Matrix Factorization

MatrixFactorization.java

package prediction;

import org.apache.commons.math3.linear.Array2DRowRealMatrix;
import org.apache.commons.math3.linear.ArrayRealVector;

/**
 * Item based interpolation
 * 
 * @author Daniel Kohlsdorf
 */
public class MatrixFactorization implements Predictor {

	/**
	 * Learning rate
	 */
	public static final double ALPHA = 0.000002;
	/**
	 * Bias
	 */
	public static final double BETA = 0.002;
	/**
	 * Not set field
	 */
	public static final double LATENT = Double.NaN;
	
	private Array2DRowRealMatrix items, P, Q;	
	
	public MatrixFactorization(double items[][]) {
		this.items = new Array2DRowRealMatrix(items);
	}
		
	public void itemInterpolation(int iterations, int K) {
		
		// initalize smaller matricies
		int N = items.getRowDimension();
		int M = items.getColumnDimension();
		Array2DRowRealMatrix p = new Array2DRowRealMatrix(N, K);
		for(int i = 0; i < N; i++) {
        	for(int k = 0; k < K; k++) {
        		p.setEntry(i, k, Math.random() * 0.1);
        	}
		}
		Array2DRowRealMatrix q = new Array2DRowRealMatrix(K, M);
		for(int j = 0; j < M; j++) {
        	for(int k = 0; k < K; k++) {
        		q.setEntry(k, j, Math.random() * 0.1);
        	}
		}
		
		// minimize reconstruction error
		double last_e = 0;
	    iter:
		for(int iter = 0; iter < iterations; iter++) {
			for(int i = 0; i < N; i++) {
				for(int j = 0; j < M; j++) {
	                if(!Double.isNaN(items.getEntry(i, j))) {
	                	ArrayRealVector vec_p = new ArrayRealVector(p.getRow(i));
	                	ArrayRealVector vec_q = new ArrayRealVector(q.getColumn(j));
	                	double euv = items.getEntry(i, j) - vec_p.dotProduct(vec_q);
	                	for(int k = 0; k < K; k++) {
	                		p.setEntry(i, k, p.getEntry(i, k) + ALPHA * (2 * euv * q.getEntry(k, j)  - BETA * p.getEntry(i, k)));
	                		q.setEntry(k, j, q.getEntry(k, j) + ALPHA * (2 * euv * p.getEntry(i, k)  - BETA * q.getEntry(k, j)));
	                	}
	                }

				}
			}
			if(iter % 100 == 0) {
				double e = 0;
				for(int i = 0; i < N; i++) {
					for(int j = 0; j < M; j++) {
						if(!Double.isNaN(items.getEntry(i, j))) {
		                	ArrayRealVector vec_p = new ArrayRealVector(p.getRow(i));
		                	ArrayRealVector vec_q = new ArrayRealVector(q.getColumn(j));
							e += Math.pow(items.getEntry(i, j) - vec_p.dotProduct(vec_q), 2);
							for (int k = 0; k < K; k++) {
								e += (BETA / 2.0) * Math.pow(p.getEntry(i, k), 2) + Math.pow(q.getEntry(k, j),2);
							}
						}
					}
				}
				if(Math.abs(last_e - e) < 1e-6) {
					break iter;
				}
				last_e = e;
			}
		}
		P = p;
		Q = q;
		items = (Array2DRowRealMatrix) p.multiply(q);
	}
	
	public Array2DRowRealMatrix getItems() {
		return items;
	}
	
	public Array2DRowRealMatrix getP() {
		return P;
	}
	
	public Array2DRowRealMatrix getQ() {
		return Q;
	}
	
	public static void main(String[] args) {
		MatrixFactorization rec = new  MatrixFactorization(new double[][]{
				     {5,3,LATENT,1},
				     {4,LATENT,LATENT,1},
				     {1,1,LATENT,5},
				     {1,LATENT,LATENT,4},
				     {LATENT,1,5,4},
		});
		rec.itemInterpolation(5000, 2);
		System.out.println(rec.getItems());
	}
	
}