# Clustering - RDD-based API

2020-01-21

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).

The spark.mllib package 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 spark.mllib implementation includes a parallelized variant of the k-means++ method called kmeans||. The implementation in spark.mllib has the following parameters:

• k is the number of desired clusters. Note that it is possible for fewer than k clusters to be returned, for example, if there are fewer than k distinct points to cluster.
• maxIterations is the maximum number of iterations to run.
• initializationMode specifies either random initialization or initialization via k-means||.
• runs This param has no effect since Spark 2.0.0.
• initializationSteps determines the number of steps in the k-means|| algorithm.
• epsilon determines the distance threshold within which we consider k-means to have converged.
• initialModel is an optional set of cluster centers used for initialization. If this parameter is supplied, only one run is performed.

Examples

The following code snippets can be executed in spark-shell. In the following example after loading and parsing data, we use the [KMeans](api/scala/index.html#org.apache.spark.mllib.clustering.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. Refer to the [KMeans Scala docs](api/scala/index.html#org.apache.spark.mllib.clustering.KMeans) and [KMeansModel Scala docs](api/scala/index.html#org.apache.spark.mllib.clustering.KMeansModel) for details on the API. {% include_example scala/org/apache/spark/examples/mllib/KMeansExample.scala %}
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: Refer to the [KMeans Java docs](api/java/org/apache/spark/mllib/clustering/KMeans.html) and [KMeansModel Java docs](api/java/org/apache/spark/mllib/clustering/KMeansModel.html) for details on the API. {% include_example java/org/apache/spark/examples/mllib/JavaKMeansExample.java %}
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. Refer to the [KMeans Python docs](api/python/pyspark.mllib.html#pyspark.mllib.clustering.KMeans) and [KMeansModel Python docs](api/python/pyspark.mllib.html#pyspark.mllib.clustering.KMeansModel) for more details on the API. {% include_example python/mllib/k_means_example.py %}

## 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 spark.mllib implementation uses the expectation-maximization algorithm to induce the maximum-likelihood model given a set of samples. The implementation has the following parameters:

• k is the number of desired clusters.
• convergenceTol is the maximum change in log-likelihood at which we consider convergence achieved.
• maxIterations is the maximum number of iterations to perform without reaching convergence.
• initialModel is an optional starting point from which to start the EM algorithm. If this parameter is omitted, a random starting point will be constructed from the data.

Examples

In the following example after loading and parsing data, we use a [GaussianMixture](api/scala/index.html#org.apache.spark.mllib.clustering.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. Refer to the [GaussianMixture Scala docs](api/scala/index.html#org.apache.spark.mllib.clustering.GaussianMixture) and [GaussianMixtureModel Scala docs](api/scala/index.html#org.apache.spark.mllib.clustering.GaussianMixtureModel) for details on the API. {% include_example scala/org/apache/spark/examples/mllib/GaussianMixtureExample.scala %}
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: Refer to the [GaussianMixture Java docs](api/java/org/apache/spark/mllib/clustering/GaussianMixture.html) and [GaussianMixtureModel Java docs](api/java/org/apache/spark/mllib/clustering/GaussianMixtureModel.html) for details on the API. {% include_example java/org/apache/spark/examples/mllib/JavaGaussianMixtureExample.java %}
In the following example after loading and parsing data, we use a [GaussianMixture](api/python/pyspark.mllib.html#pyspark.mllib.clustering.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. Refer to the [GaussianMixture Python docs](api/python/pyspark.mllib.html#pyspark.mllib.clustering.GaussianMixture) and [GaussianMixtureModel Python docs](api/python/pyspark.mllib.html#pyspark.mllib.clustering.GaussianMixtureModel) for more details on the API. {% include_example python/mllib/gaussian_mixture_example.py %}

## Power iteration clustering (PIC)

Power iteration clustering (PIC) is a scalable and efficient algorithm for clustering vertices of a graph given pairwise similarities 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. spark.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. spark.mllib's PIC implementation takes the following (hyper-)parameters:

• k: number of clusters
• maxIterations: maximum number of power iterations
• initializationMode: initialization model. This can be either "random", which is the default, to use a random vector as vertex properties, or "degree" to use normalized sum similarities.

Examples

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

[PowerIterationClustering](api/scala/index.html#org.apache.spark.mllib.clustering.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](api/scala/index.html#org.apache.spark.mllib.clustering.PowerIterationClusteringModel), which contains the computed clustering assignments. Refer to the [PowerIterationClustering Scala docs](api/scala/index.html#org.apache.spark.mllib.clustering.PowerIterationClustering) and [PowerIterationClusteringModel Scala docs](api/scala/index.html#org.apache.spark.mllib.clustering.PowerIterationClusteringModel) for details on the API. {% include_example scala/org/apache/spark/examples/mllib/PowerIterationClusteringExample.scala %}
[PowerIterationClustering](api/java/org/apache/spark/mllib/clustering/PowerIterationClustering.html) 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](api/java/org/apache/spark/mllib/clustering/PowerIterationClusteringModel.html) which contains the computed clustering assignments. Refer to the [PowerIterationClustering Java docs](api/java/org/apache/spark/mllib/clustering/PowerIterationClustering.html) and [PowerIterationClusteringModel Java docs](api/java/org/apache/spark/mllib/clustering/PowerIterationClusteringModel.html) for details on the API. {% include_example java/org/apache/spark/examples/mllib/JavaPowerIterationClusteringExample.java %}
[PowerIterationClustering](api/python/pyspark.mllib.html#pyspark.mllib.clustering.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](api/python/pyspark.mllib.html#pyspark.mllib.clustering.PowerIterationClustering), which contains the computed clustering assignments. Refer to the [PowerIterationClustering Python docs](api/python/pyspark.mllib.html#pyspark.mllib.clustering.PowerIterationClustering) and [PowerIterationClusteringModel Python docs](api/python/pyspark.mllib.html#pyspark.mllib.clustering.PowerIterationClusteringModel) for more details on the API. {% include_example python/mllib/power_iteration_clustering_example.py %}

## 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:

• Topics correspond to cluster centers, and documents correspond to examples (rows) in a dataset.
• Topics and documents both exist in a feature space, where feature vectors are vectors of word counts (bag of words).
• Rather than estimating a clustering using a traditional distance, LDA uses a function based on a statistical model of how text documents are generated.

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):

• k: Number of topics (i.e., cluster centers)
• optimizer: Optimizer to use for learning the LDA model, either EMLDAOptimizer or OnlineLDAOptimizer
• docConcentration: Dirichlet parameter for prior over documents' distributions over topics. Larger values encourage smoother inferred distributions.
• topicConcentration: Dirichlet parameter for prior over topics' distributions over terms (words). Larger values encourage smoother inferred distributions.
• maxIterations: Limit on the number of iterations.
• checkpointInterval: If using checkpointing (set in the Spark configuration), this parameter specifies the frequency with which checkpoints will be created. If maxIterations is large, using checkpointing can help reduce shuffle file sizes on disk and help with failure recovery.

All of spark.mllib's LDA models support:

• describeTopics: Returns topics as arrays of most important terms and term weights
• topicsMatrix: Returns a vocabSize by k matrix where each column is a topic

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:

• docConcentration: Only symmetric priors are supported, so all values in the provided k-dimensional vector must be identical. All values must also be $> 1.0$. Providing Vector(-1) results in default behavior (uniform k dimensional vector with value $(50 / k) + 1$
• topicConcentration: Only symmetric priors supported. Values must be $> 1.0$. Providing -1 results in defaulting to a value of $0.1 + 1$.
• maxIterations: The maximum number of EM iterations.

Note: It is important to do enough iterations. In early iterations, EM often has useless topics, but those topics improve dramatically after more iterations. Using at least 20 and possibly 50-100 iterations is often reasonable, depending on your dataset.

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:

• topTopicsPerDocument: The top topics and their weights for each document in the training corpus
• topDocumentsPerTopic: The top documents for each topic and the corresponding weight of the topic in the documents.
• logPrior: log probability of the estimated topics and document-topic distributions given the hyperparameters docConcentration and topicConcentration
• logLikelihood: log likelihood of the training corpus, given the inferred topics and document-topic distributions

Online Variational Bayes

Implemented in OnlineLDAOptimizer and LocalLDAModel.

For the parameters provided to LDA:

• docConcentration: Asymmetric priors can be used by passing in a vector with values equal to the Dirichlet parameter in each of the k dimensions. Values should be $>= 0$. Providing Vector(-1) results in default behavior (uniform k dimensional vector with value $(1.0 / k)$)
• topicConcentration: Only symmetric priors supported. Values must be $>= 0$. Providing -1 results in defaulting to a value of $(1.0 / k)$.
• maxIterations: Maximum number of minibatches to submit.

In addition, OnlineLDAOptimizer accepts the following parameters:

• miniBatchFraction: Fraction of corpus sampled and used at each iteration
• optimizeDocConcentration: If set to true, performs maximum-likelihood estimation of the hyperparameter docConcentration (aka alpha) after each minibatch and sets the optimized docConcentration in the returned LocalLDAModel
• tau0 and kappa: Used for learning-rate decay, which is computed by $(\tau_0 + iter)^{-\kappa}$ where $iter$ is the current number of iterations.

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

• logLikelihood(documents): Calculates a lower bound on the provided documents given the inferred topics.
• logPerplexity(documents): Calculates an upper bound on the perplexity of the provided documents given the inferred topics.

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.

Refer to the [LDA Scala docs](api/scala/index.html#org.apache.spark.mllib.clustering.LDA) and [DistributedLDAModel Scala docs](api/scala/index.html#org.apache.spark.mllib.clustering.DistributedLDAModel) for details on the API. {% include_example scala/org/apache/spark/examples/mllib/LatentDirichletAllocationExample.scala %}
Refer to the [LDA Java docs](api/java/org/apache/spark/mllib/clustering/LDA.html) and [DistributedLDAModel Java docs](api/java/org/apache/spark/mllib/clustering/DistributedLDAModel.html) for details on the API. {% include_example java/org/apache/spark/examples/mllib/JavaLatentDirichletAllocationExample.java %}
Refer to the [LDA Python docs](api/python/pyspark.mllib.html#pyspark.mllib.clustering.LDA) and [LDAModel Python docs](api/python/pyspark.mllib.html#pyspark.mllib.clustering.LDAModel) for more details on the API. {% include_example python/mllib/latent_dirichlet_allocation_example.py %}

## Bisecting k-means

Bisecting K-means can often be much faster than regular K-means, but it will generally produce a different clustering.

Bisecting k-means is a kind of hierarchical clustering. Hierarchical clustering is one of the most commonly used method of cluster analysis which seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two types:

• Agglomerative: This is a "bottom up" approach: each observation starts in its own cluster, and pairs of clusters are merged as one moves up the hierarchy.
• Divisive: This is a "top down" approach: all observations start in one cluster, and splits are performed recursively as one moves down the hierarchy.

Bisecting k-means algorithm is a kind of divisive algorithms. The implementation in MLlib has the following parameters:

• k: the desired number of leaf clusters (default: 4). The actual number could be smaller if there are no divisible leaf clusters.
• maxIterations: the max number of k-means iterations to split clusters (default: 20)
• minDivisibleClusterSize: the minimum number of points (if >= 1.0) or the minimum proportion of points (if < 1.0) of a divisible cluster (default: 1)
• seed: a random seed (default: hash value of the class name)

Examples

Refer to the [BisectingKMeans Scala docs](api/scala/index.html#org.apache.spark.mllib.clustering.BisectingKMeans) and [BisectingKMeansModel Scala docs](api/scala/index.html#org.apache.spark.mllib.clustering.BisectingKMeansModel) for details on the API. {% include_example scala/org/apache/spark/examples/mllib/BisectingKMeansExample.scala %}
Refer to the [BisectingKMeans Java docs](api/java/org/apache/spark/mllib/clustering/BisectingKMeans.html) and [BisectingKMeansModel Java docs](api/java/org/apache/spark/mllib/clustering/BisectingKMeansModel.html) for details on the API. {% include_example java/org/apache/spark/examples/mllib/JavaBisectingKMeansExample.java %}
Refer to the [BisectingKMeans Python docs](api/python/pyspark.mllib.html#pyspark.mllib.clustering.BisectingKMeans) and [BisectingKMeansModel Python docs](api/python/pyspark.mllib.html#pyspark.mllib.clustering.BisectingKMeansModel) for more details on the API. {% include_example python/mllib/bisecting_k_means_example.py %}

## Streaming k-means

When data arrive in a stream, we may want to estimate clusters dynamically, updating them as new data arrive. spark.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:

$$c_{t+1} = \frac{c_tn_t\alpha + x_tm_t}{n_t\alpha+m_t}$$ $$n_{t+1} = n_t + m_t$$

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.

Refer to the [StreamingKMeans Scala docs](api/scala/index.html#org.apache.spark.mllib.clustering.StreamingKMeans) for details on the API. And Refer to [Spark Streaming Programming Guide](streaming-programming-guide.html#initializing) for details on StreamingContext. {% include_example scala/org/apache/spark/examples/mllib/StreamingKMeansExample.scala %}
Refer to the [StreamingKMeans Python docs](api/python/pyspark.mllib.html#pyspark.mllib.clustering.StreamingKMeans) for more details on the API. And Refer to [Spark Streaming Programming Guide](streaming-programming-guide.html#initializing) for details on StreamingContext. {% include_example python/mllib/streaming_k_means_example.py %}

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!