/**
* 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.function.Functions;
import org.apache.mahout.math.list.IntArrayList;
import org.apache.mahout.math.map.OpenIntObjectHashMap;
import java.util.Iterator;
/** 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 Y) {
this.numFeatures = numFeatures;
this.lambda = lambda;
this.alpha = alpha;
this.Y = Y;
YtransposeY = YtransposeY(Y);
}
public Vector solve(Vector ratings) {
return solve(YtransposeY.plus(YtransponseCuMinusIYPlusLambdaI(ratings)), YtransponseCuPu(ratings));
}
private static Vector solve(Matrix A, Matrix y) {
return new QRDecomposition(A).solve(y).viewColumn(0);
}
protected double confidence(double rating) {
return 1 + alpha * rating;
}
/* Y' Y */
private Matrix YtransposeY(OpenIntObjectHashMap<Vector> Y) {
Matrix compactedY = new DenseMatrix(Y.size(), numFeatures);
IntArrayList indexes = Y.keys();
indexes.quickSort();
int row = 0;
for (int index : indexes.elements()) {
compactedY.assignRow(row++, Y.get(index));
}
return compactedY.transpose().times(compactedY);
}
/** Y' (Cu - I) Y + λ I */
private Matrix YtransponseCuMinusIYPlusLambdaI(Vector userRatings) {
Preconditions.checkArgument(userRatings.isSequentialAccess(), "need sequential access to ratings!");
/* (Cu -I) Y */
OpenIntObjectHashMap<Vector> CuMinusIY = new OpenIntObjectHashMap<Vector>();
Iterator<Vector.Element> ratings = userRatings.iterateNonZero();
while (ratings.hasNext()) {
Vector.Element e = ratings.next();
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 */
ratings = userRatings.iterateNonZero();
while (ratings.hasNext()) {
Vector.Element e = ratings.next();
for (Vector.Element feature : Y.get(e.index())) {
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 YtransponseCuPu(Vector userRatings) {
Preconditions.checkArgument(userRatings.isSequentialAccess(), "need sequential access to ratings!");
Vector YtransponseCuPu = new DenseVector(numFeatures);
Iterator<Vector.Element> ratings = userRatings.iterateNonZero();
while (ratings.hasNext()) {
Vector.Element e = ratings.next();
YtransponseCuPu.assign(Y.get(e.index()).times(confidence(e.get())), Functions.PLUS);
}
return columnVectorAsMatrix(YtransponseCuPu);
}
private Matrix columnVectorAsMatrix(Vector v) {
Matrix matrix = new DenseMatrix(numFeatures, 1);
for (Vector.Element e : v) {
matrix.setQuick(e.index(), 0, e.get());
}
return matrix;
}
}