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| <a href="svdmf_8sql__in.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">/* ----------------------------------------------------------------------- */</span><span class="comment">/** </span> |
| <a name="l00002"></a>00002 <span class="comment"> *</span> |
| <a name="l00003"></a>00003 <span class="comment"> * @file svdmf.sql_in</span> |
| <a name="l00004"></a>00004 <span class="comment"> *</span> |
| <a name="l00005"></a>00005 <span class="comment"> * @brief SQL functions for SVD Matrix Factorization</span> |
| <a name="l00006"></a>00006 <span class="comment"> * @date January 2011</span> |
| <a name="l00007"></a>00007 <span class="comment"> *</span> |
| <a name="l00008"></a>00008 <span class="comment"> * @sa For a brief introduction to SVD Matrix Factorization, see the module</span> |
| <a name="l00009"></a>00009 <span class="comment"> * description \ref grp_svdmf.</span> |
| <a name="l00010"></a>00010 <span class="comment"> *</span> |
| <a name="l00011"></a>00011 <span class="comment"> */</span><span class="comment">/* ----------------------------------------------------------------------- */</span> |
| <a name="l00012"></a>00012 |
| <a name="l00013"></a>00013 m4_include(`SQLCommon.m4<span class="stringliteral">')</span> |
| <a name="l00014"></a>00014 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00015"></a>00015 <span class="comment">/**</span> |
| <a name="l00016"></a>00016 <span class="comment">@addtogroup grp_svdmf </span> |
| <a name="l00017"></a>00017 <span class="comment"></span> |
| <a name="l00018"></a>00018 <span class="comment">@about</span> |
| <a name="l00019"></a>00019 <span class="comment"></span> |
| <a name="l00020"></a>00020 <span class="comment">This module implements "partial SVD decomposition" method for representing a sparse matrix using a low-rank approximation.</span> |
| <a name="l00021"></a>00021 <span class="comment">Mathematically, this algorithm seeks to find matrices U and V that, for any given A, minimizes:\n</span> |
| <a name="l00022"></a>00022 <span class="comment">\f[ ||\boldsymbol A - \boldsymbol UV ||_2 </span> |
| <a name="l00023"></a>00023 <span class="comment">\f]</span> |
| <a name="l00024"></a>00024 <span class="comment">subject to \f$ rank(\boldsymbol UV) \leq k \f$, where \f$ ||\cdot||_2 \f$ denotes the Frobenius norm and \f$ k \leq rank(\boldsymbol A)\f$.</span> |
| <a name="l00025"></a>00025 <span class="comment">If A is \f$ m \times n \f$, then U will be \f$ m \times k \f$ and V will be \f$ k \times n \f$.</span> |
| <a name="l00026"></a>00026 <span class="comment"></span> |
| <a name="l00027"></a>00027 <span class="comment">This algorithm is not intended to do the full decomposition, or to be used as part of</span> |
| <a name="l00028"></a>00028 <span class="comment">inverse procedure. It effectively computes the SVD of a low-rank approximation of A (preferably sparse), with the singular values absorbed in U and V. </span> |
| <a name="l00029"></a>00029 <span class="comment">Code is based on the write-up as appears at [1], with some modifications.</span> |
| <a name="l00030"></a>00030 <span class="comment"></span> |
| <a name="l00031"></a>00031 <span class="comment"></span> |
| <a name="l00032"></a>00032 <span class="comment">@input</span> |
| <a name="l00033"></a>00033 <span class="comment">The <b>input matrix</b> is expected to be of the following form:</span> |
| <a name="l00034"></a>00034 <span class="comment"><pre>{TABLE|VIEW} <em>input_table</em> (</span> |
| <a name="l00035"></a>00035 <span class="comment"> <em>col_num</em> INTEGER,</span> |
| <a name="l00036"></a>00036 <span class="comment"> <em>row_num</em> INTEGER,</span> |
| <a name="l00037"></a>00037 <span class="comment"> <em>value</em> FLOAT </span> |
| <a name="l00038"></a>00038 <span class="comment">)</pre></span> |
| <a name="l00039"></a>00039 <span class="comment"></span> |
| <a name="l00040"></a>00040 <span class="comment">Input is contained in a table where column number and row number for each cell</span> |
| <a name="l00041"></a>00041 <span class="comment">are sequential; that is to say that if the data was written as a matrix, those values would be the</span> |
| <a name="l00042"></a>00042 <span class="comment">actual row and column numbers and not some random identifiers. All rows and columns must be associated with a value.</span> |
| <a name="l00043"></a>00043 <span class="comment">There should not be any missing row, columns or values.</span> |
| <a name="l00044"></a>00044 <span class="comment"></span> |
| <a name="l00045"></a>00045 <span class="comment">@usage</span> |
| <a name="l00046"></a>00046 <span class="comment">The SVD function is called as follows:</span> |
| <a name="l00047"></a>00047 <span class="comment"><pre>SELECT \ref svdmf_run( '<em>input_table</em>', '<em>col_name</em>',</span> |
| <a name="l00048"></a>00048 <span class="comment"> '<em>row_name</em>', '<em>value</em>', <em>num_features</em>);</pre></span> |
| <a name="l00049"></a>00049 <span class="comment">The function returns two tables \c matrix_u and \c matrix_v, which represent the matrices U and V in table format.</span> |
| <a name="l00050"></a>00050 <span class="comment"></span> |
| <a name="l00051"></a>00051 <span class="comment">@examp</span> |
| <a name="l00052"></a>00052 <span class="comment"></span> |
| <a name="l00053"></a>00053 <span class="comment">-# Prepare an input table/view:</span> |
| <a name="l00054"></a>00054 <span class="comment">\code</span> |
| <a name="l00055"></a>00055 <span class="comment">CREATE TABLE svd_test (</span> |
| <a name="l00056"></a>00056 <span class="comment"> col INT,</span> |
| <a name="l00057"></a>00057 <span class="comment"> row INT,</span> |
| <a name="l00058"></a>00058 <span class="comment"> val FLOAT</span> |
| <a name="l00059"></a>00059 <span class="comment">);</span> |
| <a name="l00060"></a>00060 <span class="comment">\endcode </span> |
| <a name="l00061"></a>00061 <span class="comment">-# Populate the input table with some data. e.g.:</span> |
| <a name="l00062"></a>00062 <span class="comment">\code</span> |
| <a name="l00063"></a>00063 <span class="comment">sql> INSERT INTO svd_test SELECT (g.a%1000)+1, g.a/1000+1, random() FROM generate_series(1,1000) AS g(a);</span> |
| <a name="l00064"></a>00064 <span class="comment">\endcode </span> |
| <a name="l00065"></a>00065 <span class="comment">-# Call svdmf_run() stored procedure, e.g.: </span> |
| <a name="l00066"></a>00066 <span class="comment">\code</span> |
| <a name="l00067"></a>00067 <span class="comment">sql> select madlib.svdmf_run( 'svd_test', 'col', 'row', 'val', 3);</span> |
| <a name="l00068"></a>00068 <span class="comment">\endcode</span> |
| <a name="l00069"></a>00069 <span class="comment">-# Sample Output:</span> |
| <a name="l00070"></a>00070 <span class="comment">\code</span> |
| <a name="l00071"></a>00071 <span class="comment">INFO: ('Started svdmf_run() with parameters:',)</span> |
| <a name="l00072"></a>00072 <span class="comment">INFO: (' * input_matrix = madlib_svdsparse_test.test',)</span> |
| <a name="l00073"></a>00073 <span class="comment">INFO: (' * col_name = col_num',)</span> |
| <a name="l00074"></a>00074 <span class="comment">INFO: (' * row_name = row_num',)</span> |
| <a name="l00075"></a>00075 <span class="comment">INFO: (' * value = val',)</span> |
| <a name="l00076"></a>00076 <span class="comment">INFO: (' * num_features = 3',)</span> |
| <a name="l00077"></a>00077 <span class="comment">INFO: ('Copying the source data into a temporary table...',)</span> |
| <a name="l00078"></a>00078 <span class="comment">INFO: ('Estimating feature: 1',)</span> |
| <a name="l00079"></a>00079 <span class="comment">INFO: ('...Iteration 1: residual_error = 33345014611.1, step_size = 4.9997500125e-10, min_improvement = 1.0',)</span> |
| <a name="l00080"></a>00080 <span class="comment">INFO: ('...Iteration 2: residual_error = 33345014557.6, step_size = 5.49972501375e-10, min_improvement = 1.0',)</span> |
| <a name="l00081"></a>00081 <span class="comment">INFO: ('...Iteration 3: residual_error = 33345014054.3, step_size = 6.04969751512e-10, min_improvement = 1.0',)</span> |
| <a name="l00082"></a>00082 <span class="comment">...</span> |
| <a name="l00083"></a>00083 <span class="comment">INFO: ('...Iteration 78: residual_error = 2.02512133868, step_size = 5.78105354457e-10, min_improvement = 1.0',)</span> |
| <a name="l00084"></a>00084 <span class="comment">INFO: ('...Iteration 79: residual_error = 0.893810181282, step_size = 6.35915889903e-10, min_improvement = 1.0',)</span> |
| <a name="l00085"></a>00085 <span class="comment">INFO: ('...Iteration 80: residual_error = 0.34496773222, step_size = 6.99507478893e-10, min_improvement = 1.0',)</span> |
| <a name="l00086"></a>00086 <span class="comment">INFO: ('Swapping residual error matrix...',)</span> |
| <a name="l00087"></a>00087 <span class="comment"> svdmf_run </span> |
| <a name="l00088"></a>00088 <span class="comment">--------------------------------------------------------------------------------------------</span> |
| <a name="l00089"></a>00089 <span class="comment"> </span> |
| <a name="l00090"></a>00090 <span class="comment"> Finished SVD matrix factorisation for madlib_svdsparse_test.test (row_num, col_num, val). </span> |
| <a name="l00091"></a>00091 <span class="comment"> Results: </span> |
| <a name="l00092"></a>00092 <span class="comment"> * total error = 0.34496773222</span> |
| <a name="l00093"></a>00093 <span class="comment"> * number of estimated features = 1</span> |
| <a name="l00094"></a>00094 <span class="comment"> Output:</span> |
| <a name="l00095"></a>00095 <span class="comment"> * table : madlib.matrix_u</span> |
| <a name="l00096"></a>00096 <span class="comment"> * table : madlib.matrix_v</span> |
| <a name="l00097"></a>00097 <span class="comment"> Time elapsed: 4 minutes 47.86839 seconds.</span> |
| <a name="l00098"></a>00098 <span class="comment"></span> |
| <a name="l00099"></a>00099 <span class="comment">\endcode</span> |
| <a name="l00100"></a>00100 <span class="comment"></span> |
| <a name="l00101"></a>00101 <span class="comment">@literature</span> |
| <a name="l00102"></a>00102 <span class="comment"></span> |
| <a name="l00103"></a>00103 <span class="comment">[1] Simon Funk, Netflix Update: Try This at Home, December 11 2006,</span> |
| <a name="l00104"></a>00104 <span class="comment"> http://sifter.org/~simon/journal/20061211.html</span> |
| <a name="l00105"></a>00105 <span class="comment"></span> |
| <a name="l00106"></a>00106 <span class="comment">@sa File svdmf.sql_in documenting the SQL functions.</span> |
| <a name="l00107"></a>00107 <span class="comment"></span> |
| <a name="l00108"></a>00108 <span class="comment">@internal</span> |
| <a name="l00109"></a>00109 <span class="comment">@sa namespace svdmf (documenting the implementation in Python)</span> |
| <a name="l00110"></a>00110 <span class="comment">@endinternal </span> |
| <a name="l00111"></a>00111 <span class="comment"></span> |
| <a name="l00112"></a>00112 <span class="comment">*/</span> |
| <a name="l00113"></a>00113 <span class="comment"></span> |
| <a name="l00114"></a>00114 <span class="comment">/**</span> |
| <a name="l00115"></a>00115 <span class="comment"> * @brief Partial SVD decomposition of a sparse matrix into U and V components</span> |
| <a name="l00116"></a>00116 <span class="comment"> *</span> |
| <a name="l00117"></a>00117 <span class="comment"> * This function takes as input the table representation of a sparse matrix and</span> |
| <a name="l00118"></a>00118 <span class="comment"> * decomposes it into the specified set of most significant features of matrices</span> |
| <a name="l00119"></a>00119 <span class="comment"> * of U and V matrix. </span> |
| <a name="l00120"></a>00120 <span class="comment"> *</span> |
| <a name="l00121"></a>00121 <span class="comment"> * @param input_table Name of the table/view with the source data</span> |
| <a name="l00122"></a>00122 <span class="comment"> * @param col_name Name of the column containing cell column number</span> |
| <a name="l00123"></a>00123 <span class="comment"> * @param row_name Name of the column containing cell row number</span> |
| <a name="l00124"></a>00124 <span class="comment"> * @param value Name of the column containing cell value</span> |
| <a name="l00125"></a>00125 <span class="comment"> * @param num_features Rank of desired approximation</span> |
| <a name="l00126"></a>00126 <span class="comment"> * </span> |
| <a name="l00127"></a>00127 <span class="comment"> */</span> |
| <a name="l00128"></a>00128 CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.svdmf_run( |
| <a name="l00129"></a>00129 input_table TEXT, col_name TEXT, row_name TEXT, value TEXT, num_features INT |
| <a name="l00130"></a>00130 ) |
| <a name="l00131"></a>00131 RETURNS TEXT |
| <a name="l00132"></a>00132 AS $$ |
| <a name="l00133"></a>00133 |
| <a name="l00134"></a>00134 PythonFunctionBodyOnly(`svd_mf', `svdmf<span class="stringliteral">')</span> |
| <a name="l00135"></a>00135 <span class="stringliteral"> </span> |
| <a name="l00136"></a>00136 <span class="stringliteral"> # schema_madlib comes from PythonFunctionBodyOnly</span> |
| <a name="l00137"></a>00137 <span class="stringliteral"> return svdmf.svdmf_run( schema_madlib, input_table, col_name, row_name, value, num_features);</span> |
| <a name="l00138"></a>00138 <span class="stringliteral"></span> |
| <a name="l00139"></a>00139 <span class="stringliteral">$$ LANGUAGE plpythonu;</span> |
| <a name="l00140"></a>00140 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00141"></a>00141 <span class="comment">/**</span> |
| <a name="l00142"></a>00142 <span class="comment"> * @brief Partial SVD decomposition of a sparse matrix into U and V components</span> |
| <a name="l00143"></a>00143 <span class="comment"> *</span> |
| <a name="l00144"></a>00144 <span class="comment"> * This function takes as input the table representation of a sparse matrix and</span> |
| <a name="l00145"></a>00145 <span class="comment"> * decomposes it into the specified set of most significant features of matrices</span> |
| <a name="l00146"></a>00146 <span class="comment"> * of U and V matrix. </span> |
| <a name="l00147"></a>00147 <span class="comment"> *</span> |
| <a name="l00148"></a>00148 <span class="comment"> * @param input_table Name of the table/view with the source data</span> |
| <a name="l00149"></a>00149 <span class="comment"> * @param col_name Name of the column containing cell column number</span> |
| <a name="l00150"></a><a class="code" href="svdmf_8sql__in.html#a6cff34415cca23aa0a826cc08a6283f5">00150</a> <span class="comment"> * @param row_name Name of the column containing cell row number</span> |
| <a name="l00151"></a>00151 <span class="comment"> * @param value Name of the column containing cell value</span> |
| <a name="l00152"></a>00152 <span class="comment"> * @param num_features Rank of desired approximation</span> |
| <a name="l00153"></a>00153 <span class="comment"> * @param num_iterations Maximum number if iterations to perform regardless of convergence</span> |
| <a name="l00154"></a>00154 <span class="comment"> * @param min_error Acceptable level of error in convergence.</span> |
| <a name="l00155"></a>00155 <span class="comment"> * </span> |
| <a name="l00156"></a>00156 <span class="comment"> */</span> |
| <a name="l00157"></a>00157 |
| <a name="l00158"></a>00158 CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.svdmf_run( |
| <a name="l00159"></a>00159 input_table TEXT, col_name TEXT, row_name TEXT, value TEXT, num_features INT, num_iterations INT, min_error FLOAT |
| <a name="l00160"></a>00160 ) |
| <a name="l00161"></a>00161 RETURNS TEXT |
| <a name="l00162"></a>00162 AS $$ |
| <a name="l00163"></a>00163 |
| <a name="l00164"></a>00164 PythonFunctionBodyOnly(`svd_mf', `svdmf<span class="stringliteral">')</span> |
| <a name="l00165"></a>00165 <span class="stringliteral"></span> |
| <a name="l00166"></a>00166 <span class="stringliteral"> # schema_madlib comes from PythonFunctionBodyOnly</span> |
| <a name="l00167"></a>00167 <span class="stringliteral"> return svdmf.svdmf_run_full( schema_madlib, input_table, col_name, row_name, value, num_features, num_iterations, min_error);</span> |
| <a name="l00168"></a>00168 <span class="stringliteral"></span> |
| <a name="l00169"></a>00169 <span class="stringliteral">$$ LANGUAGE plpythonu;</span> |
| </pre></div></div> |
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