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<h1 class="title"><a href="ml-guide.html">ML</a> - Multilayer perceptron classifier</h1>
<p><code>\[
\newcommand{\R}{\mathbb{R}}
\newcommand{\E}{\mathbb{E}}
\newcommand{\x}{\mathbf{x}}
\newcommand{\y}{\mathbf{y}}
\newcommand{\wv}{\mathbf{w}}
\newcommand{\av}{\mathbf{\alpha}}
\newcommand{\bv}{\mathbf{b}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\id}{\mathbf{I}}
\newcommand{\ind}{\mathbf{1}}
\newcommand{\0}{\mathbf{0}}
\newcommand{\unit}{\mathbf{e}}
\newcommand{\one}{\mathbf{1}}
\newcommand{\zero}{\mathbf{0}}
\]</code></p>
<p>Multilayer perceptron classifier (MLPC) is a classifier based on the <a href="https://en.wikipedia.org/wiki/Feedforward_neural_network">feedforward artificial neural network</a>.
MLPC consists of multiple layers of nodes.
Each layer is fully connected to the next layer in the network. Nodes in the input layer represent the input data. All other nodes maps inputs to the outputs
by performing linear combination of the inputs with the node’s weights <code>$\wv$</code> and bias <code>$\bv$</code> and applying an activation function.
It can be written in matrix form for MLPC with <code>$K+1$</code> layers as follows:
<code>\[
\mathrm{y}(\x) = \mathrm{f_K}(...\mathrm{f_2}(\wv_2^T\mathrm{f_1}(\wv_1^T \x+b_1)+b_2)...+b_K)
\]</code>
Nodes in intermediate layers use sigmoid (logistic) function:
<code>\[
\mathrm{f}(z_i) = \frac{1}{1 + e^{-z_i}}
\]</code>
Nodes in the output layer use softmax function:
<code>\[
\mathrm{f}(z_i) = \frac{e^{z_i}}{\sum_{k=1}^N e^{z_k}}
\]</code>
The number of nodes <code>$N$</code> in the output layer corresponds to the number of classes.</p>
<p>MLPC employes backpropagation for learning the model. We use logistic loss function for optimization and L-BFGS as optimization routine.</p>
<p><strong>Examples</strong></p>
<div class="codetabs">
<div data-lang="scala">
<div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.ml.classification.MultilayerPerceptronClassifier</span>
<span class="k">import</span> <span class="nn">org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator</span>
<span class="k">import</span> <span class="nn">org.apache.spark.mllib.util.MLUtils</span>
<span class="k">import</span> <span class="nn">org.apache.spark.sql.Row</span>
<span class="c1">// Load training data</span>
<span class="k">val</span> <span class="n">data</span> <span class="k">=</span> <span class="nc">MLUtils</span><span class="o">.</span><span class="n">loadLibSVMFile</span><span class="o">(</span><span class="n">sc</span><span class="o">,</span> <span class="s">"data/mllib/sample_multiclass_classification_data.txt"</span><span class="o">).</span><span class="n">toDF</span><span class="o">()</span>
<span class="c1">// Split the data into train and test</span>
<span class="k">val</span> <span class="n">splits</span> <span class="k">=</span> <span class="n">data</span><span class="o">.</span><span class="n">randomSplit</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="mf">0.6</span><span class="o">,</span> <span class="mf">0.4</span><span class="o">),</span> <span class="n">seed</span> <span class="k">=</span> <span class="mi">1234L</span><span class="o">)</span>
<span class="k">val</span> <span class="n">train</span> <span class="k">=</span> <span class="n">splits</span><span class="o">(</span><span class="mi">0</span><span class="o">)</span>
<span class="k">val</span> <span class="n">test</span> <span class="k">=</span> <span class="n">splits</span><span class="o">(</span><span class="mi">1</span><span class="o">)</span>
<span class="c1">// specify layers for the neural network: </span>
<span class="c1">// input layer of size 4 (features), two intermediate of size 5 and 4 and output of size 3 (classes)</span>
<span class="k">val</span> <span class="n">layers</span> <span class="k">=</span> <span class="nc">Array</span><span class="o">[</span><span class="kt">Int</span><span class="o">](</span><span class="mi">4</span><span class="o">,</span> <span class="mi">5</span><span class="o">,</span> <span class="mi">4</span><span class="o">,</span> <span class="mi">3</span><span class="o">)</span>
<span class="c1">// create the trainer and set its parameters</span>
<span class="k">val</span> <span class="n">trainer</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">MultilayerPerceptronClassifier</span><span class="o">()</span>
<span class="o">.</span><span class="n">setLayers</span><span class="o">(</span><span class="n">layers</span><span class="o">)</span>
<span class="o">.</span><span class="n">setBlockSize</span><span class="o">(</span><span class="mi">128</span><span class="o">)</span>
<span class="o">.</span><span class="n">setSeed</span><span class="o">(</span><span class="mi">1234L</span><span class="o">)</span>
<span class="o">.</span><span class="n">setMaxIter</span><span class="o">(</span><span class="mi">100</span><span class="o">)</span>
<span class="c1">// train the model</span>
<span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="n">trainer</span><span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">train</span><span class="o">)</span>
<span class="c1">// compute precision on the test set</span>
<span class="k">val</span> <span class="n">result</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">transform</span><span class="o">(</span><span class="n">test</span><span class="o">)</span>
<span class="k">val</span> <span class="n">predictionAndLabels</span> <span class="k">=</span> <span class="n">result</span><span class="o">.</span><span class="n">select</span><span class="o">(</span><span class="s">"prediction"</span><span class="o">,</span> <span class="s">"label"</span><span class="o">)</span>
<span class="k">val</span> <span class="n">evaluator</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">MulticlassClassificationEvaluator</span><span class="o">()</span>
<span class="o">.</span><span class="n">setMetricName</span><span class="o">(</span><span class="s">"precision"</span><span class="o">)</span>
<span class="n">println</span><span class="o">(</span><span class="s">"Precision:"</span> <span class="o">+</span> <span class="n">evaluator</span><span class="o">.</span><span class="n">evaluate</span><span class="o">(</span><span class="n">predictionAndLabels</span><span class="o">))</span></code></pre></div>
</div>
<div data-lang="java">
<div class="highlight"><pre><code class="language-java" data-lang="java"><span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaRDD</span><span class="o">;</span>
<span class="kn">import</span> <span class="nn">org.apache.spark.ml.classification.MultilayerPerceptronClassificationModel</span><span class="o">;</span>
<span class="kn">import</span> <span class="nn">org.apache.spark.ml.classification.MultilayerPerceptronClassifier</span><span class="o">;</span>
<span class="kn">import</span> <span class="nn">org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator</span><span class="o">;</span>
<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.regression.LabeledPoint</span><span class="o">;</span>
<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.util.MLUtils</span><span class="o">;</span>
<span class="c1">// Load training data</span>
<span class="n">String</span> <span class="n">path</span> <span class="o">=</span> <span class="s">"data/mllib/sample_multiclass_classification_data.txt"</span><span class="o">;</span>
<span class="n">JavaRDD</span><span class="o"><</span><span class="n">LabeledPoint</span><span class="o">></span> <span class="n">data</span> <span class="o">=</span> <span class="n">MLUtils</span><span class="o">.</span><span class="na">loadLibSVMFile</span><span class="o">(</span><span class="n">sc</span><span class="o">,</span> <span class="n">path</span><span class="o">).</span><span class="na">toJavaRDD</span><span class="o">();</span>
<span class="n">DataFrame</span> <span class="n">dataFrame</span> <span class="o">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="na">createDataFrame</span><span class="o">(</span><span class="n">data</span><span class="o">,</span> <span class="n">LabeledPoint</span><span class="o">.</span><span class="na">class</span><span class="o">);</span>
<span class="c1">// Split the data into train and test</span>
<span class="n">DataFrame</span><span class="o">[]</span> <span class="n">splits</span> <span class="o">=</span> <span class="n">dataFrame</span><span class="o">.</span><span class="na">randomSplit</span><span class="o">(</span><span class="k">new</span> <span class="kt">double</span><span class="o">[]{</span><span class="mf">0.6</span><span class="o">,</span> <span class="mf">0.4</span><span class="o">},</span> <span class="mi">1234L</span><span class="o">);</span>
<span class="n">DataFrame</span> <span class="n">train</span> <span class="o">=</span> <span class="n">splits</span><span class="o">[</span><span class="mi">0</span><span class="o">];</span>
<span class="n">DataFrame</span> <span class="n">test</span> <span class="o">=</span> <span class="n">splits</span><span class="o">[</span><span class="mi">1</span><span class="o">];</span>
<span class="c1">// specify layers for the neural network:</span>
<span class="c1">// input layer of size 4 (features), two intermediate of size 5 and 4 and output of size 3 (classes)</span>
<span class="kt">int</span><span class="o">[]</span> <span class="n">layers</span> <span class="o">=</span> <span class="k">new</span> <span class="kt">int</span><span class="o">[]</span> <span class="o">{</span><span class="mi">4</span><span class="o">,</span> <span class="mi">5</span><span class="o">,</span> <span class="mi">4</span><span class="o">,</span> <span class="mi">3</span><span class="o">};</span>
<span class="c1">// create the trainer and set its parameters</span>
<span class="n">MultilayerPerceptronClassifier</span> <span class="n">trainer</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">MultilayerPerceptronClassifier</span><span class="o">()</span>
<span class="o">.</span><span class="na">setLayers</span><span class="o">(</span><span class="n">layers</span><span class="o">)</span>
<span class="o">.</span><span class="na">setBlockSize</span><span class="o">(</span><span class="mi">128</span><span class="o">)</span>
<span class="o">.</span><span class="na">setSeed</span><span class="o">(</span><span class="mi">1234L</span><span class="o">)</span>
<span class="o">.</span><span class="na">setMaxIter</span><span class="o">(</span><span class="mi">100</span><span class="o">);</span>
<span class="c1">// train the model</span>
<span class="n">MultilayerPerceptronClassificationModel</span> <span class="n">model</span> <span class="o">=</span> <span class="n">trainer</span><span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">train</span><span class="o">);</span>
<span class="c1">// compute precision on the test set</span>
<span class="n">DataFrame</span> <span class="n">result</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="na">transform</span><span class="o">(</span><span class="n">test</span><span class="o">);</span>
<span class="n">DataFrame</span> <span class="n">predictionAndLabels</span> <span class="o">=</span> <span class="n">result</span><span class="o">.</span><span class="na">select</span><span class="o">(</span><span class="s">"prediction"</span><span class="o">,</span> <span class="s">"label"</span><span class="o">);</span>
<span class="n">MulticlassClassificationEvaluator</span> <span class="n">evaluator</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">MulticlassClassificationEvaluator</span><span class="o">()</span>
<span class="o">.</span><span class="na">setMetricName</span><span class="o">(</span><span class="s">"precision"</span><span class="o">);</span>
<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">"Precision = "</span> <span class="o">+</span> <span class="n">evaluator</span><span class="o">.</span><span class="na">evaluate</span><span class="o">(</span><span class="n">predictionAndLabels</span><span class="o">));</span></code></pre></div>
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