/**
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.mahout.math.als;
import com.google.common.base.Preconditions;
import org.apache.mahout.math.DenseMatrix;
import org.apache.mahout.math.DenseVector;
import org.apache.mahout.math.Matrix;
import org.apache.mahout.math.QRDecomposition;
import org.apache.mahout.math.Vector;
import org.apache.mahout.math.Vector.Element;
import org.apache.mahout.math.function.Functions;
import org.apache.mahout.math.list.IntArrayList;
import org.apache.mahout.math.map.OpenIntObjectHashMap;
/** see <a href="http://research.yahoo.com/pub/2433">Collaborative Filtering for Implicit Feedback Datasets</a> */
public class ImplicitFeedbackAlternatingLeastSquaresSolver {
private final int numFeatures;
private final double alpha;
private final double lambda;
private final OpenIntObjectHashMap<Vector> Y;
private final Matrix YtransposeY;
public ImplicitFeedbackAlternatingLeastSquaresSolver(int numFeatures, double lambda, double alpha,
OpenIntObjectHashMap<Vector> Y) {
this.numFeatures = numFeatures;
this.lambda = lambda;
this.alpha = alpha;
this.Y = Y;
YtransposeY = getYtransposeY(Y);
}
public Vector solve(Vector ratings) {
return solve(YtransposeY.plus(getYtransponseCuMinusIYPlusLambdaI(ratings)), getYtransponseCuPu(ratings));
}
private static Vector solve(Matrix A, Matrix y) {
return new QRDecomposition(A).solve(y).viewColumn(0);
}
double confidence(double rating) {
return 1 + alpha * rating;
}
/* Y' Y */
private Matrix getYtransposeY(OpenIntObjectHashMap<Vector> Y) {
IntArrayList indexes = Y.keys();
indexes.quickSort();
int numIndexes = indexes.size();
double[][] YtY = new double[numFeatures][numFeatures];
// Compute Y'Y by dot products between the 'columns' of Y
for (int i = 0; i < numFeatures; i++) {
for (int j = i; j < numFeatures; j++) {
double dot = 0;
for (int k = 0; k < numIndexes; k++) {
Vector row = Y.get(indexes.getQuick(k));
dot += row.getQuick(i) * row.getQuick(j);
}
YtY[i][j] = dot;
if (i != j) {
YtY[j][i] = dot;
}
}
}
return new DenseMatrix(YtY, true);
}
/** Y' (Cu - I) Y + λ I */
private Matrix getYtransponseCuMinusIYPlusLambdaI(Vector userRatings) {
Preconditions.checkArgument(userRatings.isSequentialAccess(), "need sequential access to ratings!");
/* (Cu -I) Y */
OpenIntObjectHashMap<Vector> CuMinusIY = new OpenIntObjectHashMap<Vector>(userRatings.getNumNondefaultElements());
for (Element e : userRatings.nonZeroes()) {
CuMinusIY.put(e.index(), Y.get(e.index()).times(confidence(e.get()) - 1));
}
Matrix YtransponseCuMinusIY = new DenseMatrix(numFeatures, numFeatures);
/* Y' (Cu -I) Y by outer products */
for (Element e : userRatings.nonZeroes()) {
for (Vector.Element feature : Y.get(e.index()).all()) {
Vector partial = CuMinusIY.get(e.index()).times(feature.get());
YtransponseCuMinusIY.viewRow(feature.index()).assign(partial, Functions.PLUS);
}
}
/* Y' (Cu - I) Y + λ I add lambda on the diagonal */
for (int feature = 0; feature < numFeatures; feature++) {
YtransponseCuMinusIY.setQuick(feature, feature, YtransponseCuMinusIY.getQuick(feature, feature) + lambda);
}
return YtransponseCuMinusIY;
}
/** Y' Cu p(u) */
private Matrix getYtransponseCuPu(Vector userRatings) {
Preconditions.checkArgument(userRatings.isSequentialAccess(), "need sequential access to ratings!");
Vector YtransponseCuPu = new DenseVector(numFeatures);
for (Element e : userRatings.nonZeroes()) {
YtransponseCuPu.assign(Y.get(e.index()).times(confidence(e.get())), Functions.PLUS);
}
return columnVectorAsMatrix(YtransponseCuPu);
}
private Matrix columnVectorAsMatrix(Vector v) {
double[][] matrix = new double[numFeatures][1];
for (Vector.Element e : v.all()) {
matrix[e.index()][0] = e.get();
}
return new DenseMatrix(matrix, true);
}
}