ML - 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. 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

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))

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));