/* * (C) Copyright 2005, Gregor Heinrich (gregor :: arbylon : net) (This file is * part of the org.knowceans experimental software packages.) *//* * LdaGibbsSampler is free software; you can redistribute it and/or modify it * under the terms of the GNU General Public License as published by the Free * Software Foundation; either version 2 of the License, or (at your option) any * later version. *//* * LdaGibbsSampler is distributed in the hope that it will be useful, but * WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. *//* * You should have received a copy of the GNU General Public License along with * this program; if not, write to the Free Software Foundation, Inc., 59 Temple * Place, Suite 330, Boston, MA 02111-1307 USA *//* * Created on Mar 6, 2005 */package org.knowceans.gibbstest;import java.text.DecimalFormat;import java.text.NumberFormat;/** * Gibbs sampler for estimating the best assignments of topics for words and * documents in a corpus. The algorithm is introduced in Tom Griffiths' paper * "Gibbs sampling in the generative model of Latent Dirichlet Allocation" * (2002). * * @author heinrich */public class LdaGibbsSampler { /** * document data (term lists) */ int[][] documents; /** * vocabulary size */ int V; /** * number of topics */ int K; /** * Dirichlet parameter (document--topic associations) */ double alpha; /** * Dirichlet parameter (topic--term associations) */ double beta; /** * topic assignments for each word. */ int z[][]; /** * cwt[i][j] number of instances of word i (term?) assigned to topic j. */ int[][] nw; /** * na[i][j] number of words in document i assigned to topic j. */ int[][] nd; /** * nwsum[j] total number of words assigned to topic j. */ int[] nwsum; /** * nasum[i] total number of words in document i. */ int[] ndsum; /** * cumulative statistics of theta */ double[][] thetasum; /** * cumulative statistics of phi */ double[][] phisum; /** * size of statistics */ int numstats; /** * sampling lag (?) */ private static int THIN_INTERVAL = 20; /** * burn-in period */ private static int BURN_IN = 100; /** * max iterations */ private static int ITERATIONS = 1000; /** * sample lag (if -1 only one sample taken) */ private static int SAMPLE_LAG; private static int dispcol = 0; /** * Initialise the Gibbs sampler with data. * * @param V * vocabulary size * @param data */ public LdaGibbsSampler(int[][] documents, int V) { this.documents = documents; this.V = V; } /** * Initialisation: Must start with an assignment of observations to topics ? * Many alternatives are possible, I chose to perform random assignments * with equal probabilities * * @param K * number of topics * @return z assignment of topics to words */ public void initialState(int K) { int i; int M = documents.length; // initialise count variables. nw = new int[V][K]; nd = new int[M][K]; nwsum = new int[K]; ndsum = new int[M]; // The z_i are are initialised to values in [1,K] to determine the // initial state of the Markov chain. z = new int[M][]; for (int m = 0; m < M; m++) { int N = documents[m].length; z[m] = new int[N]; for (int n = 0; n < N; n++) { int topic = (int) (Math.random() * K); z[m][n] = topic; // number of instances of word i assigned to topic j nw[documents[m][n]][topic]++; // number of words in document i assigned to topic j. nd[m][topic]++; // total number of words assigned to topic j. nwsum[topic]++; } // total number of words in document i ndsum[m] = N; } } /** * Main method: Select initial state ? Repeat a large number of times: 1. * Select an element 2. Update conditional on other elements. If * appropriate, output summary for each run. * * @param K * number of topics * @param alpha * symmetric prior parameter on document--topic associations * @param beta * symmetric prior parameter on topic--term associations */ private void gibbs(int K, double alpha, double beta) { this.K = K; this.alpha = alpha; this.beta = beta; // init sampler statistics if (SAMPLE_LAG > 0) { thetasum = new double[documents.length][K]; phisum = new double[K][V]; numstats = 0; } // initial state of the Markov chain: initialState(K); System.out.println("Sampling " + ITERATIONS + " iterations with burn-in of " + BURN_IN + " (B/S=" + THIN_INTERVAL + ")."); for (int i = 0; i < ITERATIONS; i++) { // for all z_i for (int m = 0; m < z.length; m++) { for (int n = 0; n < z[m].length; n++) { // (z_i = z[m][n]) // sample from p(z_i|z_-i, w) int topic = sampleFullConditional(m, n); z[m][n] = topic; } } if ((i < BURN_IN) && (i % THIN_INTERVAL == 0)) { System.out.print("B"); dispcol++; } // display progress if ((i > BURN_IN) && (i % THIN_INTERVAL == 0)) { System.out.print("S"); dispcol++; } // get statistics after burn-in if ((i > BURN_IN) && (SAMPLE_LAG > 0) && (i % SAMPLE_LAG == 0)) { updateParams(); System.out.print("|"); if (i % THIN_INTERVAL != 0) dispcol++; } if (dispcol >= 100) { System.out.println(); dispcol = 0; } } } /** * Sample a topic z_i from the full conditional distribution: p(z_i = j | * z_-i, w) = (n_-i,j(w_i) + beta)/(n_-i,j(.) + W * beta) * (n_-i,j(d_i) + * alpha)/(n_-i,.(d_i) + K * alpha) * * @param m * document * @param n * word */ private int sampleFullConditional(int m, int n) { // remove z_i from the count variables int topic = z[m][n]; nw[documents[m][n]][topic]--; nd[m][topic]--; nwsum[topic]--; ndsum[m]--; // do multinomial sampling via cumulative method: double[] p = new double[K]; for (int k = 0; k < K; k++) { p[k] = (nw[documents[m][n]][k] + beta) / (nwsum[k] + V * beta) * (nd[m][k] + alpha) / (ndsum[m] + K * alpha); } // cumulate multinomial parameters for (int k = 1; k < p.length; k++) { p[k] += p[k - 1]; } // scaled sample because of unnormalised p[] double u = Math.random() * p[K - 1]; for (topic = 0; topic < p.length; topic++) { if (u < p[topic]) break; } // add newly estimated z_i to count variables nw[documents[m][n]][topic]++; nd[m][topic]++; nwsum[topic]++; ndsum[m]++; return topic; } /** * Add to the statistics the values of theta and phi for the current state. */ private void updateParams() { for (int m = 0; m < documents.length; m++) { for (int k = 0; k < K; k++) { thetasum[m][k] += (nd[m][k] + alpha) / (ndsum[m] + K * alpha); } } for (int k = 0; k < K; k++) { for (int w = 0; w < V; w++) { phisum[k][w] += (nw[w][k] + beta) / (nwsum[k] + V * beta); } } numstats++; } /** * Retrieve estimated document--topic associations. If sample lag > 0 then * the mean value of all sampled statistics for theta[][] is taken. * * @return theta multinomial mixture of document topics (M x K) */ public double[][] getTheta() { double[][] theta = new double[documents.length][K]; if (SAMPLE_LAG > 0) { for (int m = 0; m < documents.length; m++) { for (int k = 0; k < K; k++) { theta[m][k] = thetasum[m][k] / numstats; } } } else { for (int m = 0; m < documents.length; m++) { for (int k = 0; k < K; k++) { theta[m][k] = (nd[m][k] + alpha) / (ndsum[m] + K * alpha); } } } return theta; } /** * Retrieve estimated topic--word associations. If sample lag > 0 then the * mean value of all sampled statistics for phi[][] is taken. * * @return phi multinomial mixture of topic words (K x V) */ public double[][] getPhi() { double[][] phi = new double[K][V]; if (SAMPLE_LAG > 0) { for (int k = 0; k < K; k++) { for (int w = 0; w < V; w++) { phi[k][w] = phisum[k][w] / numstats; } } } else { for (int k = 0; k < K; k++) { for (int w = 0; w < V; w++) { phi[k][w] = (nw[w][k] + beta) / (nwsum[k] + V * beta); } } } return phi; } /** * Print table of multinomial data * * @param data * vector of evidence * @param fmax * max frequency in display * @return the scaled histogram bin values */ public static void hist(double[] data, int fmax) { double[] hist = new double[data.length]; // scale maximum double hmax = 0; for (int i = 0; i < data.length; i++) { hmax = Math.max(data[i], hmax); } double shrink = fmax / hmax; for (int i = 0; i < data.length; i++) { hist[i] = shrink * data[i]; } NumberFormat nf = new DecimalFormat("00"); String scale = ""; for (int i = 1; i < fmax / 10 + 1; i++) { scale += " . " + i % 10; } System.out.println("x" + nf.format(hmax / fmax) + "\t0" + scale); for (int i = 0; i < hist.length; i++) { System.out.print(i + "\t|"); for (int j = 0; j < Math.round(hist[i]); j++) { if ((j + 1) % 10 == 0) System.out.print("]"); else System.out.print("|"); } System.out.println(); } } /** * Configure the gibbs sampler * * @param iterations * number of total iterations * @param burnIn * number of burn-in iterations * @param thinInterval * update statistics interval * @param sampleLag * sample interval (-1 for just one sample at the end) */ public void configure(int iterations, int burnIn, int thinInterval, int sampleLag) { ITERATIONS = iterations; BURN_IN = burnIn; THIN_INTERVAL = thinInterval; SAMPLE_LAG = sampleLag; } /** * Driver with example data. * * @param args */ public static void main(String[] args) { // words in documents int[][] documents = { {1, 4, 3, 2, 3, 1, 4, 3, 2, 3, 1, 4, 3, 2, 3, 6}, {2, 2, 4, 2, 4, 2, 2, 2, 2, 4, 2, 2}, {1, 6, 5, 6, 0, 1, 6, 5, 6, 0, 1, 6, 5, 6, 0, 0}, {5, 6, 6, 2, 3, 3, 6, 5, 6, 2, 2, 6, 5, 6, 6, 6, 0}, {2, 2, 4, 4, 4, 4, 1, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 0}, {5, 4, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2}}; // vocabulary int V = 7; int M = documents.length; // # topics int K = 2; // good values alpha = 2, beta = .5 double alpha = 2; double beta = .5; System.out.println("Latent Dirichlet Allocation using Gibbs Sampling."); LdaGibbsSampler lda = new LdaGibbsSampler(documents, V); lda.configure(10000, 2000, 100, 10); lda.gibbs(K, alpha, beta); double[][] theta = lda.getTheta(); double[][] phi = lda.getPhi(); System.out.println(); System.out.println(); System.out.println("Document--Topic Associations, Theta[d][k] (alpha=" + alpha + ")"); System.out.print("d\\k\t"); for (int m = 0; m < theta[0].length; m++) { System.out.print(" " + m % 10 + " "); } System.out.println(); for (int m = 0; m < theta.length; m++) { System.out.print(m + "\t"); for (int k = 0; k < theta[m].length; k++) { // System.out.print(theta[m][k] + " "); System.out.print(shadeDouble(theta[m][k], 1) + " "); } System.out.println(); } System.out.println(); System.out.println("Topic--Term Associations, Phi[k][w] (beta=" + beta + ")"); System.out.print("k\\w\t"); for (int w = 0; w < phi[0].length; w++) { System.out.print(" " + w % 10 + " "); } System.out.println(); for (int k = 0; k < phi.length; k++) { System.out.print(k + "\t"); for (int w = 0; w < phi[k].length; w++) { // System.out.print(phi[k][w] + " "); System.out.print(shadeDouble(phi[k][w], 1) + " "); } System.out.println(); } } static String[] shades = {" ", ". ", ": ", ":. ", ":: ", "::. ", "::: ", ":::. ", ":::: ", "::::.", ":::::"}; static NumberFormat lnf = new DecimalFormat("00E0"); /** * create a string representation whose gray value appears as an indicator * of magnitude, cf. Hinton diagrams in statistics. * * @param d * value * @param max * maximum value * @return */ public static String shadeDouble(double d, double max) { int a = (int) Math.floor(d * 10 / max + 0.5); if (a > 10 || a < 0) { String x = lnf.format(d); a = 5 - x.length(); for (int i = 0; i < a; i++) { x += " "; } return "<" + x + ">"; } return "[" + shades[a] + "]"; }}
