MLlib - Clustering

Clustering is an unsupervised learning problem whereby we aim to group subsets of entities with one another based on some notion of similarity. Clustering is often used for exploratory analysis and/or as a component of a hierarchical supervised learning pipeline (in which distinct classifiers or regression models are trained for each cluster).

MLlib supports the following models:

K-means

k-means is one of the most commonly used clustering algorithms that clusters the data points into a predefined number of clusters. The MLlib implementation includes a parallelized variant of the k-means++ method called kmeans||. The implementation in MLlib has the following parameters:

Examples

The following code snippets can be executed in spark-shell.

In the following example after loading and parsing data, we use the KMeans object to cluster the data into two clusters. The number of desired clusters is passed to the algorithm. We then compute Within Set Sum of Squared Error (WSSSE). You can reduce this error measure by increasing k. In fact the optimal k is usually one where there is an “elbow” in the WSSSE graph.

import org.apache.spark.mllib.clustering.{KMeans, KMeansModel}
import org.apache.spark.mllib.linalg.Vectors

// Load and parse the data
val data = sc.textFile("data/mllib/kmeans_data.txt")
val parsedData = data.map(s => Vectors.dense(s.split(' ').map(_.toDouble))).cache()

// Cluster the data into two classes using KMeans
val numClusters = 2
val numIterations = 20
val clusters = KMeans.train(parsedData, numClusters, numIterations)

// Evaluate clustering by computing Within Set Sum of Squared Errors
val WSSSE = clusters.computeCost(parsedData)
println("Within Set Sum of Squared Errors = " + WSSSE)

// Save and load model
clusters.save(sc, "myModelPath")
val sameModel = KMeansModel.load(sc, "myModelPath")

All of MLlib’s methods use Java-friendly types, so you can import and call them there the same way you do in Scala. The only caveat is that the methods take Scala RDD objects, while the Spark Java API uses a separate JavaRDD class. You can convert a Java RDD to a Scala one by calling .rdd() on your JavaRDD object. A self-contained application example that is equivalent to the provided example in Scala is given below:

import org.apache.spark.api.java.*;
import org.apache.spark.api.java.function.Function;
import org.apache.spark.mllib.clustering.KMeans;
import org.apache.spark.mllib.clustering.KMeansModel;
import org.apache.spark.mllib.linalg.Vector;
import org.apache.spark.mllib.linalg.Vectors;
import org.apache.spark.SparkConf;

public class KMeansExample {
  public static void main(String[] args) {
    SparkConf conf = new SparkConf().setAppName("K-means Example");
    JavaSparkContext sc = new JavaSparkContext(conf);

    // Load and parse data
    String path = "data/mllib/kmeans_data.txt";
    JavaRDD<String> data = sc.textFile(path);
    JavaRDD<Vector> parsedData = data.map(
      new Function<String, Vector>() {
        public Vector call(String s) {
          String[] sarray = s.split(" ");
          double[] values = new double[sarray.length];
          for (int i = 0; i < sarray.length; i++)
            values[i] = Double.parseDouble(sarray[i]);
          return Vectors.dense(values);
        }
      }
    );
    parsedData.cache();

    // Cluster the data into two classes using KMeans
    int numClusters = 2;
    int numIterations = 20;
    KMeansModel clusters = KMeans.train(parsedData.rdd(), numClusters, numIterations);

    // Evaluate clustering by computing Within Set Sum of Squared Errors
    double WSSSE = clusters.computeCost(parsedData.rdd());
    System.out.println("Within Set Sum of Squared Errors = " + WSSSE);

    // Save and load model
    clusters.save(sc.sc(), "myModelPath");
    KMeansModel sameModel = KMeansModel.load(sc.sc(), "myModelPath");
  }
}

The following examples can be tested in the PySpark shell.

In the following example after loading and parsing data, we use the KMeans object to cluster the data into two clusters. The number of desired clusters is passed to the algorithm. We then compute Within Set Sum of Squared Error (WSSSE). You can reduce this error measure by increasing k. In fact the optimal k is usually one where there is an “elbow” in the WSSSE graph.

from pyspark.mllib.clustering import KMeans, KMeansModel
from numpy import array
from math import sqrt

# Load and parse the data
data = sc.textFile("data/mllib/kmeans_data.txt")
parsedData = data.map(lambda line: array([float(x) for x in line.split(' ')]))

# Build the model (cluster the data)
clusters = KMeans.train(parsedData, 2, maxIterations=10,
        runs=10, initializationMode="random")

# Evaluate clustering by computing Within Set Sum of Squared Errors
def error(point):
    center = clusters.centers[clusters.predict(point)]
    return sqrt(sum([x**2 for x in (point - center)]))

WSSSE = parsedData.map(lambda point: error(point)).reduce(lambda x, y: x + y)
print("Within Set Sum of Squared Error = " + str(WSSSE))

# Save and load model
clusters.save(sc, "myModelPath")
sameModel = KMeansModel.load(sc, "myModelPath")

Gaussian mixture

A Gaussian Mixture Model represents a composite distribution whereby points are drawn from one of k Gaussian sub-distributions, each with its own probability. The MLlib implementation uses the expectation-maximization algorithm to induce the maximum-likelihood model given a set of samples. The implementation has the following parameters:

Examples

In the following example after loading and parsing data, we use a GaussianMixture object to cluster the data into two clusters. The number of desired clusters is passed to the algorithm. We then output the parameters of the mixture model.

import org.apache.spark.mllib.clustering.GaussianMixture
import org.apache.spark.mllib.clustering.GaussianMixtureModel
import org.apache.spark.mllib.linalg.Vectors

// Load and parse the data
val data = sc.textFile("data/mllib/gmm_data.txt")
val parsedData = data.map(s => Vectors.dense(s.trim.split(' ').map(_.toDouble))).cache()

// Cluster the data into two classes using GaussianMixture
val gmm = new GaussianMixture().setK(2).run(parsedData)

// Save and load model
gmm.save(sc, "myGMMModel")
val sameModel = GaussianMixtureModel.load(sc, "myGMMModel")

// output parameters of max-likelihood model
for (i <- 0 until gmm.k) {
  println("weight=%f\nmu=%s\nsigma=\n%s\n" format
    (gmm.weights(i), gmm.gaussians(i).mu, gmm.gaussians(i).sigma))
}

All of MLlib’s methods use Java-friendly types, so you can import and call them there the same way you do in Scala. The only caveat is that the methods take Scala RDD objects, while the Spark Java API uses a separate JavaRDD class. You can convert a Java RDD to a Scala one by calling .rdd() on your JavaRDD object. A self-contained application example that is equivalent to the provided example in Scala is given below:

import org.apache.spark.api.java.*;
import org.apache.spark.api.java.function.Function;
import org.apache.spark.mllib.clustering.GaussianMixture;
import org.apache.spark.mllib.clustering.GaussianMixtureModel;
import org.apache.spark.mllib.linalg.Vector;
import org.apache.spark.mllib.linalg.Vectors;
import org.apache.spark.SparkConf;

public class GaussianMixtureExample {
  public static void main(String[] args) {
    SparkConf conf = new SparkConf().setAppName("GaussianMixture Example");
    JavaSparkContext sc = new JavaSparkContext(conf);

    // Load and parse data
    String path = "data/mllib/gmm_data.txt";
    JavaRDD<String> data = sc.textFile(path);
    JavaRDD<Vector> parsedData = data.map(
      new Function<String, Vector>() {
        public Vector call(String s) {
          String[] sarray = s.trim().split(" ");
          double[] values = new double[sarray.length];
          for (int i = 0; i < sarray.length; i++)
            values[i] = Double.parseDouble(sarray[i]);
          return Vectors.dense(values);
        }
      }
    );
    parsedData.cache();

    // Cluster the data into two classes using GaussianMixture
    GaussianMixtureModel gmm = new GaussianMixture().setK(2).run(parsedData.rdd());

    // Save and load GaussianMixtureModel
    gmm.save(sc.sc(), "myGMMModel");
    GaussianMixtureModel sameModel = GaussianMixtureModel.load(sc.sc(), "myGMMModel");
    // Output the parameters of the mixture model
    for(int j=0; j<gmm.k(); j++) {
        System.out.printf("weight=%f\nmu=%s\nsigma=\n%s\n",
            gmm.weights()[j], gmm.gaussians()[j].mu(), gmm.gaussians()[j].sigma());
    }
  }
}

In the following example after loading and parsing data, we use a GaussianMixture object to cluster the data into two clusters. The number of desired clusters is passed to the algorithm. We then output the parameters of the mixture model.

from pyspark.mllib.clustering import GaussianMixture
from numpy import array

# Load and parse the data
data = sc.textFile("data/mllib/gmm_data.txt")
parsedData = data.map(lambda line: array([float(x) for x in line.strip().split(' ')]))

# Build the model (cluster the data)
gmm = GaussianMixture.train(parsedData, 2)

# output parameters of model
for i in range(2):
    print ("weight = ", gmm.weights[i], "mu = ", gmm.gaussians[i].mu,
        "sigma = ", gmm.gaussians[i].sigma.toArray())

Power iteration clustering (PIC)

Power iteration clustering (PIC) is a scalable and efficient algorithm for clustering vertices of a graph given pairwise similarties as edge properties, described in Lin and Cohen, Power Iteration Clustering. It computes a pseudo-eigenvector of the normalized affinity matrix of the graph via power iteration and uses it to cluster vertices. MLlib includes an implementation of PIC using GraphX as its backend. It takes an RDD of (srcId, dstId, similarity) tuples and outputs a model with the clustering assignments. The similarities must be nonnegative. PIC assumes that the similarity measure is symmetric. A pair (srcId, dstId) regardless of the ordering should appear at most once in the input data. If a pair is missing from input, their similarity is treated as zero. MLlib’s PIC implementation takes the following (hyper-)parameters:

Examples

In the following, we show code snippets to demonstrate how to use PIC in MLlib.

PowerIterationClustering implements the PIC algorithm. It takes an RDD of (srcId: Long, dstId: Long, similarity: Double) tuples representing the affinity matrix. Calling PowerIterationClustering.run returns a PowerIterationClusteringModel, which contains the computed clustering assignments.

import org.apache.spark.mllib.clustering.{PowerIterationClustering, PowerIterationClusteringModel}
import org.apache.spark.mllib.linalg.Vectors

// Load and parse the data
val data = sc.textFile("data/mllib/pic_data.txt")
val similarities = data.map { line =>
  val parts = line.split(' ')
  (parts(0).toLong, parts(1).toLong, parts(2).toDouble)
}

// Cluster the data into two classes using PowerIterationClustering
val pic = new PowerIterationClustering()
  .setK(2)
  .setMaxIterations(10)
val model = pic.run(similarities)

model.assignments.foreach { a =>
  println(s"${a.id} -> ${a.cluster}")
}

// Save and load model
model.save(sc, "myModelPath")
val sameModel = PowerIterationClusteringModel.load(sc, "myModelPath")

A full example that produces the experiment described in the PIC paper can be found under examples/.

PowerIterationClustering implements the PIC algorithm. It takes an JavaRDD of (srcId: Long, dstId: Long, similarity: Double) tuples representing the affinity matrix. Calling PowerIterationClustering.run returns a PowerIterationClusteringModel which contains the computed clustering assignments.

import scala.Tuple2;
import scala.Tuple3;

import org.apache.spark.api.java.JavaRDD;
import org.apache.spark.api.java.function.Function;
import org.apache.spark.mllib.clustering.PowerIterationClustering;
import org.apache.spark.mllib.clustering.PowerIterationClusteringModel;

// Load and parse the data
JavaRDD<String> data = sc.textFile("data/mllib/pic_data.txt");
JavaRDD<Tuple3<Long, Long, Double>> similarities = data.map(
  new Function<String, Tuple3<Long, Long, Double>>() {
    public Tuple3<Long, Long, Double> call(String line) {
      String[] parts = line.split(" ");
      return new Tuple3<>(new Long(parts[0]), new Long(parts[1]), new Double(parts[2]));
    }
  }
);

// Cluster the data into two classes using PowerIterationClustering
PowerIterationClustering pic = new PowerIterationClustering()
  .setK(2)
  .setMaxIterations(10);
PowerIterationClusteringModel model = pic.run(similarities);

for (PowerIterationClustering.Assignment a: model.assignments().toJavaRDD().collect()) {
  System.out.println(a.id() + " -> " + a.cluster());
}

// Save and load model
model.save(sc.sc(), "myModelPath");
PowerIterationClusteringModel sameModel = PowerIterationClusteringModel.load(sc.sc(), "myModelPath");

PowerIterationClustering implements the PIC algorithm. It takes an RDD of (srcId: Long, dstId: Long, similarity: Double) tuples representing the affinity matrix. Calling PowerIterationClustering.run returns a PowerIterationClusteringModel, which contains the computed clustering assignments.

from __future__ import print_function
from pyspark.mllib.clustering import PowerIterationClustering, PowerIterationClusteringModel

# Load and parse the data
data = sc.textFile("data/mllib/pic_data.txt")
similarities = data.map(lambda line: tuple([float(x) for x in line.split(' ')]))

# Cluster the data into two classes using PowerIterationClustering
model = PowerIterationClustering.train(similarities, 2, 10)

model.assignments().foreach(lambda x: print(str(x.id) + " -> " + str(x.cluster)))

# Save and load model
model.save(sc, "myModelPath")
sameModel = PowerIterationClusteringModel.load(sc, "myModelPath")

Latent Dirichlet allocation (LDA)

Latent Dirichlet allocation (LDA) is a topic model which infers topics from a collection of text documents. LDA can be thought of as a clustering algorithm as follows:

LDA supports different inference algorithms via setOptimizer function. EMLDAOptimizer learns clustering using expectation-maximization on the likelihood function and yields comprehensive results, while OnlineLDAOptimizer uses iterative mini-batch sampling for online variational inference and is generally memory friendly.

LDA takes in a collection of documents as vectors of word counts and the following parameters (set using the builder pattern):

All of MLlib’s LDA models support:

Note: LDA is still an experimental feature under active development. As a result, certain features are only available in one of the two optimizers / models generated by the optimizer. Currently, a distributed model can be converted into a local model, but not vice-versa.

The following discussion will describe each optimizer/model pair separately.

Expectation Maximization

Implemented in EMLDAOptimizer and DistributedLDAModel.

For the parameters provided to LDA:

EMLDAOptimizer produces a DistributedLDAModel, which stores not only the inferred topics but also the full training corpus and topic distributions for each document in the training corpus. A DistributedLDAModel supports:

Online Variational Bayes

Implemented in OnlineLDAOptimizer and LocalLDAModel.

For the parameters provided to LDA:

In addition, OnlineLDAOptimizer accepts the following parameters:

OnlineLDAOptimizer produces a LocalLDAModel, which only stores the inferred topics. A LocalLDAModel supports:

Examples

In the following example, we load word count vectors representing a corpus of documents. We then use LDA to infer three topics from the documents. The number of desired clusters is passed to the algorithm. We then output the topics, represented as probability distributions over words.

import org.apache.spark.mllib.clustering.{LDA, DistributedLDAModel}
import org.apache.spark.mllib.linalg.Vectors

// Load and parse the data
val data = sc.textFile("data/mllib/sample_lda_data.txt")
val parsedData = data.map(s => Vectors.dense(s.trim.split(' ').map(_.toDouble)))
// Index documents with unique IDs
val corpus = parsedData.zipWithIndex.map(_.swap).cache()

// Cluster the documents into three topics using LDA
val ldaModel = new LDA().setK(3).run(corpus)

// Output topics. Each is a distribution over words (matching word count vectors)
println("Learned topics (as distributions over vocab of " + ldaModel.vocabSize + " words):")
val topics = ldaModel.topicsMatrix
for (topic <- Range(0, 3)) {
  print("Topic " + topic + ":")
  for (word <- Range(0, ldaModel.vocabSize)) { print(" " + topics(word, topic)); }
  println()
}

// Save and load model.
ldaModel.save(sc, "myLDAModel")
val sameModel = DistributedLDAModel.load(sc, "myLDAModel")
import scala.Tuple2;

import org.apache.spark.api.java.*;
import org.apache.spark.api.java.function.Function;
import org.apache.spark.mllib.clustering.DistributedLDAModel;
import org.apache.spark.mllib.clustering.LDA;
import org.apache.spark.mllib.linalg.Matrix;
import org.apache.spark.mllib.linalg.Vector;
import org.apache.spark.mllib.linalg.Vectors;
import org.apache.spark.SparkConf;

public class JavaLDAExample {
  public static void main(String[] args) {
    SparkConf conf = new SparkConf().setAppName("LDA Example");
    JavaSparkContext sc = new JavaSparkContext(conf);

    // Load and parse the data
    String path = "data/mllib/sample_lda_data.txt";
    JavaRDD<String> data = sc.textFile(path);
    JavaRDD<Vector> parsedData = data.map(
        new Function<String, Vector>() {
          public Vector call(String s) {
            String[] sarray = s.trim().split(" ");
            double[] values = new double[sarray.length];
            for (int i = 0; i < sarray.length; i++)
              values[i] = Double.parseDouble(sarray[i]);
            return Vectors.dense(values);
          }
        }
    );
    // Index documents with unique IDs
    JavaPairRDD<Long, Vector> corpus = JavaPairRDD.fromJavaRDD(parsedData.zipWithIndex().map(
        new Function<Tuple2<Vector, Long>, Tuple2<Long, Vector>>() {
          public Tuple2<Long, Vector> call(Tuple2<Vector, Long> doc_id) {
            return doc_id.swap();
          }
        }
    ));
    corpus.cache();

    // Cluster the documents into three topics using LDA
    DistributedLDAModel ldaModel = new LDA().setK(3).run(corpus);

    // Output topics. Each is a distribution over words (matching word count vectors)
    System.out.println("Learned topics (as distributions over vocab of " + ldaModel.vocabSize()
        + " words):");
    Matrix topics = ldaModel.topicsMatrix();
    for (int topic = 0; topic < 3; topic++) {
      System.out.print("Topic " + topic + ":");
      for (int word = 0; word < ldaModel.vocabSize(); word++) {
        System.out.print(" " + topics.apply(word, topic));
      }
      System.out.println();
    }

    ldaModel.save(sc.sc(), "myLDAModel");
    DistributedLDAModel sameModel = DistributedLDAModel.load(sc.sc(), "myLDAModel");
  }
}
from pyspark.mllib.clustering import LDA, LDAModel
from pyspark.mllib.linalg import Vectors

# Load and parse the data
data = sc.textFile("data/mllib/sample_lda_data.txt")
parsedData = data.map(lambda line: Vectors.dense([float(x) for x in line.strip().split(' ')]))
# Index documents with unique IDs
corpus = parsedData.zipWithIndex().map(lambda x: [x[1], x[0]]).cache()

# Cluster the documents into three topics using LDA
ldaModel = LDA.train(corpus, k=3)

# Output topics. Each is a distribution over words (matching word count vectors)
print("Learned topics (as distributions over vocab of " + str(ldaModel.vocabSize()) + " words):")
topics = ldaModel.topicsMatrix()
for topic in range(3):
    print("Topic " + str(topic) + ":")
    for word in range(0, ldaModel.vocabSize()):
        print(" " + str(topics[word][topic]))
		
# Save and load model
model.save(sc, "myModelPath")
sameModel = LDAModel.load(sc, "myModelPath")

Streaming k-means

When data arrive in a stream, we may want to estimate clusters dynamically, updating them as new data arrive. MLlib provides support for streaming k-means clustering, with parameters to control the decay (or “forgetfulness”) of the estimates. The algorithm uses a generalization of the mini-batch k-means update rule. For each batch of data, we assign all points to their nearest cluster, compute new cluster centers, then update each cluster using:

\begin{equation} c_{t+1} = \frac{c_tn_t\alpha + x_tm_t}{n_t\alpha+m_t} \end{equation} \begin{equation} n_{t+1} = n_t + m_t \end{equation}

Where $c_t$ is the previous center for the cluster, $n_t$ is the number of points assigned to the cluster thus far, $x_t$ is the new cluster center from the current batch, and $m_t$ is the number of points added to the cluster in the current batch. The decay factor $\alpha$ can be used to ignore the past: with $\alpha$=1 all data will be used from the beginning; with $\alpha$=0 only the most recent data will be used. This is analogous to an exponentially-weighted moving average.

The decay can be specified using a halfLife parameter, which determines the correct decay factor a such that, for data acquired at time t, its contribution by time t + halfLife will have dropped to 0.5. The unit of time can be specified either as batches or points and the update rule will be adjusted accordingly.

Examples

This example shows how to estimate clusters on streaming data.

First we import the neccessary classes.

import org.apache.spark.mllib.linalg.Vectors
import org.apache.spark.mllib.regression.LabeledPoint
import org.apache.spark.mllib.clustering.StreamingKMeans

Then we make an input stream of vectors for training, as well as a stream of labeled data points for testing. We assume a StreamingContext ssc has been created, see Spark Streaming Programming Guide for more info.

val trainingData = ssc.textFileStream("/training/data/dir").map(Vectors.parse)
val testData = ssc.textFileStream("/testing/data/dir").map(LabeledPoint.parse)

We create a model with random clusters and specify the number of clusters to find

val numDimensions = 3
val numClusters = 2
val model = new StreamingKMeans()
  .setK(numClusters)
  .setDecayFactor(1.0)
  .setRandomCenters(numDimensions, 0.0)

Now register the streams for training and testing and start the job, printing the predicted cluster assignments on new data points as they arrive.

model.trainOn(trainingData)
model.predictOnValues(testData.map(lp => (lp.label, lp.features))).print()

ssc.start()
ssc.awaitTermination()

First we import the neccessary classes.

from pyspark.mllib.linalg import Vectors
from pyspark.mllib.regression import LabeledPoint
from pyspark.mllib.clustering import StreamingKMeans

Then we make an input stream of vectors for training, as well as a stream of labeled data points for testing. We assume a StreamingContext ssc has been created, see Spark Streaming Programming Guide for more info.

def parse(lp):
    label = float(lp[lp.find('(') + 1: lp.find(',')])
    vec = Vectors.dense(lp[lp.find('[') + 1: lp.find(']')].split(','))
    return LabeledPoint(label, vec)

trainingData = ssc.textFileStream("/training/data/dir").map(Vectors.parse)
testData = ssc.textFileStream("/testing/data/dir").map(parse)

We create a model with random clusters and specify the number of clusters to find

model = StreamingKMeans(k=2, decayFactor=1.0).setRandomCenters(3, 1.0, 0)

Now register the streams for training and testing and start the job, printing the predicted cluster assignments on new data points as they arrive.

model.trainOn(trainingData)
print(model.predictOnValues(testData.map(lambda lp: (lp.label, lp.features))))

ssc.start()
ssc.awaitTermination()

As you add new text files with data the cluster centers will update. Each training point should be formatted as [x1, x2, x3], and each test data point should be formatted as (y, [x1, x2, x3]), where y is some useful label or identifier (e.g. a true category assignment). Anytime a text file is placed in /training/data/dir the model will update. Anytime a text file is placed in /testing/data/dir you will see predictions. With new data, the cluster centers will change!