net.librec.recommender.cf.ranking.LDARecommender Maven / Gradle / Ivy
/**
* Copyright (C) 2016 LibRec
*
* This file is part of LibRec.
* LibRec is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* LibRec 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 General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with LibRec. If not, see
*
* Remarks: This implementation of LDA is for implicit feedback, where users are regarded as documents
* and items as words. To directly apply LDA to explicit ratings, Ian Porteous et al. (AAAI 2008, Section Bi-LDA)
* mentioned that, one way is to treat items as documents and ratings as words. We did not provide such an LDA
* implementation for explicit ratings. Instead, we provide recommender {@code URP} as an alternative LDA model for
* explicit ratings.
*
* @author guoguibing and Keqiang Wang
*/
@ModelData({"isRanking", "lda", "userTopicProbs", "topicItemProbs", "trainMatrix"})
public class LDARecommender extends ProbabilisticGraphicalRecommender {
/**
* Dirichlet hyper-parameters of user-topic distribution: typical value is 50/K
*/
protected float initAlpha;
/**
* Dirichlet hyper-parameters of topic-item distribution, typical value is 0.01
*/
protected float initBeta;
/**
* entry[k, i]: number of tokens assigned to topic k, given item i.
*/
protected DenseMatrix topicItemNumbers;
/**
* entry[u, k]: number of tokens assigned to topic k, given user u.
*/
protected DenseMatrix userTopicNumbers;
/**
* topic assignment as list from the iterator of trainMatrix
*/
protected List topicAssignments;
/**
* entry[u]: number of tokens rated by user u.
*/
protected DenseVector userTokenNumbers;
/**
* entry[k]: number of tokens assigned to topic t.
*/
protected DenseVector topicTokenNumbers;
/**
* number of topics
*/
protected int numTopics;
/**
* vector of hyperparameters for alpha and beta
*/
protected DenseVector alpha, beta;
/**
* cumulative statistics of theta, phi
*/
protected DenseMatrix userTopicProbsSum, topicItemProbsSum;
/**
* posterior probabilities of parameters
*/
protected DenseMatrix userTopicProbs, topicItemProbs;
/**
* size of statistics
*/
protected int numStats = 0;
/**
* setup
* init member method
*
* @throws LibrecException if error occurs
*/
protected void setup() throws LibrecException {
super.setup();
numTopics = conf.getInt("rec.topic.number", 10);
userTopicProbsSum = new DenseMatrix(numUsers, numTopics);
topicItemProbsSum = new DenseMatrix(numTopics, numItems);
// initialize count variables.
userTopicNumbers = new DenseMatrix(numUsers, numTopics);
userTokenNumbers = new DenseVector(numUsers);
topicItemNumbers = new DenseMatrix(numTopics, numItems);
topicTokenNumbers = new DenseVector(numTopics);
// default value:
// homas L Griffiths and Mark Steyvers. Finding scientific topics.
// Proceedings of the National Academy of Sciences, 101(suppl 1):5228–5235, 2004.
initAlpha = conf.getFloat("rec.user.dirichlet.prior", 50.0f / numTopics);
initBeta = conf.getFloat("rec.topic.dirichlet.prior", 0.01f);
alpha = new DenseVector(numTopics);
alpha.setAll(initAlpha);
beta = new DenseVector(numItems);
beta.setAll(initBeta);
// The z_u,i are initialized to values in [0, K-1] to determine the initial state of the Markov chain.
topicAssignments = new ArrayList<>(trainMatrix.size());
for (MatrixEntry matrixEntry : trainMatrix) {
int userIdx = matrixEntry.row();
int itemIdx = matrixEntry.column();
int num = (int) (matrixEntry.get());
for(int numIdx = 0; numIdx < num; numIdx++) {
int topicIdx = Randoms.uniform(numTopics); // 0 ~ k-1
// assign a topic t to pair (u, i)
topicAssignments.add(topicIdx);
// number of items of user u assigned to topic t.
userTopicNumbers.add(userIdx, topicIdx, 1);
// total number of items of user u
userTokenNumbers.add(userIdx, 1);
// number of instances of item i assigned to topic t
topicItemNumbers.add(topicIdx, itemIdx, 1);
// total number of words assigned to topic t.
topicTokenNumbers.add(topicIdx, 1);
}
}
}
@Override
protected void eStep() {
double sumAlpha = alpha.sum();
double sumBeta = beta.sum();
// Gibbs sampling from full conditional distribution
int topicAssignmentsIdx = 0;
for (MatrixEntry matrixEntry : trainMatrix) {
int userIdx = matrixEntry.row();
int itemIdx = matrixEntry.column();
int num = (int) (matrixEntry.get());
for (int numIdx = 0; numIdx < num; numIdx++) {
int topicIdx = topicAssignments.get(topicAssignmentsIdx); // topic
userTopicNumbers.add(userIdx, topicIdx, -1);
userTokenNumbers.add(userIdx, -1);
topicItemNumbers.add(topicIdx, itemIdx, -1);
topicTokenNumbers.add(topicIdx, -1);
// do multinomial sampling via cumulative method:
double[] p = new double[numTopics];
for (topicIdx = 0; topicIdx < numTopics; topicIdx++) {
p[topicIdx] = (userTopicNumbers.get(userIdx, topicIdx) + alpha.get(topicIdx)) / (userTokenNumbers.get(userIdx)
+ sumAlpha) * (topicItemNumbers.get(topicIdx, itemIdx) + beta.get(itemIdx))
/ (topicTokenNumbers.get(topicIdx) + sumBeta);
}
// cumulating multinomial parameters
for (topicIdx = 1; topicIdx < p.length; topicIdx++) {
p[topicIdx] += p[topicIdx - 1];
}
// scaled sample because of unnormalized p[], randomly sampled a new topic t
double rand = Randoms.uniform() * p[numTopics - 1];
for (topicIdx = 0; topicIdx < p.length; topicIdx++) {
if (rand < p[topicIdx])
break;
}
// add newly estimated z_i to count variables
userTopicNumbers.add(userIdx, topicIdx, 1);
userTokenNumbers.add(userIdx, 1);
topicItemNumbers.add(topicIdx, itemIdx, 1);
topicTokenNumbers.add(topicIdx, 1);
topicAssignments.set(topicAssignmentsIdx, topicIdx);
topicAssignmentsIdx ++;
}
}
}
@Override
protected void mStep() {
double sumAlpha = alpha.sum();
double sumBeta = beta.sum();
double topicAlpha, itemBeta;
// update alpha vector
for (int topicIdx = 0; topicIdx < numTopics; topicIdx++) {
topicAlpha = alpha.get(topicIdx);
double numerator = 0, denominator = 0;
for (int itemIdx = 0; itemIdx < numUsers; itemIdx++) {
numerator += digamma(userTopicNumbers.get(itemIdx, topicIdx) + topicAlpha) - digamma(topicAlpha);
denominator += digamma(userTokenNumbers.get(itemIdx) + sumAlpha) - digamma(sumAlpha);
}
if (numerator != 0)
alpha.set(topicIdx, topicAlpha * (numerator / denominator));
}
// update beta_k
for (int itemIdx = 0; itemIdx < numItems; itemIdx++) {
itemBeta = beta.get(itemIdx);
double numerator = 0, denominator = 0;
for (int topicIdx = 0; topicIdx < numTopics; topicIdx++) {
numerator += digamma(topicItemNumbers.get(topicIdx, itemIdx) + itemBeta) - digamma(itemBeta);
denominator += digamma(topicTokenNumbers.get(topicIdx) + sumBeta) - digamma(sumBeta);
}
if (numerator != 0)
beta.set(itemIdx, itemBeta * (numerator / denominator));
}
}
/**
* Add to the statistics the values of theta and phi for the current state.
*/
protected void readoutParams() {
double sumAlpha = alpha.sum();
double sumBeta = beta.sum();
double val;
for (int userIdx = 0; userIdx < numUsers; userIdx++) {
for (int factorIdx = 0; factorIdx < numTopics; factorIdx++) {
val = (userTopicNumbers.get(userIdx, factorIdx) + alpha.get(factorIdx)) / (userTokenNumbers.get(userIdx) + sumAlpha);
userTopicProbsSum.add(userIdx, factorIdx, val);
}
}
for (int factorIdx = 0; factorIdx < numTopics; factorIdx++) {
for (int itemIdx = 0; itemIdx < numItems; itemIdx++) {
val = (topicItemNumbers.get(factorIdx, itemIdx) + beta.get(itemIdx)) / (topicTokenNumbers.get(factorIdx) + sumBeta);
topicItemProbsSum.add(factorIdx, itemIdx, val);
}
}
numStats++;
}
@Override
protected void estimateParams() {
userTopicProbs = userTopicProbsSum.scale(1.0 / numStats);
topicItemProbs = topicItemProbsSum.scale(1.0 / numStats);
}
@Override
protected double predict(int userIdx, int itemIdx) throws LibrecException {
return DenseMatrix.product(userTopicProbs, userIdx, topicItemProbs, itemIdx);
}
}