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/*
* File: ProbabilisticLatentSemanticAnalysis.java
* Authors: Justin Basilico
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright March 18, 2009, Sandia Corporation.
* Under the terms of Contract DE-AC04-94AL85000, there is a non-exclusive
* license for use of this work by or on behalf of the U.S. Government. Export
* of this program may require a license from the United States Government.
* See CopyrightHistory.txt for complete details.
*
*/
package gov.sandia.cognition.text.topic;
import gov.sandia.cognition.algorithm.event.AbstractIterativeAlgorithmListener;
import gov.sandia.cognition.algorithm.IterativeAlgorithm;
import gov.sandia.cognition.annotation.PublicationReference;
import gov.sandia.cognition.annotation.PublicationReferences;
import gov.sandia.cognition.annotation.PublicationType;
import gov.sandia.cognition.evaluator.Evaluator;
import gov.sandia.cognition.learning.algorithm.AbstractAnytimeBatchLearner;
import gov.sandia.cognition.learning.data.DatasetUtil;
import gov.sandia.cognition.math.matrix.Matrix;
import gov.sandia.cognition.math.matrix.MatrixFactory;
import gov.sandia.cognition.math.matrix.Vector;
import gov.sandia.cognition.math.matrix.VectorFactory;
import gov.sandia.cognition.math.matrix.VectorFactoryContainer;
import gov.sandia.cognition.math.matrix.VectorInputEvaluator;
import gov.sandia.cognition.math.matrix.VectorOutputEvaluator;
import gov.sandia.cognition.math.matrix.VectorUtil;
import gov.sandia.cognition.math.matrix.Vectorizable;
import gov.sandia.cognition.util.AbstractCloneableSerializable;
import gov.sandia.cognition.util.ArgumentChecker;
import gov.sandia.cognition.util.Randomized;
import java.io.PrintStream;
import java.text.DecimalFormat;
import java.text.NumberFormat;
import java.util.Collection;
import java.util.Random;
/**
* An implementation of the Probabilistic Latent Semantic Analysis (PLSA)
* algorithm.
*
* @author Justin Basilico
* @since 3.0
*/
@PublicationReferences(
references={
@PublicationReference(
author="Thomas Hofmann",
title="Probabilistic Latent Semantic Analysis",
year=1999,
type=PublicationType.Conference,
publication="Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI)",
pages={289, 296},
url="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.1187"
),
@PublicationReference(
author="Thomas Hofmann",
title="Probabilistic Latent Semantic Indexing",
year=1999,
type=PublicationType.Conference,
publication="Proceedings of the 22nd Conference of the ACM Special Interest Group on Information Retreival (SIGIR)",
pages={50, 57},
url="http://portal.acm.org/citation.cfm?id=312649"
),
@PublicationReference(
author="Thomas Hofmann",
title="Unsupervised Learning by Probabilistic Latent Semantic Analysis",
year=2001,
type=PublicationType.Journal,
publication="Machine Learning",
pages={177, 196},
url="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.130.6341"
)
}
)
public class ProbabilisticLatentSemanticAnalysis
extends AbstractAnytimeBatchLearner, ProbabilisticLatentSemanticAnalysis.Result>
implements Randomized, VectorFactoryContainer
{
// TODO: Make use of sparseness.
/** The default requested rank is {@value}. */
public static final int DEFAULT_REQUESTED_RANK = 10;
/** The default maximum number of iterations is {@value}. */
public static final int DEFAULT_MAX_ITERATIONS = 250;
/** The default minimum change is {@value}. */
public static final double DEFAULT_MINIMUM_CHANGE = 1e-10;
/** The requested rank to reduce the dimensionality to. */
protected int requestedRank;
/** The minimum change required in log-likelihood to continue iterating.
* Used for a stopping criteria. */
protected double minimumChange;
/** The random number generator to use. */
protected Random random;
/** The vector factory. */
protected VectorFactory vectorFactory;
/** The matrix factory. */
protected MatrixFactory matrixFactory;
/** The document-by-term matrix. */
protected transient Matrix documentsByTerms;
/** The number of terms. */
protected transient int termCount;
/** The number of documents. */
protected transient int documentCount;
/** The number of latent variables. */
protected transient int latentCount;
/** The information about each of the latent variables. */
protected transient LatentData[] latents;
/** The current log-likelihood of the algorithm. */
protected transient double logLikelihood;
/** The change in log-likelihood of the algorithm from the current
* iteration. */
protected transient double changeOfLogLikelihood;
/** The result being produced by the algorithm. */
protected transient Result result;
/**
* Creates a new ProbabilisticSemanticAnalysis with default parameters.
*/
public ProbabilisticLatentSemanticAnalysis()
{
this(DEFAULT_REQUESTED_RANK);
}
/**
* Creates a new ProbabilisticLatentSemanticAnalysis with default parameters
* and the given random number generator.
*
* @param random
* The random number generator to use.
*/
public ProbabilisticLatentSemanticAnalysis(
final Random random)
{
this(DEFAULT_REQUESTED_RANK, DEFAULT_MINIMUM_CHANGE, random);
}
/**
* Creates a new ProbabilisticLatentSemanticAnalysis with the given rank
* and otherwise default parameters.
*
* @param requestedRank
* The requested rank. Must be non-negative.
*/
public ProbabilisticLatentSemanticAnalysis(
final int requestedRank)
{
this(requestedRank, DEFAULT_MINIMUM_CHANGE, new Random());
}
/**
* Creates a new ProbabilisticLatentSemanticAnalysis with the given
* parameters.
*
* @param requestedRank
* The requested rank. Must be non-negative.
* @param minimumChange
* The minimum change in log-likelihood to stop.
* @param random
* The random number generator to use.
*/
public ProbabilisticLatentSemanticAnalysis(
final int requestedRank,
final double minimumChange,
final Random random)
{
super(DEFAULT_MAX_ITERATIONS);
this.setRequestedRank(requestedRank);
this.setRandom(random);
this.setMinimumChange(minimumChange);
this.setVectorFactory(VectorFactory.getDefault());
this.setMatrixFactory(MatrixFactory.getDefault());
}
@Override
protected boolean initializeAlgorithm()
{
final Collection documents = this.getData();
this.documentsByTerms = this.getMatrixFactory().copyRowVectors(documents);
this.termCount = DatasetUtil.getDimensionality(documents);
this.documentCount = documents.size();
this.latentCount = Math.min(this.documentCount, this.getRequestedRank());
// Set up the latent variable information.
this.latents = new LatentData[this.latentCount];
for (int i = 0; i < this.latentCount; i++)
{
final LatentData latent = new LatentData();
this.latents[i] = latent;
latent.index = i;
// Initialize the latent data.
latent.pLatentGivenDocumentTerm =
this.getMatrixFactory().createMatrix(
this.documentCount, this.termCount);
latent.pTermGivenLatent = this.getVectorFactory().createUniformRandom(
this.termCount, 0.0, 1.0, this.getRandom());
VectorUtil.divideByNorm1Equals(latent.pTermGivenLatent);
latent.pDocumentGivenLatent = this.getVectorFactory().createUniformRandom(
this.documentCount, 0.0, 1.0, this.getRandom());
VectorUtil.divideByNorm1Equals(latent.pDocumentGivenLatent);
// Uniform prior on latent classes.
latent.pLatent = 1.0 / latentCount;
}
this.logLikelihood = Double.MIN_VALUE;
this.changeOfLogLikelihood = 0.0;
this.result = new Result(this.termCount, this.latents);
return true;
}
@Override
protected boolean step()
{
// E-step:
for (int i = 0; i < this.documentCount; i++)
{
for (int j = 0; j < this.termCount; j++)
{
double sum = 0.0;
for (LatentData latent : this.latents)
{
final double value =
latent.pLatent
* latent.pDocumentGivenLatent.getElement(i)
* latent.pTermGivenLatent.getElement(j);
latent.pLatentGivenDocumentTerm.setElement(i, j, value);
sum += value;
}
if (sum != 0.0)
{
for (LatentData latent : this.latents)
{
double value =
latent.pLatentGivenDocumentTerm.getElement(i, j);
value /= sum;
latent.pLatentGivenDocumentTerm.setElement(i, j, value);
}
}
}
}
// M-step:
double pLatentSum = 0.0;
for (LatentData latent : this.latents)
{
// This matrix forms the basis for the m-step. It multiplies the
// count of occurrences of the term in a document by the probability
// of the aspect given the document and term. The probabilities for
// documents and terms
final Matrix countsTimesProbabilities =
this.documentsByTerms.dotTimes(latent.pLatentGivenDocumentTerm);
// To get the term probabilities, we sum over documents.
latent.pTermGivenLatent = countsTimesProbabilities.sumOfRows();
// To get the document probabilities, we sum over terms.
latent.pDocumentGivenLatent = countsTimesProbabilities.sumOfColumns();
// To get the aspect probability, we sum across the whole matrix,
// which is the same as summing across one of the summed rows or
// columns. Here we pick documents because normally the number of
// words is larger than the number of documents.
latent.pLatent = latent.pDocumentGivenLatent.sum();
// Make the vectors into probabilities by making them sum to one.
VectorUtil.divideByNorm1Equals(latent.pTermGivenLatent);
VectorUtil.divideByNorm1Equals(latent.pDocumentGivenLatent);
// We use the aspect sum to normalize the aspect probabilities to
// sum to one.
pLatentSum += latent.pLatent;
}
// Normalize the probabilities of the latent classes so that they sum
// to one.
if (pLatentSum != 0.0)
{
for (LatentData latent : this.latents)
{
latent.pLatent /= pLatentSum;
}
}
// Compute the log-likelihood
final double previousLogLikelihood = this.logLikelihood;
this.logLikelihood = 0.0;
for (int i = 0; i < this.documentCount; i++)
{
for (int j = 0; j < this.termCount; j++)
{
double pDocumentTerm = 0.0;
for (LatentData latent : this.latents)
{
pDocumentTerm +=
latent.pLatent
* latent.pDocumentGivenLatent.getElement(i)
* latent.pTermGivenLatent.getElement(j);
}
if (pDocumentTerm != 0.0)
{
this.logLikelihood += this.documentsByTerms.getElement(i, j)
* Math.log(pDocumentTerm);
}
}
}
// The stopping criteria is based on the change in log-likelihood.
final double change = this.logLikelihood - previousLogLikelihood;
this.changeOfLogLikelihood = change;
return Math.abs(change) > this.getMinimumChange();
}
@Override
protected void cleanupAlgorithm()
{
this.latents = null;
this.documentsByTerms = null;
}
public Result getResult()
{
return this.result;
}
public Random getRandom()
{
return this.random;
}
public void setRandom(
final Random random)
{
this.random = random;
}
/**
* Gets the vector factory to use.
*
* @return
* The vector factory to use.
*/
public VectorFactory getVectorFactory()
{
return this.vectorFactory;
}
/**
* Sets the vector factory to use.
*
* @param vectorFactory
* The vector factory to use.
*/
public void setVectorFactory(
final VectorFactory vectorFactory)
{
this.vectorFactory = vectorFactory;
}
/**
* Gets the matrix factory to use.
*
* @return
* The matrix factory to use.
*/
public MatrixFactory getMatrixFactory()
{
return this.matrixFactory;
}
/**
* Sets the matrix factory to use.
*
* @param matrixFactory
* The matrix factory to use.
*/
public void setMatrixFactory(
final MatrixFactory matrixFactory)
{
this.matrixFactory = matrixFactory;
}
/**
* Gets the requested rank to conduct the analysis for. It is the number
* of latent variables to use.
*
* @return
* The requested rank. Must be positive.
*/
public int getRequestedRank()
{
return this.requestedRank;
}
/**
* Sets the requested rank to conduct the analysis for. It is the number
* of latent variables to use.
*
* @param requestedRank
* The requested rank. Must be positive.
*/
public void setRequestedRank(
final int requestedRank)
{
ArgumentChecker.assertIsPositive("requestedRank", requestedRank);
this.requestedRank = requestedRank;
}
/**
* Gets the minimum change in log-likelihood to allow before stopping the
* algorithm.
*
* @return
* The minimum change in log-likelihood to allow before stopping.
* Must be non-negative.
*/
public double getMinimumChange()
{
return this.minimumChange;
}
/**
* Sets the minimum change in log-likelihood to allow before stopping the
* algorithm.
*
* @param minimumChange
* The minimum change in log-likelihood to allow before stopping.
* Must be non-negative.
*/
public void setMinimumChange(
final double minimumChange)
{
ArgumentChecker.assertIsNonNegative("minimumChange", minimumChange);
this.minimumChange = minimumChange;
}
/**
* The information about each latent variable.
*/
public static class LatentData
{
/** The index of the latent variable. */
int index;
/** The probability of the latent variable given the document and term.
*/
Matrix pLatentGivenDocumentTerm;
/** The probability of each term given the latent variable. */
Vector pTermGivenLatent;
/** The probability of each vector given the latent variable. */
Vector pDocumentGivenLatent;
/** The probability of the latent variable. */
double pLatent;
}
/**
* The dimensionality transform created by probabilistic latent semantic
* analysis.
*/
public static class Result
extends AbstractCloneableSerializable
implements Evaluator,
VectorInputEvaluator,
VectorOutputEvaluator
{
/** The number of terms. */
protected int termCount;
/** The number of latent variables. */
protected int latentCount;
/** The latent variable data. */
protected LatentData[] latents;
/** The maximum number of iterations for the E-M evaluation. */
protected int maxIterations;
/** The minimum change in log-likelihood for the E-M evaluation. */
protected double minimumChange;
/**
* Creates a new probabilistic latent semantic analysis transform.
*
* @param termCount
* The number of terms.
* @param latents
* The latent variable data.
*/
public Result(
final int termCount,
final LatentData[] latents)
{
super();
this.termCount = termCount;
this.latentCount = latents.length;
this.latents = latents;
this.maxIterations = DEFAULT_MAX_ITERATIONS;
this.minimumChange = DEFAULT_MINIMUM_CHANGE;
}
public Vector evaluate(
final Vectorizable input)
{
final Vector query = input.convertToVector();
final Matrix pLatentGivenQueryTerm =
MatrixFactory.getDefault().createMatrix(
this.latentCount, this.termCount);
final Vector pQueryGivenLatent =
VectorFactory.getDefault().createVector(
this.latentCount,
1.0 / this.latentCount);
double logLikelihood = Double.MIN_VALUE;
for (int iteration = 1; iteration <= this.maxIterations; iteration++)
{
final double previousLogLikelihood = logLikelihood;
logLikelihood = this.step(
query, pLatentGivenQueryTerm, pQueryGivenLatent);
final double change = logLikelihood - previousLogLikelihood;
if (Math.abs(change) <= this.minimumChange)
{
break;
}
}
return pQueryGivenLatent;
}
/**
* Take a step of the expectation-maximization algorithm for computing
* the probability of the query given each latent variable.
*
* @param query
* The query to evaluate.
* @param pLatentGivenQueryTerm
* The probability of each latent variable given each term in the
* query.
* @param pQueryGivenLatent
* The probability of the query given each latent variable.
* @return
* The log-likelihood of the query.
*/
protected double step(
final Vector query,
final Matrix pLatentGivenQueryTerm,
final Vector pQueryGivenLatent)
{
// E-step:
// Compute p(z|q, w). We loop over terms because for each term
// we normalize by latent values.
for (int j = 0; j < this.termCount; j++)
{
double sum = 0.0;
for (LatentData latent : this.latents)
{
final int k = latent.index;
final double value =
latent.pLatent
* pQueryGivenLatent.getElement(k)
* latent.pTermGivenLatent.getElement(j);
pLatentGivenQueryTerm.setElement(k, j, value);
sum += value;
}
if (sum != 0.0)
{
for (LatentData latent : this.latents)
{
final int i = latent.index;
double value = pLatentGivenQueryTerm.getElement(i, j);
value /= sum;
pLatentGivenQueryTerm.setElement(i, j, value);
}
}
}
// M-step:
// We only modify the p(q|z) since we hold the rest fixed from
// the
for (LatentData latent : this.latents)
{
final int k = latent.index;
double sum = 0.0;
for (int j = 0; j < this.termCount; j++)
{
final double value = query.getElement(j)
* pLatentGivenQueryTerm.getElement(k, j);
sum += value;
}
pQueryGivenLatent.setElement(k, sum);
}
// Normalize.
VectorUtil.divideByNorm1Equals(pQueryGivenLatent);
double logLikelihood = 0.0;
for (int j = 0; j < this.termCount; j++)
{
double pQueryTerm = 0.0;
for (LatentData latent : latents)
{
final int k = latent.index;
pQueryTerm +=
latent.pLatent
* latent.pTermGivenLatent.getElement(j)
* pQueryGivenLatent.getElement(k);
}
if (pQueryTerm != 0.0)
{
logLikelihood += query.getElement(j)
* Math.log(pQueryTerm);
}
}
return logLikelihood;
}
public int getInputDimensionality()
{
return this.termCount;
}
public int getOutputDimensionality()
{
return this.latents.length;
}
}
/**
* Prints out the status of the probabilistic latent semantic analysis
* algorithm. Can be useful for debugging and other purposes.
*/
public static class StatusPrinter
extends AbstractIterativeAlgorithmListener
{
/** The stream to write the status to. */
protected PrintStream out;
/**
* Creates a new {@code StatusPrinter} writing to {@code System.out}.
*/
public StatusPrinter()
{
this(System.out);
}
/**
* Creates a new {@code StatusPrinter} writing to the given stream.
*
* @param out
* The print stream to write status to.
*/
public StatusPrinter(
final PrintStream out)
{
super();
this.out = out;
}
public void stepStarted(
final IterativeAlgorithm algorithm)
{
final ProbabilisticLatentSemanticAnalysis plsa =
(ProbabilisticLatentSemanticAnalysis) algorithm;
NumberFormat format = new DecimalFormat("0.00");
out.println("Iteration " + plsa.getIteration());
for (ProbabilisticLatentSemanticAnalysis.LatentData latent
: plsa.result.latents)
{
out.println(" Latent " + latent.index);
out.println(" p(z) = " + format.format(latent.pLatent));
out.println(" p(t|z) = " + latent.pTermGivenLatent.toString(format));
out.println(" p(d|z) = " + latent.pDocumentGivenLatent.toString(format));
}
}
public void stepEnded(
final IterativeAlgorithm algorithm)
{
final ProbabilisticLatentSemanticAnalysis plsa =
(ProbabilisticLatentSemanticAnalysis) algorithm;
out.println("Log likelihood: " + plsa.logLikelihood);
out.println("Change: " + plsa.changeOfLogLikelihood);
}
}
}