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The S-Space Package is a collection of algorithms for building
Semantic Spaces as well as a highly-scalable library for designing new
distributional semantics algorithms. Distributional algorithms process text
corpora and represent the semantic for words as high dimensional feature
vectors. This package also includes matrices, vectors, and numerous
clustering algorithms. These approaches are known by many names, such as
word spaces, semantic spaces, or distributed semantics and rest upon the
Distributional Hypothesis: words that appear in similar contexts have
similar meanings.
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/*
* Copyright 2011 Keith Stevens
*
* This file is part of the S-Space package and is covered under the terms and
* conditions therein.
*
* The S-Space package is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License version 2 as published
* by the Free Software Foundation and distributed hereunder to you.
*
* THIS SOFTWARE IS PROVIDED "AS IS" AND NO REPRESENTATIONS OR WARRANTIES,
* EXPRESS OR IMPLIED ARE MADE. BY WAY OF EXAMPLE, BUT NOT LIMITATION, WE MAKE
* NO REPRESENTATIONS OR WARRANTIES OF MERCHANT- ABILITY OR FITNESS FOR ANY
* PARTICULAR PURPOSE OR THAT THE USE OF THE LICENSED SOFTWARE OR DOCUMENTATION
* WILL NOT INFRINGE ANY THIRD PARTY PATENTS, COPYRIGHTS, TRADEMARKS OR OTHER
* RIGHTS.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see David Cheng , Ravi Kannan ,
* Santosh Vempala , Grant Wang (2003) A Divid-and-Merge Methodology for
* Clustering. Available here.
*
*
This implementation implements a subclass of the {@link
* BaseSpectralCut} and simply computes the second eigen vector for a data set.
*
* @see BaseSpectralCut
* @see SpectralClustering
*
* @author Keith Stevens
*/
public class CKVWSpectralClustering06 implements Clustering {
/**
* The proper prefix.
*/
public static final String PROPERTY_PREFIX =
"edu.ucla.sspace.clustering.CKVWSpectralClustering06";
/**
* The property used to use K-Means as the objective function.
*/
public static final String USE_KMEANS =
PROPERTY_PREFIX + ".useKMeans";
/**
* {@inheritDoc}
*/
public Assignments cluster(Matrix matrix, Properties props) {
SpectralClustering cluster = new SpectralClustering(
.2, new SuperSpectralGenerator());
return cluster.cluster(matrix);
}
/**
* {@inheritDoc}
*/
public Assignments cluster(Matrix matrix,
int numClusters,
Properties props) {
SpectralClustering cluster = new SpectralClustering(
.2, new SuperSpectralGenerator());
return cluster.cluster(
matrix, numClusters, props.getProperty(USE_KMEANS) != null);
}
/**
* An internal spectral cut implementation that is based on the referred to
* paper. See paper for details.
*/
public class SuperSpectralCut extends BaseSpectralCut {
/**
* {@inheritDoc}
*/
protected DoubleVector computeSecondEigenVector(Matrix matrix,
int vectorLength) {
// Compute pi, and D. Pi is the normalized form of rho. D a
// diagonal matrix with sqrt(pi) as the values along the diagonal.
// Also compute pi * D^-1.
DoubleVector pi = new DenseVector(vectorLength);
DoubleVector D = new DenseVector(vectorLength);
DoubleVector piDInverse = new DenseVector(vectorLength);
for (int i = 0; i < vectorLength; ++i) {
double piValue = rho.get(i)/pSum;
pi.set(i, piValue);
if (piValue > 0d) {
D.set(i, Math.sqrt(piValue));
piDInverse.set(i, piValue / D.get(i));
}
}
// Create the second largest eigenvector of the a scaled form of the
// row normalized affinity matrix. The computation is using the
// power method such that the affinity matrix is never explicitly
// computed.
// piDInverse serves as a vector which is similar to the first eigen
// vector. The second eigen vector is assumed to be orthogonal to
// piDInverse. This algorithm makes O(log(matrix.rows())) passes
// through the data matrix.
// Step 1, generate a random vector, v, that is orthogonal to
// pi*D-Inverse.
DoubleVector v = new DenseVector(vectorLength);
for (int i = 0; i < v.length(); ++i)
v.set(i, Math.random());
// Make log(matrix.rows()) passes.
int log = (int) Statistics.log2(vectorLength);
for (int k = 0; k < log; ++k) {
// start the orthonormalizing the eigen vector.
v = orthonormalize(v, piDInverse);
// Step 2, repeated, (a) normalize v (b) set v = Q*v, where Q =
// D * R-Inverse * matrix * matrix-Transpose * D-Inverse.
// v = Q*v is broken into 4 sub steps that allow for sparse
// multiplications.
// Step 2b-1) v = D-Inverse*v.
for (int i = 0; i < vectorLength; ++ i)
if (D.get(i) != 0d)
v.set(i, v.get(i) / D.get(i));
// Step 2b-2) v = matrix-Transpose * v.
DoubleVector newV = computeMatrixTransposeV(matrix, v);
// Step 2b-3) v = matrix * v.
computeMatrixDotV(matrix, newV, v);
// Step 2b-4) v = D*R-Inverse * v. Note that R is a diagonal
// matrix with rho as the values along the diagonal.
for (int i = 0; i < vectorLength; ++i) {
double oldValue = v.get(i);
double newValue = oldValue * D.get(i) / rho.get(i);
v.set(i, newValue);
}
}
return v;
}
}
public String toString() {
return "CKVWSpectralClustering06";
}
/**
* A simple generator for creating instances of the {@link SpectralCut}
* class.
*/
public class SuperSpectralGenerator implements Generator {
/**
* {@inheritDoc}
*/
public EigenCut generate() {
return new SuperSpectralCut();
}
}
}