="l00817"></a><span class="lineno"> 817</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.svm_generate_nd_data(output_table text, num <span class="keywordtype">int</span>, dim <span class="keywordtype">int</span>) RETURNS VOID AS $$</div> |
| <div class="line"><a name="l00818"></a><span class="lineno"> 818</span>  plpy.execute("drop table if exists " + output_table);</div> |
| <div class="line"><a name="l00819"></a><span class="lineno"> 819</span>  plpy.execute("create table " + output_table + " ( <span class="keywordtype">id</span> <span class="keywordtype">int</span>, ind float8[] ) m4_ifdef(`__GREENPLUM__', `distributed by (<span class="keywordtype">id</span>)')")</div> |
| <div class="line"><a name="l00820"></a><span class="lineno"> 820</span>  plpy.execute("INSERT INTO " + output_table + " SELECT a.val, MADLIB_SCHEMA.__svm_random_ind2(" + str(dim) + ") FROM (SELECT generate_series(1," + str(num) + ") AS val) AS a")</div> |
| <div class="line"><a name="l00821"></a><span class="lineno"> 821</span> $$ LANGUAGE 'plpythonu';</div> |
| <div class="line"><a name="l00822"></a><span class="lineno"> 822</span> </div> |
| <div class="line"><a name="l00823"></a><span class="lineno"> 823</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00824"></a><span class="lineno"> 824</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00825"></a><span class="lineno"> 825</span> <span class="comment"> * @brief Normalizes the data stored in a table, and save the normalized data in a new table. </span></div> |
| <div class="line"><a name="l00826"></a><span class="lineno"> 826</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00827"></a><span class="lineno"> 827</span> <span class="comment"> * @param input_table Name of table/view containing the data points to be scored</span></div> |
| <div class="line"><a name="l00828"></a><span class="lineno"> 828</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00829"></a><span class="lineno"> 829</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.<a class="code" href="online__sv_8sql__in.html#a78bb07d8f4aee80c3bbc8e8176e512be" title="Normalizes the data stored in a table, and save the normalized data in a new table. ">svm_data_normalization</a>(input_table TEXT) RETURNS VOID AS $$</div> |
| <div class="line"><a name="l00830"></a><span class="lineno"> 830</span>  output_table = input_table + "_scaled";</div> |
| <div class="line"><a name="l00831"></a><span class="lineno"> 831</span>  plpy.execute("DROP TABLE IF EXISTS " + output_table);</div> |
| <div class="line"><a name="l00832"></a><span class="lineno"> 832</span>  plpy.execute("CREATE TABLE " + output_table + " ( <span class="keywordtype">id</span> <span class="keywordtype">int</span>, ind float8[], label <span class="keywordtype">int</span> ) m4_ifdef(`__GREENPLUM__', `distributed by (<span class="keywordtype">id</span>)')");</div> |
| <div class="line"><a name="l00833"></a><span class="lineno"> 833</span>  plpy.execute("INSERT INTO " + output_table + " SELECT <span class="keywordtype">id</span>, MADLIB_SCHEMA.svm_normalization(ind), label FROM " + input_table);</div> |
| <div class="line"><a name="l00834"></a><span class="lineno"> 834</span>  plpy.info("output table: %s" % output_table)</div> |
| <div class="line"><a name="l00835"></a><span class="lineno"> 835</span> $$ LANGUAGE plpythonu;</div> |
| <div class="line"><a name="l00836"></a><span class="lineno"> 836</span> </div> |
| <div class="line"><a name="l00837"></a><span class="lineno"> 837</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00838"></a><span class="lineno"> 838</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00839"></a><span class="lineno"> 839</span> <span class="comment"> * @brief This is the linear support vector classification function</span></div> |
| <div class="line"><a name="l00840"></a><span class="lineno"> 840</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00841"></a><span class="lineno"> 841</span> <span class="comment"> * @param input_table The name of the table/view with the training data</span></div> |
| <div class="line"><a name="l00842"></a><span class="lineno"> 842</span> <span class="comment"> * @param model_table The name of the table under which we want to store the learned model</span></div> |
| <div class="line"><a name="l00843"></a><span class="lineno"> 843</span> <span class="comment"> * @param parallel A flag indicating whether the system should learn multiple models in parallel</span></div> |
| <div class="line"><a name="l00844"></a><span class="lineno"> 844</span> <span class="comment"> * @return A summary of the learning process</span></div> |
| <div class="line"><a name="l00845"></a><span class="lineno"> 845</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00846"></a><span class="lineno"> 846</span> <span class="comment"> * @internal </span></div> |
| <div class="line"><a name="l00847"></a><span class="lineno"> 847</span> <span class="comment"> * @sa This function is a wrapper for online_sv::lsvm_classification().</span></div> |
| <div class="line"><a name="l00848"></a><span class="lineno"> 848</span> <span class="comment">*/</span> </div> |
| <div class="line"><a name="l00849"></a><span class="lineno"> 849</span> CREATE OR REPLACE FUNCTION </div> |
| <div class="line"><a name="l00850"></a><span class="lineno"> 850</span> MADLIB_SCHEMA.<a class="code" href="online__sv_8sql__in.html#a75d126981ae4bf2e6641627501f0a2a5" title="This is the linear support vector classification function. ">lsvm_classification</a>(input_table text, model_table text, parallel <span class="keywordtype">bool</span>) </div> |
| <div class="line"><a name="l00851"></a><span class="lineno"><a class="code" href="online__sv_8sql__in.html#a78bb07d8f4aee80c3bbc8e8176e512be"> 851</a></span> RETURNS SETOF MADLIB_SCHEMA.lsvm_sgd_result</div> |
| <div class="line"><a name="l00852"></a><span class="lineno"> 852</span> AS $$</div> |
| <div class="line"><a name="l00853"></a><span class="lineno"> 853</span>  PythonFunctionBodyOnly(`kernel_machines', `online_sv')</div> |
| <div class="line"><a name="l00854"></a><span class="lineno"> 854</span>  <span class="preprocessor"># schema_madlib comes from PythonFunctionBodyOnly</span></div> |
| <div class="line"><a name="l00855"></a><span class="lineno"> 855</span> <span class="preprocessor"></span> <span class="keywordflow">return</span> online_sv.lsvm_classification( schema_madlib, input_table, model_table, parallel);</div> |
| <div class="line"><a name="l00856"></a><span class="lineno"> 856</span> $$ LANGUAGE <span class="stringliteral">'plpythonu'</span>;</div> |
| <div class="line"><a name="l00857"></a><span class="lineno"> 857</span> </div> |
| <div class="line"><a name="l00858"></a><span class="lineno"> 858</span> </div> |
| <div class="line"><a name="l00859"></a><span class="lineno"> 859</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00860"></a><span class="lineno"> 860</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00861"></a><span class="lineno"> 861</span> <span class="comment"> * @brief This is the linear support vector classification function</span></div> |
| <div class="line"><a name="l00862"></a><span class="lineno"> 862</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00863"></a><span class="lineno"> 863</span> <span class="comment"> * @param input_table The name of the table/view with the training data</span></div> |
| <div class="line"><a name="l00864"></a><span class="lineno"> 864</span> <span class="comment"> * @param model_table The name of the table under which we want to store the learned model</span></div> |
| <div class="line"><a name="l00865"></a><span class="lineno"> 865</span> <span class="comment"> * @param parallel A flag indicating whether the system should learn multiple models in parallel</span></div> |
| <div class="line"><a name="l00866"></a><span class="lineno"> 866</span> <span class="comment"> * @param verbose Verbosity of reporting</span></div> |
| <div class="line"><a name="l00867"></a><span class="lineno"> 867</span> <span class="comment"> * @param eta Initial learning rate in (0,1]</span></div> |
| <div class="line"><a name="l00868"></a><span class="lineno"> 868</span> <span class="comment"> * @param reg Regularization parameter, often chosen by cross-validation</span></div> |
| <div class="line"><a name="l00869"></a><span class="lineno"> 869</span> <span class="comment"> * @return A summary of the learning process</span></div> |
| <div class="line"><a name="l00870"></a><span class="lineno"> 870</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00871"></a><span class="lineno"><a class="code" href="online__sv_8sql__in.html#a75d126981ae4bf2e6641627501f0a2a5"> 871</a></span> <span class="comment"> * @internal </span></div> |
| <div class="line"><a name="l00872"></a><span class="lineno"> 872</span> <span class="comment"> * @sa This function is a wrapper for online_sv::lsvm_classification().</span></div> |
| <div class="line"><a name="l00873"></a><span class="lineno"> 873</span> <span class="comment">*/</span> </div> |
| <div class="line"><a name="l00874"></a><span class="lineno"> 874</span> CREATE OR REPLACE FUNCTION </div> |
| <div class="line"><a name="l00875"></a><span class="lineno"> 875</span> MADLIB_SCHEMA.lsvm_classification(input_table text, model_table text, parallel <span class="keywordtype">bool</span>, verbose <span class="keywordtype">bool</span>, eta float8, reg float8)</div> |
| <div class="line"><a name="l00876"></a><span class="lineno"> 876</span> RETURNS SETOF MADLIB_SCHEMA.lsvm_sgd_result</div> |
| <div class="line"><a name="l00877"></a><span class="lineno"> 877</span> AS $$</div> |
| <div class="line"><a name="l00878"></a><span class="lineno"> 878</span> </div> |
| <div class="line"><a name="l00879"></a><span class="lineno"> 879</span>  PythonFunctionBodyOnly(`kernel_machines<span class="stringliteral">', `online_sv'</span>)</div> |
| <div class="line"><a name="l00880"></a><span class="lineno"> 880</span>  </div> |
| <div class="line"><a name="l00881"></a><span class="lineno"> 881</span>  <span class="preprocessor"># schema_madlib comes from PythonFunctionBodyOnly</span></div> |
| <div class="line"><a name="l00882"></a><span class="lineno"> 882</span> <span class="preprocessor"></span> <span class="keywordflow">return</span> online_sv.lsvm_classification( schema_madlib, input_table, model_table, parallel, verbose, eta, reg);</div> |
| <div class="line"><a name="l00883"></a><span class="lineno"> 883</span> </div> |
| <div class="line"><a name="l00884"></a><span class="lineno"> 884</span> $$ LANGUAGE <span class="stringliteral">'plpythonu'</span>;</div> |
| <div class="line"><a name="l00885"></a><span class="lineno"> 885</span> </div> |
| <div class="line"><a name="l00886"></a><span class="lineno"> 886</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00887"></a><span class="lineno"> 887</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00888"></a><span class="lineno"> 888</span> <span class="comment"> * @brief Scores the data points stored in a table using a learned linear support-vector model</span></div> |
| <div class="line"><a name="l00889"></a><span class="lineno"> 889</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00890"></a><span class="lineno"> 890</span> <span class="comment"> * @param input_table Name of table/view containing the data points to be scored</span></div> |
| <div class="line"><a name="l00891"></a><span class="lineno"> 891</span> <span class="comment"> * @param data_col Name of column in input_table containing the data points</span></div> |
| <div class="line"><a name="l00892"></a><span class="lineno"> 892</span> <span class="comment"> * @param id_col Name of column in input_table containing the integer identifier of data points</span></div> |
| <div class="line"><a name="l00893"></a><span class="lineno"> 893</span> <span class="comment"> * @param model_table Name of table where the learned model to be used is stored</span></div> |
| <div class="line"><a name="l00894"></a><span class="lineno"> 894</span> <span class="comment"> * @param output_table Name of table to store the results </span></div> |
| <div class="line"><a name="l00895"></a><span class="lineno"> 895</span> <span class="comment"> * @param parallel A flag indicating whether the model to be used was learned in parallel</span></div> |
| <div class="line"><a name="l00896"></a><span class="lineno"><a class="code" href="online__sv_8sql__in.html#a50896def00d0e0950bec3d95b387e6b9"> 896</a></span> <span class="comment"> * @return Textual summary of the algorithm run</span></div> |
| <div class="line"><a name="l00897"></a><span class="lineno"> 897</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00898"></a><span class="lineno"> 898</span> <span class="comment"> * @internal </span></div> |
| <div class="line"><a name="l00899"></a><span class="lineno"> 899</span> <span class="comment"> * @sa This function is a wrapper for online_sv::lsvm_predict_batch().</span></div> |
| <div class="line"><a name="l00900"></a><span class="lineno"> 900</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00901"></a><span class="lineno"> 901</span> CREATE OR REPLACE FUNCTION</div> |
| <div class="line"><a name="l00902"></a><span class="lineno"> 902</span> MADLIB_SCHEMA.lsvm_predict_batch(input_table text, data_col text, id_col text, model_table text, output_table text, parallel <span class="keywordtype">bool</span>)</div> |
| <div class="line"><a name="l00903"></a><span class="lineno"> 903</span> RETURNS TEXT</div> |
| <div class="line"><a name="l00904"></a><span class="lineno"> 904</span> AS $$</div> |
| <div class="line"><a name="l00905"></a><span class="lineno"> 905</span> </div> |
| <div class="line"><a name="l00906"></a><span class="lineno"> 906</span>  PythonFunctionBodyOnly(`kernel_machines<span class="stringliteral">', `online_sv'</span>)</div> |
| <div class="line"><a name="l00907"></a><span class="lineno"> 907</span>  </div> |
| <div class="line"><a name="l00908"></a><span class="lineno"> 908</span>  <span class="preprocessor"># schema_madlib comes from PythonFunctionBodyOnly</span></div> |
| <div class="line"><a name="l00909"></a><span class="lineno"> 909</span> <span class="preprocessor"></span> <span class="keywordflow">return</span> online_sv.lsvm_predict_batch( schema_madlib, input_table, data_col, id_col, model_table, output_table, parallel);</div> |
| <div class="line"><a name="l00910"></a><span class="lineno"> 910</span>  </div> |
| <div class="line"><a name="l00911"></a><span class="lineno"> 911</span> $$ LANGUAGE <span class="stringliteral">'plpythonu'</span>;</div> |
| <div class="line"><a name="l00912"></a><span class="lineno"> 912</span> </div> |
| <div class="line"><a name="l00913"></a><span class="lineno"> 913</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00914"></a><span class="lineno"> 914</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00915"></a><span class="lineno"> 915</span> <span class="comment"> * @brief Evaluates a linear support-vector model on a given data point</span></div> |
| <div class="line"><a name="l00916"></a><span class="lineno"> 916</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00917"></a><span class="lineno"> 917</span> <span class="comment"> * @param model_table The table storing the learned model \f$ f \f$ to be used</span></div> |
| <div class="line"><a name="l00918"></a><span class="lineno"> 918</span> <span class="comment"> * @param ind The data point \f$ \boldsymbol x \f$</span></div> |
| <div class="line"><a name="l00919"></a><span class="lineno"> 919</span> <span class="comment"> * @return This function returns \f$ f(\boldsymbol x) \f$</span></div> |
| <div class="line"><a name="l00920"></a><span class="lineno"> 920</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00921"></a><span class="lineno"> 921</span> CREATE OR REPLACE FUNCTION </div> |
| <div class="line"><a name="l00922"></a><span class="lineno"> 922</span> MADLIB_SCHEMA.lsvm_predict(model_table text, ind float8[]) RETURNS FLOAT8 AS $$</div> |
| <div class="line"><a name="l00923"></a><span class="lineno"><a class="code" href="online__sv_8sql__in.html#a1c0a002f50250133c0ef1d3c43c6d338"> 923</a></span> </div> |
| <div class="line"><a name="l00924"></a><span class="lineno"> 924</span>  PythonFunctionBodyOnly(`kernel_machines<span class="stringliteral">', `online_sv'</span>)</div> |
| <div class="line"><a name="l00925"></a><span class="lineno"> 925</span>  </div> |
| <div class="line"><a name="l00926"></a><span class="lineno"> 926</span>  <span class="preprocessor"># schema_madlib comes from PythonFunctionBodyOnly</span></div> |
| <div class="line"><a name="l00927"></a><span class="lineno"> 927</span> <span class="preprocessor"></span> <span class="keywordflow">return</span> online_sv.lsvm_predict(schema_madlib, model_table, ind);</div> |
| <div class="line"><a name="l00928"></a><span class="lineno"> 928</span> </div> |
| <div class="line"><a name="l00929"></a><span class="lineno"> 929</span> $$ LANGUAGE plpythonu;</div> |
| <div class="line"><a name="l00930"></a><span class="lineno"> 930</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00931"></a><span class="lineno"> 931</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00932"></a><span class="lineno"> 932</span> <span class="comment"> * @brief Evaluates multiple linear support-vector models on a data point</span></div> |
| <div class="line"><a name="l00933"></a><span class="lineno"> 933</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00934"></a><span class="lineno"> 934</span> <span class="comment"> * @param model_table The table storing the learned models to be used.</span></div> |
| <div class="line"><a name="l00935"></a><span class="lineno"> 935</span> <span class="comment"> * @param ind The data point \f$ \boldsymbol x \f$</span></div> |
| <div class="line"><a name="l00936"></a><span class="lineno"> 936</span> <span class="comment"> * @return This function returns a table, a row for each model.</span></div> |
| <div class="line"><a name="l00937"></a><span class="lineno"> 937</span> <span class="comment"> * Moreover, the last row contains the average value, over all models.</span></div> |
| <div class="line"><a name="l00938"></a><span class="lineno"> 938</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00939"></a><span class="lineno"> 939</span> <span class="comment"> * The different models are assumed to be named <tt><em>model_table</em>0</tt>,</span></div> |
| <div class="line"><a name="l00940"></a><span class="lineno"> 940</span> <span class="comment"> * <tt><em>model_table</em>1</tt>, ....</span></div> |
| <div class="line"><a name="l00941"></a><span class="lineno"> 941</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00942"></a><span class="lineno"> 942</span> CREATE OR REPLACE FUNCTION</div> |
| <div class="line"><a name="l00943"></a><span class="lineno"><a class="code" href="online__sv_8sql__in.html#a5fe084c8364c0657097410458f8ea1e9"> 943</a></span> MADLIB_SCHEMA.lsvm_predict_combo(model_table text, ind float8[]) RETURNS SETOF MADLIB_SCHEMA.svm_model_pr AS $$</div> |
| <div class="line"><a name="l00944"></a><span class="lineno"> 944</span> </div> |
| <div class="line"><a name="l00945"></a><span class="lineno"> 945</span>  PythonFunctionBodyOnly(`kernel_machines<span class="stringliteral">', `online_sv'</span>)</div> |
| <div class="line"><a name="l00946"></a><span class="lineno"> 946</span>  </div> |
| <div class="line"><a name="l00947"></a><span class="lineno"> 947</span>  <span class="preprocessor"># schema_madlib comes from PythonFunctionBodyOnly</span></div> |
| <div class="line"><a name="l00948"></a><span class="lineno"> 948</span> <span class="preprocessor"></span> <span class="keywordflow">return</span> online_sv.lsvm_predict_combo( schema_madlib, model_table, ind);</div> |
| <div class="line"><a name="l00949"></a><span class="lineno"> 949</span> </div> |
| <div class="line"><a name="l00950"></a><span class="lineno"> 950</span> $$ LANGUAGE plpythonu;</div> |
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