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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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package edu.ucla.sspace.matrix;

import edu.ucla.sspace.vector.SparseDoubleVector;


/**
 * @author Keith Stevens
 */
public class PageRank implements MatrixRank {

    private final double alpha;

    private final double beta;

    private final int numIterations;

    public PageRank() {
        this(.85, 50);
    }

    public PageRank(double alpha, int numIterations) {
        this.alpha = alpha;
        this.beta = 1-alpha;
        this.numIterations = numIterations;
    }

    /**
     * {@inheritDoc}
     */
    public double[] rank(Matrix adj) {
        return rank(adj, initialRanks(adj.rows()));
    }

    /**
     * {@inheritDoc}
     */
    public double[] rank(SparseMatrix adj) {
        return rank(adj, initialRanks(adj.rows()));
    }

    /**
     * {@inheritDoc}
     */
    public double[] rank(Matrix adj, double[] initialRanks) {
        if (adj instanceof SparseMatrix)
            return rank((SparseMatrix) adj, initialRanks);

        double[] ranks = initialRanks;
        double[] columnSums =
            TransformStatistics.extractStatistics(adj).columnSums;

        for (int i = 0; i < numIterations; i++) {
            double[] newRanks = new double[adj.rows()];
            for (int r = 0; r < adj.rows(); ++r)
                for (int c = 0; c < adj.columns(); ++c)
                    newRanks[r] += adj.get(r, c) / columnSums[c] * ranks[r];
            for (int r = 0; r < adj.rows(); ++r)
                newRanks[r] = alpha * newRanks[r] + beta * initialRanks[r];
            ranks = newRanks;
        }
        return ranks;
    }

    /**
     * {@inheritDoc}
     */
    public double[] rank(SparseMatrix adj, double[] initialRanks) {
        double[] ranks = initialRanks;
        double[] columnSums =
            TransformStatistics.extractStatistics(adj).columnSums;

        for (int i = 0; i < numIterations; i++) {
            double[] newRanks = new double[adj.rows()];
            for (int r = 0; r < adj.rows(); ++r)
                for (int c : adj.getRowVector(r).getNonZeroIndices())
                    newRanks[r] += adj.get(r, c) / columnSums[c] * ranks[r];

            for (int r = 0; r < adj.rows(); ++r)
                newRanks[r] = alpha * newRanks[r] + beta * initialRanks[r];
            ranks = newRanks;
        }
        return ranks;
    }

    /**
     * {@inheritDoc}
     */
    public double[] initialRanks(int numRows) {
        double[] evenRanks = new double[numRows];
        for (int n = 0; n < numRows; ++n)
            evenRanks[n] = 1.0/n;
        return evenRanks;
    }
}