jlibwiigee/src/org/wiigee/logic/HMM.java

/*
 * wiigee - accelerometerbased gesture recognition
 * Copyright (C) 2007, 2008 Benjamin Poppinga
 * 
 * Developed at University of Oldenburg
 * Contact: benjamin.poppinga@informatik.uni-oldenburg.de
 *
 * This file is part of wiigee.
 *
 * wiigee is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * This program 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 Lesser General Public License for more details.
 * 
 * You should have received a copy of the GNU Lesser General Public License along
 * with this program; if not, write to the Free Software Foundation, Inc.,
 * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
 */

package org.wiigee.logic;
import java.text.DecimalFormat;
import java.util.Vector;
import org.wiigee.util.Log;

/**
 * This is a Hidden Markov Model implementation which internally provides
 * the basic algorithms for training and recognition (forward and backward
 * algorithm). Since a regular Hidden Markov Model doesn't provide a possibility
 * to train multiple sequences, this implementation has been optimized for this
 * purposes using some state-of-the-art technologies described in several papers.
 *
 * @author Benjamin 'BePo' Poppinga
 *
 */

public class HMM {
	/** The number of states */
	protected int numStates;

	/** The number of observations */
	protected int numObservations;

	/** The initial probabilities for each state: p[state] */
	protected double pi[];

	/** The state change probability to switch from state A to
	 * state B: a[stateA][stateB] */
	protected double a[][];

	/** The probability to emit symbol S in state A: b[stateA][symbolS] */
	protected double b[][];

	/**
	 * Initialize the Hidden Markov Model in a left-to-right version.
	 * 
	 * @param numStates Number of states
	 * @param numObservations Number of observations
	 */
	public HMM(int numStates, int numObservations) {
		this.numStates = numStates;
		this.numObservations = numObservations;
		pi = new double[numStates];
		a = new double[numStates][numStates];
		b = new double[numStates][numObservations];
		this.reset();
	}
	
	/**
	 * Reset the Hidden Markov Model to the initial left-to-right values.
	 *
	 */
	private void reset() {
		int jumplimit = 2;
		
		// set startup probability
		pi[0] = 1;
		for(int i=1; i<numStates; i++) {
			pi[i] = 0;
		}
		
		// set state change probabilities in the left-to-right version
		// NOTE: i now that this is dirty and very static. :)
		for(int i=0; i<numStates; i++) {
			for(int j=0; j<numStates; j++) {
				if(i==numStates-1 && j==numStates-1) { // last row
					a[i][j] = 1.0;
				} else if(i==numStates-2 && j==numStates-2) { // next to last row
					a[i][j] = 0.5;
				} else if(i==numStates-2 && j==numStates-1) { // next to last row
					a[i][j] = 0.5;
				} else if(i<=j && i>j-jumplimit-1) {
					a[i][j] = 1.0/(jumplimit+1);
				} else {
					a[i][j] = 0.0;
				}
			}
		}
		
		
		// emission probability
		for(int i=0; i<numStates; i++) {
			for(int j=0; j<numObservations; j++) {
				b[i][j] = 1.0/(double)numObservations;
			}
		}
	}

	/**
	 * Trains the Hidden Markov Model with multiple sequences.
	 * This method is normally not known to basic hidden markov
	 * models, because they usually use the Baum-Welch-Algorithm.
	 * This method is NOT the traditional Baum-Welch-Algorithm.
	 * 
	 * If you want to know in detail how it works please consider
	 * my Individuelles Projekt paper on the wiigee Homepage. Also
	 * there exist some english literature on the world wide web.
	 * Try to search for some papers by Rabiner or have a look at
	 * Vesa-Matti Mäntylä - "Discrete Hidden Markov Models with
	 * application to isolated user-dependent hand gesture recognition". 
	 * 
	 */
	public void train(Vector<int[]> trainsequence) {

		double[][] a_new = new double[a.length][a.length];
		double[][] b_new = new double[b.length][b[0].length];
		// re calculate state change probability a
		for(int i=0; i<a.length; i++) {
			for(int j=0; j<a[i].length; j++) {	
				double zaehler=0;
				double nenner=0;
			
				for(int k=0; k<trainsequence.size(); k++) {
					int[] sequence = trainsequence.elementAt(k);
					
					double[][] fwd = this.forwardProc(sequence);
					double[][] bwd = this.backwardProc(sequence);
					double prob = this.getProbability(sequence);
		
					double zaehler_innersum=0;
					double nenner_innersum=0;
					
					
					for(int t=0; t<sequence.length-1; t++) {
						zaehler_innersum+=fwd[i][t]*a[i][j]*b[j][sequence[t+1]]*bwd[j][t+1];
						nenner_innersum+=fwd[i][t]*bwd[i][t];
					}
					zaehler+=(1/prob)*zaehler_innersum;
					nenner+=(1/prob)*nenner_innersum;
				} // k
		
				a_new[i][j] = zaehler/nenner;
			} // j
		} // i
		
		// re calculate emission probability b
		for(int i=0; i<b.length; i++) { // zustaende
			for(int j=0; j<b[i].length; j++) {	// symbole
				double zaehler=0;
				double nenner=0;
			
				for(int k=0; k<trainsequence.size(); k++) {
					int[] sequence = trainsequence.elementAt(k);
					
					double[][] fwd = this.forwardProc(sequence);
					double[][] bwd = this.backwardProc(sequence);
					double prob = this.getProbability(sequence);
		
					double zaehler_innersum=0;
					double nenner_innersum=0;
					
					
					for(int t=0; t<sequence.length-1; t++) {
						if(sequence[t]==j) {
							zaehler_innersum+=fwd[i][t]*bwd[i][t];
						}
						nenner_innersum+=fwd[i][t]*bwd[i][t];
					}
					zaehler+=(1/prob)*zaehler_innersum;
					nenner+=(1/prob)*nenner_innersum;
				} // k
		
				b_new[i][j] = zaehler/nenner;
			} // j
		} // i
	
		this.a=a_new;
		this.b=b_new;
	}
	
	/**
	 * Traditional Forward Algorithm.
	 * 
	 * @param o the observationsequence O
	 * @return Array[State][Time] 
	 * 
	 */
	protected double[][] forwardProc(int[] o) {
		double[][] f = new double[numStates][o.length];
		for (int l = 0; l < f.length; l++) {
			f[l][0] = pi[l] * b[l][o[0]];
		}
		for (int i = 1; i < o.length; i++) {
			for (int k = 0; k < f.length; k++) {
				double sum = 0;
				for (int l = 0; l < numStates; l++) {
					sum += f[l][i-1] * a[l][k];
				}
				f[k][i] = sum * b[k][o[i]];
			}
		}
		return f;
	}
	
	/**
	 * Returns the probability that a observation sequence O belongs
	 * to this Hidden Markov Model without using the bayes classifier.
	 * Internally the well known forward algorithm is used.
	 * 
	 * @param o observation sequence
	 * @return probability that sequence o belongs to this hmm
	 */
	public double getProbability(int[] o) {
		double prob = 0.0;
		double[][] forward = this.forwardProc(o);
		//	add probabilities
		for (int i = 0; i < forward.length; i++) { // for every state
			prob += forward[i][forward[i].length - 1];
		}
		return prob;
	}
	

	/**
	 * Backward algorithm.
	 * 
	 * @param o observation sequence o
	 * @return Array[State][Time]
	 */
	protected double[][] backwardProc(int[] o) {
		int T = o.length;
		double[][] bwd = new double[numStates][T];
		/* Basisfall */
		for (int i = 0; i < numStates; i++)
			bwd[i][T - 1] = 1;
		/* Induktion */
		for (int t = T - 2; t >= 0; t--) {
			for (int i = 0; i < numStates; i++) {
				bwd[i][t] = 0;
				for (int j = 0; j < numStates; j++)
					bwd[i][t] += (bwd[j][t + 1] * a[i][j] * b[j][o[t + 1]]);
			}
		}
		return bwd;
	}

	

	/** 
	 * Prints everything about this model, including
	 * all values. For debug purposes or if you want
	 * to comprehend what happend to the model.
	 * 
	 */
	public void print() {
		DecimalFormat fmt = new DecimalFormat();
		fmt.setMinimumFractionDigits(5);
		fmt.setMaximumFractionDigits(5);
		for (int i = 0; i < numStates; i++)
			Log.write("pi(" + i + ") = " + fmt.format(pi[i]));
		Log.write("");
		for (int i = 0; i < numStates; i++) {
			for (int j = 0; j < numStates; j++)
				Log.write("a(" + i + "," + j + ") = "
						+ fmt.format(a[i][j]) + " ");
			Log.write("");
		}
		Log.write("");
		for (int i = 0; i < numStates; i++) {
			for (int k = 0; k < numObservations; k++)
				Log.write("b(" + i + "," + k + ") = "
						+ fmt.format(b[i][k]) + " ");
			Log.write("");
		}
	}
	
	public double[] getPi() {
		return this.pi;
	}
	
	public void setPi(double[] pi) {
		this.pi = pi;
	}

	public double[][] getA() {
		return this.a;
	}
	
	public void setA(double[][] a) {
		this.a = a;
	}
	
	public double[][] getB() {
		return this.b;
	}
	
	public void setB(double[][] b) {
		this.b=b;
	}
}