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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 (c) 2012, Lawrence Livermore National Security, LLC. Produced at
 * the Lawrence Livermore National Laboratory. Written by Keith Stevens,
 * [email protected] OCEC-10-073 All rights reserved. 
 *
 * 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 .
 */

package edu.ucla.sspace.clustering;

import edu.ucla.sspace.matrix.ArrayMatrix;
import edu.ucla.sspace.matrix.Matrix;
import edu.ucla.sspace.matrix.MatrixFactorization;
import edu.ucla.sspace.matrix.factorization.EigenDecomposition;

import java.util.Properties;
import java.util.logging.Logger;


/**
 * An implementation of Normalized Spectral Clustering, a stable method for
 * computing the minimum conductance over a graph by using the normalized graph
 * laplacian.  This implementation is based on 
 *
 * 
 *   
 *    
Andrew Ng, Michael
 *    Jordan, and Yair Weiss.  On Spectral Clustering: Analysis and an
 *    Algorithm. Advances in Neural Information Processing Systems.
 *    Available here
 *    
 * 
 *
 * @author Keith Stevens
 */
public class NormalizedSpectralClustering implements Clustering {

    private static final Logger LOG =
        Logger.getLogger(NormalizedSpectralClustering.class.getName());

    /**
     * {@inheritDoc}
     */
    public Assignments cluster(Matrix m, int k, Properties props) {
        assert m.rows() == m.columns();

        LOG.fine("Computing Degree of Adjacency Matrix");
        // Assume that the matrix m is symmetric.  Now compute the degrees:
        double[] degrees = new double[m.rows()];
        for (int r = 0; r < m.rows(); ++r) {
            double degree = 0;
            for (int c = 0; c < m.columns(); ++c)
                degree += m.get(r,c);
            degrees[r] = degree;
        }

        // Compute the inverse square of the degrees for the normalized
        // Laplacian.
        for (int r = 0; r < m.rows(); ++r)
            degrees[r] = Math.pow(degrees[r], -.5);

        LOG.fine("Computing Graph Laplacian");
        // Now create the normalized symmetric graph laplacian:
        Matrix L = new ArrayMatrix(m.rows(), m.columns());
        for (int r = 0; r < m.rows(); ++r)
            for (int c = 0; c < m.columns(); ++c)
                L.set(r,c, ((r == c) ? 1 : 0) -
                           degrees[r] * m.get(r,c) * degrees[c]);
        
        // Extract the top k eigen vectors and set them as the columns of our
        // new spectral decomposition matrix.  While doing this, also compute
        // the squared sum of rows.
        LOG.fine("Computing Eigenvector Decomposition");
        EigenDecomposition eigen = new EigenDecomposition();
        eigen.factorize(L, k);

        LOG.fine("Extracting Normalized Spectral Representation");
        Matrix eigenVectors = eigen.classFeatures();
        Matrix spectral = new ArrayMatrix(m.rows(), k);
        double[] rowNorms = new double[m.rows()];
        for (int c = 0; c < k; ++c) {
            for (int r = 0; r < m.rows(); ++r) {
                double value = eigenVectors.get(c, r);
                rowNorms[r] += Math.pow(value, 2);
                spectral.set(r, c, value);
            }
        }

        // Normalize each row by the squared root of the sum of squares.
        for (int r = 0; r < spectral.rows(); ++r) {
            double norm = Math.sqrt(rowNorms[r]);
            if (norm != 0d)
                for (int c = 0; c < spectral.columns(); ++c)
                    spectral.set(r,c, spectral.get(r,c) / norm);
        }

        LOG.fine("Clustering with K-Means");
        // Now cluster the data points with K-Means clustering and return the
        // assignments.
        return DirectClustering.cluster(spectral, k, 20);
    }

    /**
     * Unsupported.
     */
    public Assignments cluster(Matrix m, Properties props) {
        throw new UnsupportedOperationException(
                "Cannot cluster without a fixed number of clusters");
    }
}