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mllib/src/main/scala/org/apache/spark/mllib/clustering/OnlineLDA.scala
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| /* | ||
| * Licensed to the Apache Software Foundation (ASF) under one or more | ||
| * contributor license agreements. See the NOTICE file distributed with | ||
| * this work for additional information regarding copyright ownership. | ||
| * The ASF licenses this file to You under the Apache License, Version 2.0 | ||
| * (the "License"); you may not use this file except in compliance with | ||
| * the License. You may obtain a copy of the License at | ||
| * | ||
| * http://www.apache.org/licenses/LICENSE-2.0 | ||
| * | ||
| * Unless required by applicable law or agreed to in writing, software | ||
| * distributed under the License is distributed on an "AS IS" BASIS, | ||
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | ||
| * See the License for the specific language governing permissions and | ||
| * limitations under the License. | ||
| */ | ||
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| package org.apache.spark.mllib.clustering | ||
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| import breeze.linalg.{DenseMatrix => BDM, DenseVector => BDV, kron, sum} | ||
| import breeze.numerics._ | ||
| import breeze.stats.distributions.Gamma | ||
| import org.apache.spark.annotation.Experimental | ||
| import org.apache.spark.mllib.linalg._ | ||
| import org.apache.spark.rdd.RDD | ||
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| /** | ||
| * :: Experimental :: | ||
| * Latent Dirichlet Allocation (LDA), a topic model designed for text documents. | ||
| * | ||
| * Online LDA breaks the massive corps into mini batches and scans the corpus (doc sets) only | ||
| * once. Thus it needs not locally store or collect the documents and can be handily applied to | ||
| * streaming document collections. | ||
| * | ||
| * References: | ||
| * Hoffman, Blei and Bach, "Online Learning for Latent Dirichlet Allocation." NIPS, 2010. | ||
| */ | ||
| @Experimental | ||
| object OnlineLDA{ | ||
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| /** | ||
| * Learns an LDA model from the given data set, using online variational Bayes (VB) algorithm. | ||
| * This is just designed as a handy API. For massive corpus, it's recommended to use | ||
| * OnlineLDAOptimizer directly and call submitMiniBatch in your application, which can help | ||
| * downgrade time and space complexity by not loading the entire corpus. | ||
| * | ||
| * @param documents RDD of documents, which are term (word) count vectors paired with IDs. | ||
| * The term count vectors are "bags of words" with a fixed-size vocabulary | ||
| * (where the vocabulary size is the length of the vector). | ||
| * Document IDs must be unique and >= 0. | ||
| * @param k Number of topics to infer. | ||
| * @param batchNumber Number of batches to split input corpus. For each batch, recommendation | ||
| * size is [4, 16384]. -1 for automatic batchNumber. | ||
| * @return Inferred LDA model | ||
| */ | ||
| def run(documents: RDD[(Long, Vector)], k: Int, batchNumber: Int = -1): LDAModel = { | ||
| require(batchNumber > 0 || batchNumber == -1, | ||
| s"batchNumber must be greater or -1, but was set to $batchNumber") | ||
| require(k > 0, s"LDA k (number of clusters) must be > 0, but was set to $k") | ||
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| val vocabSize = documents.first._2.size | ||
| val D = documents.count().toInt // total documents count | ||
| val batchSize = | ||
| if (batchNumber == -1) { // auto mode | ||
| if (D / 100 > 16384) 16384 | ||
| else if (D / 100 < 4) 4 | ||
| else D / 100 | ||
| } | ||
| else { | ||
| D / batchNumber | ||
| } | ||
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| val onlineLDA = new OnlineLDAOptimizer(k, D, vocabSize) | ||
| val actualBatchNumber = Math.ceil(D.toDouble / batchSize).toInt | ||
| for(i <- 1 to actualBatchNumber){ | ||
| val batch = documents.sample(true, batchSize.toDouble / D) | ||
| onlineLDA.submitMiniBatch(batch) | ||
| } | ||
| onlineLDA.getTopicDistribution() | ||
| } | ||
| } | ||
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| /** | ||
| * :: Experimental :: | ||
| * Latent Dirichlet Allocation (LDA), a topic model designed for text documents. | ||
| * | ||
| * An online training optimizer for LDA. The Optimizer processes a subset (like 1%) of the corpus | ||
| * by each call to submitMiniBatch, and update the term-topic distribution adaptively. User can | ||
| * get the result from getTopicDistribution. | ||
| * | ||
| * References: | ||
| * Hoffman, Blei and Bach, "Online Learning for Latent Dirichlet Allocation." NIPS, 2010. | ||
| */ | ||
| @Experimental | ||
| class OnlineLDAOptimizer ( | ||
| private var k: Int, | ||
| private var D: Int, | ||
| private val vocabSize:Int) extends Serializable { | ||
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| // Initialize the variational distribution q(beta|lambda) | ||
| private var lambda = getGammaMatrix(k, vocabSize) // K * V | ||
| private var Elogbeta = dirichlet_expectation(lambda) // K * V | ||
| private var expElogbeta = exp(Elogbeta) // K * V | ||
| private var i = 0 | ||
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| /** | ||
| * Submit a a subset (like 1%) of the corpus to the Online LDA model, and it will update | ||
| * the topic distribution adaptively for the terms appearing in the subset (minibatch). | ||
| * The documents RDD can be discarded after submitMiniBatch finished. | ||
| * | ||
| * @param documents RDD of documents, which are term (word) count vectors paired with IDs. | ||
| * The term count vectors are "bags of words" with a fixed-size vocabulary | ||
| * (where the vocabulary size is the length of the vector). | ||
| * Document IDs must be unique and >= 0. | ||
| * @return Inferred LDA model | ||
| */ | ||
| def submitMiniBatch(documents: RDD[(Long, Vector)]): Unit = { | ||
| var stat = BDM.zeros[Double](k, vocabSize) | ||
| stat = documents.treeAggregate(stat)(gradient, _ += _) | ||
| update(stat, i, documents.count().toInt) | ||
| i += 1 | ||
| } | ||
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| /** | ||
| * get the topic-term distribution | ||
| */ | ||
| def getTopicDistribution(): LDAModel ={ | ||
| new LocalLDAModel(Matrices.fromBreeze(lambda).transpose) | ||
| } | ||
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| private def update(raw: BDM[Double], iter:Int, batchSize: Int): Unit ={ | ||
| // weight of the mini-batch. 1024 helps down weights early iterations | ||
| val weight = math.pow(1024 + iter, -0.5) | ||
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| // This step finishes computing the sufficient statistics for the M step | ||
| val stat = raw :* expElogbeta | ||
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| // Update lambda based on documents. | ||
| lambda = lambda * (1 - weight) + (stat * D.toDouble / batchSize.toDouble + 1.0 / k) * weight | ||
| Elogbeta = dirichlet_expectation(lambda) | ||
| expElogbeta = exp(Elogbeta) | ||
| } | ||
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| // for each document d update that document's gamma and phi | ||
| private def gradient(stat: BDM[Double], doc: (Long, Vector)): BDM[Double] = { | ||
| val termCounts = doc._2 | ||
| val (ids, cts) = termCounts match { | ||
| case v: DenseVector => (((0 until v.size).toList), v.values) | ||
| case v: SparseVector => (v.indices.toList, v.values) | ||
| case v => throw new IllegalArgumentException("Do not support vector type " + v.getClass) | ||
| } | ||
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| // Initialize the variational distribution q(theta|gamma) for the mini-batch | ||
| var gammad = new Gamma(100, 1.0 / 100.0).samplesVector(k).t // 1 * K | ||
| var Elogthetad = vector_dirichlet_expectation(gammad.t).t // 1 * K | ||
| var expElogthetad = exp(Elogthetad.t).t // 1 * K | ||
| val expElogbetad = expElogbeta(::, ids).toDenseMatrix // K * ids | ||
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| var phinorm = expElogthetad * expElogbetad + 1e-100 // 1 * ids | ||
| var meanchange = 1D | ||
| val ctsVector = new BDV[Double](cts).t // 1 * ids | ||
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| // Iterate between gamma and phi until convergence | ||
| while (meanchange > 1e-5) { | ||
| val lastgamma = gammad | ||
| // 1*K 1 * ids ids * k | ||
| gammad = (expElogthetad :* ((ctsVector / phinorm) * (expElogbetad.t))) + 1.0/k | ||
| Elogthetad = vector_dirichlet_expectation(gammad.t).t | ||
| expElogthetad = exp(Elogthetad.t).t | ||
| phinorm = expElogthetad * expElogbetad + 1e-100 | ||
| meanchange = sum(abs((gammad - lastgamma).t)) / gammad.t.size.toDouble | ||
| } | ||
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| val m1 = expElogthetad.t.toDenseMatrix.t | ||
| val m2 = (ctsVector / phinorm).t.toDenseMatrix | ||
| val outerResult = kron(m1, m2) // K * ids | ||
| for (i <- 0 until ids.size) { | ||
| stat(::, ids(i)) := (stat(::, ids(i)) + outerResult(::, i)) | ||
| } | ||
| stat | ||
| } | ||
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| private def getGammaMatrix(row:Int, col:Int): BDM[Double] ={ | ||
| val gammaRandomGenerator = new Gamma(100, 1.0 / 100.0) | ||
| val temp = gammaRandomGenerator.sample(row * col).toArray | ||
| (new BDM[Double](col, row, temp)).t | ||
| } | ||
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| private def dirichlet_expectation(alpha : BDM[Double]): BDM[Double] = { | ||
| val rowSum = sum(alpha(breeze.linalg.*, ::)) | ||
| val digAlpha = digamma(alpha) | ||
| val digRowSum = digamma(rowSum) | ||
| val result = digAlpha(::, breeze.linalg.*) - digRowSum | ||
| result | ||
| } | ||
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| private def vector_dirichlet_expectation(v : BDV[Double]): (BDV[Double]) ={ | ||
| digamma(v) - digamma(sum(v)) | ||
| } | ||
| } | ||
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