[SPARK-9846] [DOCS] User guide for Multilayer Perceptron Classifier

Added user guide for multilayer perceptron classifier:
  - Simplified description of the multilayer perceptron classifier
  - Example code for Scala and Java

Author: Alexander Ulanov <nashb@yandex.ru>

Closes #8262 from avulanov/SPARK-9846-mlpc-docs.

docs/ml-ann.md

+---
+layout: global
+title: Multilayer perceptron classifier - ML
+displayTitle: <a href="ml-guide.html">ML</a> - Multilayer perceptron classifier
+---
+
+
+`\[
+\newcommand{\R}{\mathbb{R}}
+\newcommand{\E}{\mathbb{E}}
+\newcommand{\x}{\mathbf{x}}
+\newcommand{\y}{\mathbf{y}}
+\newcommand{\wv}{\mathbf{w}}
+\newcommand{\av}{\mathbf{\alpha}}
+\newcommand{\bv}{\mathbf{b}}
+\newcommand{\N}{\mathbb{N}}
+\newcommand{\id}{\mathbf{I}}
+\newcommand{\ind}{\mathbf{1}}
+\newcommand{\0}{\mathbf{0}}
+\newcommand{\unit}{\mathbf{e}}
+\newcommand{\one}{\mathbf{1}}
+\newcommand{\zero}{\mathbf{0}}
+\]`
+
+
+Multilayer perceptron classifier (MLPC) is a classifier based on the [feedforward artificial neural network](https://en.wikipedia.org/wiki/Feedforward_neural_network). 
+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 `$\wv$` and bias `$\bv$` and applying an activation function. 
+It can be written in matrix form for MLPC with `$K+1$` layers as follows:
+`\[
+\mathrm{y}(\x) = \mathrm{f_K}(...\mathrm{f_2}(\wv_2^T\mathrm{f_1}(\wv_1^T \x+b_1)+b_2)...+b_K)
+\]`
+Nodes in intermediate layers use sigmoid (logistic) function:
+`\[
+\mathrm{f}(z_i) = \frac{1}{1 + e^{-z_i}}
+\]`
+Nodes in the output layer use softmax function:
+`\[
+\mathrm{f}(z_i) = \frac{e^{z_i}}{\sum_{k=1}^N e^{z_k}}
+\]`
+The number of nodes `$N$` in the output layer corresponds to the number of classes. 
+
+MLPC employes backpropagation for learning the model. We use logistic loss function for optimization and L-BFGS as optimization routine.
+
+**Examples**
+
+<div class="codetabs">
+
+<div data-lang="scala" markdown="1">
+
+{% highlight scala %}
+import org.apache.spark.ml.classification.MultilayerPerceptronClassifier
+import org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator
+import org.apache.spark.mllib.util.MLUtils
+import org.apache.spark.sql.Row
+
+// Load training data
+val data = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_multiclass_classification_data.txt").toDF()
+// Split the data into train and test
+val splits = data.randomSplit(Array(0.6, 0.4), seed = 1234L)
+val train = splits(0)
+val test = splits(1)
+// specify layers for the neural network: 
+// input layer of size 4 (features), two intermediate of size 5 and 4 and output of size 3 (classes)
+val layers = Array[Int](4, 5, 4, 3)
+// create the trainer and set its parameters
+val trainer = new MultilayerPerceptronClassifier()
+  .setLayers(layers)
+  .setBlockSize(128)
+  .setSeed(1234L)
+  .setMaxIter(100)
+// train the model
+val model = trainer.fit(train)
+// compute precision on the test set
+val result = model.transform(test)
+val predictionAndLabels = result.select("prediction", "label")
+val evaluator = new MulticlassClassificationEvaluator()
+  .setMetricName("precision")
+println("Precision:" + evaluator.evaluate(predictionAndLabels))
+{% endhighlight %}
+
+</div>
+
+<div data-lang="java" markdown="1">
+
+{% highlight java %}
+import org.apache.spark.api.java.JavaRDD;
+import org.apache.spark.ml.classification.MultilayerPerceptronClassificationModel;
+import org.apache.spark.ml.classification.MultilayerPerceptronClassifier;
+import org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator;
+import org.apache.spark.mllib.regression.LabeledPoint;
+import org.apache.spark.mllib.util.MLUtils;
+
+// Load training data
+String path = "data/mllib/sample_multiclass_classification_data.txt";
+JavaRDD<LabeledPoint> data = MLUtils.loadLibSVMFile(sc, path).toJavaRDD();
+DataFrame dataFrame = sqlContext.createDataFrame(data, LabeledPoint.class);
+// Split the data into train and test
+DataFrame[] splits = dataFrame.randomSplit(new double[]{0.6, 0.4}, 1234L);
+DataFrame train = splits[0];
+DataFrame test = splits[1];
+// specify layers for the neural network:
+// input layer of size 4 (features), two intermediate of size 5 and 4 and output of size 3 (classes)
+int[] layers = new int[] {4, 5, 4, 3};
+// create the trainer and set its parameters
+MultilayerPerceptronClassifier trainer = new MultilayerPerceptronClassifier()
+  .setLayers(layers)
+  .setBlockSize(128)
+  .setSeed(1234L)
+  .setMaxIter(100);
+// train the model
+MultilayerPerceptronClassificationModel model = trainer.fit(train);
+// compute precision on the test set
+DataFrame result = model.transform(test);
+DataFrame predictionAndLabels = result.select("prediction", "label");
+MulticlassClassificationEvaluator evaluator = new MulticlassClassificationEvaluator()
+  .setMetricName("precision");
+System.out.println("Precision = " + evaluator.evaluate(predictionAndLabels));
+{% endhighlight %}
+</div>
+
+</div>

docs/ml-guide.md

@@ -179,6 +179,7 @@ There are now several algorithms in the Pipelines API which are not in the lower
 * [Decision Trees for Classification and Regression](ml-decision-tree.html)
 * [Ensembles](ml-ensembles.html)
 * [Linear methods with elastic net regularization](ml-linear-methods.html)
+* [Multilayer perceptron classifier](ml-ann.html)
 
 # Code Examples