SparkMLlib之六：Clustering

Spark支持下面的模型

1. K-means
2. Gaussian mixture
3. Power iteration clustering(PIC)
4. Latent Dirichlet allocation(LDA)
5. Bisecting k-means
6. Streaming k-means

K-means

k-means是最常用的已知聚类数的聚类算法，spark.mllib的实现还包括了k-means++的并行变体kmeans||.它有下面几个参数

• k 聚类数
• maxiterations最大递归数
• initializationMode是否随机初始聚类中心，还是通过kmeans||来选择初始聚类中心
• runs 跑几次kmeans算法（这是因为kmeans可能取到局部最优解）
• initializationSteps决定kmeans||算法步数
• epsilon决定我们认为kmeans算法收敛的距离阈值

• initialModel是一个可选的用于初始化的聚类中心集

  最优的k通常为组内平方误差和的拐角点

下面是个k=2的聚类例子

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))).cach
e()
// 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")

Gaussian mixture (GMM)

参数集

• k 聚类数
• convergenceTol是我们定义的算法收敛最大对数似然变化值
• maxiterations最大递归数
• initialModel是一个EM算法的开始点，如果省略，则随机在样本数据中选择

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(_.toDoubl
e))).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))
}

Power iteration clustering(PIC)

参数集

1. k
2. maxIterations
3. initializationMode This can be either “random”, which is the default,
   to use a random vector as vertex properties, or “
   degree” to use normalized sum similarities

import org.apache.spark.mllib.clustering.{PowerIterationClustering, Power
IterationClusteringModel}
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")

Latent Dirichlet allocation(LDA)

• k
• optimizer LDA模型的优化器,选项：EMLDAOptimizer,onlineLDAOptimizer
• docConcentration:Dirichlet参数
• topicConcentration
• maxIterations

• checkpointInterval
  所有LDA模型支持

• describeTopics

• topicsMatrix

  ExpectationMaximization

  Implemented in EMLDAOptimizer and DistributedLDAModel.
  参数

• docConcentration

• topicConcentratio
• maxIteration

DistributedLDAModel支持

• topTopicsPerDocument
• topDocumentsPerTopic
• logPrior:
• logLikelihood:

Online Variational Bayes

Implemented in OnlineLDAOptimizer and LocalLDAModel.
参数

• docConcentration
• topicConcentration
• maxIterations

另外OnlineLDAOptimizer还支持下面的参数

• 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 where
  is the current number of iterations

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

• logLikelihood(documents)
• logPerplexity(documents)

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")

Bisecting k-means

Bisecting k-means通常比一般的Kmeans要快
它是一种层次聚类
参数有：

• k,叶子聚类数(默认4)
• 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)

import org.apache.spark.mllib.clustering.BisectingKMeans
import org.apache.spark.mllib.linalg.{Vector, Vectors}
// Loads and parses data
def parse(line: String): Vector = Vectors.dense(line.split(" ").map(_.toDouble))
val data = sc.textFile("data/mllib/kmeans_data.txt").map(parse).cache()
// Clustering the data into 6 clusters by BisectingKMeans.
val bkm = new BisectingKMeans().setK(6)
val model = bkm.run(data)
// Show the compute cost and the cluster centers
println(s"Compute Cost: ${model.computeCost(data)}")
model.clusterCenters.zipWithIndex.foreach { case (center, idx) =>
println(s"Cluster Center ${idx}: ${center}")
}

Streaming k-means

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

val trainingData = ssc.textFileStream("/training/data/dir").map(Vectors.parse)
val testData = ssc.textFileStream("/testing/data/dir").map(LabeledPoint.parse)
val numDimensions = 3
val numClusters = 2
val model = new StreamingKMeans()
.setK(numClusters)
.setDecayFactor(1.0)
.setRandomCenters(numDimensions, 0.0)

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