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| <div class="section" id="algorithms"> |
| <h1>Algorithms<a class="headerlink" href="#algorithms" title="Permalink to this headline">¶</a></h1> |
| <p>SystemDS support different Machine learning algorithms out of the box.</p> |
| <p>As an example the lm algorithm can be used as follows:</p> |
| <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Import numpy and SystemDS matrix</span> |
| <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span> |
| <span class="kn">from</span> <span class="nn">systemds.context</span> <span class="kn">import</span> <span class="n">SystemDSContext</span> |
| <span class="kn">from</span> <span class="nn">systemds.matrix</span> <span class="kn">import</span> <span class="n">Matrix</span> |
| <span class="kn">from</span> <span class="nn">systemds.operator.algorithm</span> <span class="kn">import</span> <span class="n">lm</span> |
| |
| <span class="c1"># Set a seed</span> |
| <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> |
| <span class="c1"># Generate matrix of feature vectors</span> |
| <span class="n">features</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">15</span><span class="p">)</span> |
| <span class="c1"># Generate a 1-column matrix of response values</span> |
| <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> |
| |
| <span class="c1"># compute the weights</span> |
| <span class="k">with</span> <span class="n">SystemDSContext</span><span class="p">()</span> <span class="k">as</span> <span class="n">sds</span><span class="p">:</span> |
| <span class="n">weights</span> <span class="o">=</span> <span class="n">lm</span><span class="p">(</span><span class="n">Matrix</span><span class="p">(</span><span class="n">sds</span><span class="p">,</span> <span class="n">features</span><span class="p">),</span> <span class="n">Matrix</span><span class="p">(</span><span class="n">sds</span><span class="p">,</span> <span class="n">y</span><span class="p">))</span><span class="o">.</span><span class="n">compute</span><span class="p">()</span> |
| <span class="nb">print</span><span class="p">(</span><span class="n">weights</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| <p>The output should be similar to:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[[</span><span class="o">-</span><span class="mf">0.11538199</span><span class="p">]</span> |
| <span class="p">[</span><span class="o">-</span><span class="mf">0.20386541</span><span class="p">]</span> |
| <span class="p">[</span><span class="o">-</span><span class="mf">0.39956035</span><span class="p">]</span> |
| <span class="p">[</span> <span class="mf">1.04078623</span><span class="p">]</span> |
| <span class="p">[</span> <span class="mf">0.4327084</span> <span class="p">]</span> |
| <span class="p">[</span> <span class="mf">0.18954599</span><span class="p">]</span> |
| <span class="p">[</span> <span class="mf">0.49858968</span><span class="p">]</span> |
| <span class="p">[</span><span class="o">-</span><span class="mf">0.26812763</span><span class="p">]</span> |
| <span class="p">[</span> <span class="mf">0.09961844</span><span class="p">]</span> |
| <span class="p">[</span><span class="o">-</span><span class="mf">0.57000751</span><span class="p">]</span> |
| <span class="p">[</span><span class="o">-</span><span class="mf">0.43386048</span><span class="p">]</span> |
| <span class="p">[</span> <span class="mf">0.55358873</span><span class="p">]</span> |
| <span class="p">[</span><span class="o">-</span><span class="mf">0.54638565</span><span class="p">]</span> |
| <span class="p">[</span> <span class="mf">0.2205885</span> <span class="p">]</span> |
| <span class="p">[</span> <span class="mf">0.37957689</span><span class="p">]]</span> |
| </pre></div> |
| </div> |
| <span class="target" id="module-systemds.operator.algorithm"></span><dl class="py function"> |
| <dt id="systemds.operator.algorithm.kmeans"> |
| <code class="sig-prename descclassname">systemds.operator.algorithm.</code><code class="sig-name descname">kmeans</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">x</span><span class="p">:</span> <span class="n">systemds.operator.operation_node.OperationNode</span></em>, <em class="sig-param"><span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">Dict<span class="p">[</span>str<span class="p">, </span>Union<span class="p">[</span>DAGNode<span class="p">, </span>str<span class="p">, </span>int<span class="p">, </span>float<span class="p">, </span>bool<span class="p">]</span><span class="p">]</span></span></em><span class="sig-paren">)</span> → systemds.operator.operation_node.OperationNode<a class="headerlink" href="#systemds.operator.algorithm.kmeans" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Performs KMeans on matrix input.</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>x</strong> – Input dataset to perform K-Means on.</p></li> |
| <li><p><strong>k</strong> – The number of centroids to use for the algorithm.</p></li> |
| <li><p><strong>runs</strong> – The number of concurrent instances of K-Means to run (with different initial centroids).</p></li> |
| <li><p><strong>max_iter</strong> – The maximum number of iterations to run the K-Means algorithm for.</p></li> |
| <li><p><strong>eps</strong> – Tolerance for the algorithm to declare convergence using WCSS change ratio.</p></li> |
| <li><p><strong>is_verbose</strong> – Boolean flag if the algorithm should be run in a verbose manner.</p></li> |
| <li><p><strong>avg_sample_size_per_centroid</strong> – The average number of records per centroid in the data samples.</p></li> |
| </ul> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><p><cite>OperationNode</cite> List containing two outputs 1. the clusters, 2 the cluster ID associated with each row in x.</p> |
| </dd> |
| </dl> |
| </dd></dl> |
| |
| <dl class="py function"> |
| <dt id="systemds.operator.algorithm.l2svm"> |
| <code class="sig-prename descclassname">systemds.operator.algorithm.</code><code class="sig-name descname">l2svm</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">x</span><span class="p">:</span> <span class="n">systemds.operator.operation_node.OperationNode</span></em>, <em class="sig-param"><span class="n">y</span><span class="p">:</span> <span class="n">systemds.operator.operation_node.OperationNode</span></em>, <em class="sig-param"><span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">Dict<span class="p">[</span>str<span class="p">, </span>Union<span class="p">[</span>DAGNode<span class="p">, </span>str<span class="p">, </span>int<span class="p">, </span>float<span class="p">, </span>bool<span class="p">]</span><span class="p">]</span></span></em><span class="sig-paren">)</span> → systemds.operator.operation_node.OperationNode<a class="headerlink" href="#systemds.operator.algorithm.l2svm" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Perform L2SVM on matrix with labels given.</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>x</strong> – Input dataset</p></li> |
| <li><p><strong>y</strong> – Input labels in shape of one column</p></li> |
| <li><p><strong>kwargs</strong> – Dictionary of extra arguments</p></li> |
| </ul> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><p><cite>OperationNode</cite> containing the model fit.</p> |
| </dd> |
| </dl> |
| </dd></dl> |
| |
| <dl class="py function"> |
| <dt id="systemds.operator.algorithm.lm"> |
| <code class="sig-prename descclassname">systemds.operator.algorithm.</code><code class="sig-name descname">lm</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">x</span><span class="p">:</span> <span class="n">systemds.operator.operation_node.OperationNode</span></em>, <em class="sig-param"><span class="n">y</span><span class="p">:</span> <span class="n">systemds.operator.operation_node.OperationNode</span></em>, <em class="sig-param"><span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">Dict<span class="p">[</span>str<span class="p">, </span>Union<span class="p">[</span>DAGNode<span class="p">, </span>str<span class="p">, </span>int<span class="p">, </span>float<span class="p">, </span>bool<span class="p">]</span><span class="p">]</span></span></em><span class="sig-paren">)</span> → systemds.operator.operation_node.OperationNode<a class="headerlink" href="#systemds.operator.algorithm.lm" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Performs LM on matrix with labels given.</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>x</strong> – Input dataset</p></li> |
| <li><p><strong>y</strong> – Input labels in shape of one column</p></li> |
| <li><p><strong>kwargs</strong> – Dictionary of extra arguments</p></li> |
| </ul> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><p><cite>OperationNode</cite> containing the model fit.</p> |
| </dd> |
| </dl> |
| </dd></dl> |
| |
| <dl class="py function"> |
| <dt id="systemds.operator.algorithm.multiLogReg"> |
| <code class="sig-prename descclassname">systemds.operator.algorithm.</code><code class="sig-name descname">multiLogReg</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">x</span><span class="p">:</span> <span class="n">systemds.operator.operation_node.OperationNode</span></em>, <em class="sig-param"><span class="n">y</span><span class="p">:</span> <span class="n">systemds.operator.operation_node.OperationNode</span></em>, <em class="sig-param"><span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">Dict<span class="p">[</span>str<span class="p">, </span>Union<span class="p">[</span>DAGNode<span class="p">, </span>str<span class="p">, </span>int<span class="p">, </span>float<span class="p">, </span>bool<span class="p">]</span><span class="p">]</span></span></em><span class="sig-paren">)</span> → systemds.operator.operation_node.OperationNode<a class="headerlink" href="#systemds.operator.algorithm.multiLogReg" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Performs Multiclass Logistic Regression on the matrix input |
| using Trust Region method.</p> |
| <p>See: Trust Region Newton Method for Logistic Regression, Lin, Weng and Keerthi, JMLR 9 (2008) 627-650)</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>x</strong> – Input dataset to perform logstic regression on</p></li> |
| <li><p><strong>y</strong> – Labels rowaligned with the input dataset</p></li> |
| <li><p><strong>icpt</strong> – Intercept, default 2, Intercept presence, shifting and rescaling X columns: |
| 0 = no intercept, no shifting, no rescaling; |
| 1 = add intercept, but neither shift nor rescale X; |
| 2 = add intercept, shift & rescale X columns to mean = 0, variance = 1</p></li> |
| <li><p><strong>tol</strong> – float tolerance for the algorithm.</p></li> |
| <li><p><strong>reg</strong> – Regularization parameter (lambda = 1/C); intercept settings are not regularized.</p></li> |
| <li><p><strong>maxi</strong> – Maximum outer iterations of the algorithm</p></li> |
| <li><p><strong>maxii</strong> – Maximum inner iterations of the algorithm |
| :return: <cite>OperationNode</cite> of a matrix containing the regression parameters trained.</p></li> |
| </ul> |
| </dd> |
| </dl> |
| </dd></dl> |
| |
| <dl class="py function"> |
| <dt id="systemds.operator.algorithm.multiLogRegPredict"> |
| <code class="sig-prename descclassname">systemds.operator.algorithm.</code><code class="sig-name descname">multiLogRegPredict</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">x</span><span class="p">:</span> <span class="n">systemds.operator.operation_node.OperationNode</span></em>, <em class="sig-param"><span class="n">b</span><span class="p">:</span> <span class="n">systemds.operator.operation_node.OperationNode</span></em>, <em class="sig-param"><span class="n">y</span><span class="p">:</span> <span class="n">systemds.operator.operation_node.OperationNode</span></em>, <em class="sig-param"><span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">Dict<span class="p">[</span>str<span class="p">, </span>Union<span class="p">[</span>DAGNode<span class="p">, </span>str<span class="p">, </span>int<span class="p">, </span>float<span class="p">, </span>bool<span class="p">]</span><span class="p">]</span></span></em><span class="sig-paren">)</span> → systemds.operator.operation_node.OperationNode<a class="headerlink" href="#systemds.operator.algorithm.multiLogRegPredict" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Performs prediction on input data x using the model trained, b.</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>x</strong> – The data to perform classification on.</p></li> |
| <li><p><strong>b</strong> – The regression parameters trained from multiLogReg.</p></li> |
| <li><p><strong>y</strong> – The Labels expected to be contained in the X dataset, to calculate accuracy.</p></li> |
| <li><p><strong>verbose</strong> – Boolean specifying if the prediction should be verbose.</p></li> |
| </ul> |
| </dd> |
| <dt class="field-even">Returns</dt> |
| <dd class="field-even"><p><cite>OperationNode</cite> List containing three outputs. |
| 1. The predicted means / probabilities |
| 2. The predicted response vector |
| 3. The scalar value of accuracy</p> |
| </dd> |
| </dl> |
| </dd></dl> |
| |
| <dl class="py function"> |
| <dt id="systemds.operator.algorithm.pca"> |
| <code class="sig-prename descclassname">systemds.operator.algorithm.</code><code class="sig-name descname">pca</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">x</span><span class="p">:</span> <span class="n">systemds.operator.operation_node.OperationNode</span></em>, <em class="sig-param"><span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">Dict<span class="p">[</span>str<span class="p">, </span>Union<span class="p">[</span>DAGNode<span class="p">, </span>str<span class="p">, </span>int<span class="p">, </span>float<span class="p">, </span>bool<span class="p">]</span><span class="p">]</span></span></em><span class="sig-paren">)</span> → systemds.operator.operation_node.OperationNode<a class="headerlink" href="#systemds.operator.algorithm.pca" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Performs PCA on the matrix input</p> |
| <dl class="field-list simple"> |
| <dt class="field-odd">Parameters</dt> |
| <dd class="field-odd"><ul class="simple"> |
| <li><p><strong>x</strong> – Input dataset to perform Principal Componenet Analysis (PCA) on.</p></li> |
| <li><p><strong>K</strong> – The number of reduced dimensions.</p></li> |
| <li><p><strong>center</strong> – Boolean specifying if the input values should be centered.</p></li> |
| <li><p><strong>scale</strong> – Boolean specifying if the input values should be scaled. |
| :return: <cite>OperationNode</cite> List containing two outputs 1. The dimensionality reduced X input, 2. A matrix to reduce dimensionality similarly on unseen data.</p></li> |
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