com.skp.experiment.math.als.hadoop.ImplicitFeedbackAlternatingLeastSquaresReasonSolver.java Source code

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/**
 * 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 com.skp.experiment.math.als.hadoop;

import java.util.HashMap;
import java.util.Iterator;
import java.util.Map;

import org.apache.mahout.math.DenseMatrix;
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 com.google.common.base.Preconditions;

/** see <a href="http://research.yahoo.com/pub/2433">Collaborative Filtering for Implicit Feedback Datasets</a> */
public class ImplicitFeedbackAlternatingLeastSquaresReasonSolver {

    private final int numFeatures;
    private final double alpha;
    private final double lambda;

    private final OpenIntObjectHashMap<Vector> Y;
    private final Matrix YtransposeY;

    @SuppressWarnings({ "rawtypes", "unchecked" })
    public ImplicitFeedbackAlternatingLeastSquaresReasonSolver(int numFeatures, double lambda, double alpha,
            OpenIntObjectHashMap Y) {
        this.numFeatures = numFeatures;
        this.lambda = lambda;
        this.alpha = alpha;
        this.Y = Y;
        YtransposeY = YtransposeY(Y);
    }

    /* 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);
    }

    /** calculate each items that this user rated and calculate similarity */
    public Map<Integer, Integer> solve(Vector recommendedItems, Vector ratings) {
        //Vector similarityVector = new DenseVector(ratings.getNumNondefaultElements());
        Map<Integer, Integer> similarities = new HashMap<Integer, Integer>();
        Matrix Wu = YtransposeY.plus(YtransponseCuMinusIYPlusLambdaI(ratings));

        Iterator<Vector.Element> recItems = recommendedItems.iterateNonZero();
        while (recItems.hasNext()) {
            Vector.Element recItem = recItems.next();
            int maxSimilarityItemID = -1;
            double maxSimilarity = 0.0;
            Iterator<Vector.Element> ratedItems = ratings.iterateNonZero();
            while (ratedItems.hasNext()) {
                Vector.Element ratedItem = ratedItems.next();
                double itemSimilarity = this.Y.get(recItem.index())
                        .dot(solve(Wu, columnVectorAsMatrix(this.Y.get(ratedItem.index()))));
                if (itemSimilarity > maxSimilarity) {
                    maxSimilarity = itemSimilarity;
                    maxSimilarityItemID = ratedItem.index();
                }
            }
            // now we have max item id
            similarities.put(recItem.index(), maxSimilarityItemID);
        }
        return similarities;
    }

    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' (Cu - I) Y +  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 +  I  add lambda on the diagonal */
        for (int feature = 0; feature < numFeatures; feature++) {
            YtransponseCuMinusIY.setQuick(feature, feature,
                    YtransponseCuMinusIY.getQuick(feature, feature) + lambda);
        }

        return YtransponseCuMinusIY;
    }

    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;
    }

}