学习来源：日撸 Java 三百行（61-70天，决策树与集成学习）_闵帆的博客——CSDN博客
矩阵分解
1.奇异值分解
奇异值分解（SVD）是一种矩阵分解算法，用于将矩阵简化为其组成部分，从而简化后续矩阵计算。SVD的表达式为：
其中：
例：矩阵
2.矩阵分解
矩阵分解算法是由奇异值分解算法（SVD）演变而来，传统的SVD只能对数据稠密的矩阵进行分解。而在推荐系统中，评分矩阵是极度稀疏的，因此对SVD进行改进来对用户对项目的评分进行预测。
3.BasicSVD
BasicSVD是最简单的矩阵分解方法，它将评分矩阵分解为两个低阶矩阵的乘积，在实际推荐计算时不再使用原矩阵，而是使用分解得到的两个低阶矩阵。
图1.评分矩阵例子
图1描述了5个用户（
4.代码部分
1）衡量矩阵分解优劣的指标采用的是MAE。即预测评分与实际评分差值的绝对值之和与预测评分数之比。MAE的值越小越好。
2）由学习因子
3）代码如下：
package JavaDay20;
import java.io.*;
import java.util.Random;
/**
* Matrix factorization for recommender systems.
*
* @author Ke-Xiong Wang
*/
public class MatrixFactorization {
/**
* Used to generate random numbers.
*/
Random rand = new Random();
/**
* Number of users.
*/
int numUsers;
/**
* Number of items.
*/
int numItems;
/**
* Number of ratings.
*/
int numRatings;
/**
* Training data.
*/
Triple[] dataset;
/**
* A parameter for controlling learning regular.
*/
double alpha;
/**
* A parameter for controlling the learning speed.
*/
double lambda;
/**
* The low rank of the small matrices.
*/
int rank;
/**
* The user matrix U.
*/
double[][] userSubspace;
/**
* The item matrix V.
*/
double[][] itemSubspace;
/**
* The lower bound of the rating value.
*/
double ratingLowerBound;
/**
* The upper bound of the rating value.
*/
double ratingUpperBound;
/**
************************
* The first constructor.
*
* @param paraFilename
* The data filename.
* @param paraNumUsers
* The number of users.
* @param paraNumItems
* The number of items.
* @param paraNumRatings
* The number of ratings.
************************
*/
public MatrixFactorization(String paraFilename, int paraNumUsers, int paraNumItems,
int paraNumRatings, double paraRatingLowerBound, double paraRatingUpperBound) {
numUsers = paraNumUsers;
numItems = paraNumItems;
numRatings = paraNumRatings;
ratingLowerBound = paraRatingLowerBound;
ratingUpperBound = paraRatingUpperBound;
try {
readData(paraFilename, paraNumUsers, paraNumItems, paraNumRatings);
// adjustUsingMeanRating();
} catch (Exception ee) {
System.out.println("File " + paraFilename + " cannot be read! " + ee);
System.exit(0);
} // Of try
}// Of the first constructor
/**
************************
* Set parameters.
*
* @param paraRank
* The given rank.
* @throws IOException
************************
*/
public void setParameters(int paraRank, double paraAlpha, double paraLambda) {
rank = paraRank;
alpha = paraAlpha;
lambda = paraLambda;
}// Of setParameters
/**
************************
* Read the data from the file.
*
* @param paraFilename
* The given file.
* @throws IOException
************************
*/
public void readData(String paraFilename, int paraNumUsers, int paraNumItems,
int paraNumRatings) throws IOException {
File tempFile = new File(paraFilename);
if (!tempFile.exists()) {
System.out.println("File " + paraFilename + " does not exists.");
System.exit(0);
} // Of if
BufferedReader tempBufferReader = new BufferedReader(new FileReader(tempFile));
// Allocate space.
dataset = new Triple[paraNumRatings];
String tempString;
String[] tempStringArray;
for (int i = 0; i < paraNumRatings; i++) {
tempString = tempBufferReader.readLine();
tempStringArray = tempString.split(",");
dataset[i] = new Triple(Integer.parseInt(tempStringArray[0]),
Integer.parseInt(tempStringArray[1]), Double.parseDouble(tempStringArray[2]));
} // Of for i
tempBufferReader.close();
}// Of readData
/**
************************
* Initialize subspaces. Each value is in [0, 1].
************************
*/
void initializeSubspaces() {
userSubspace = new double[numUsers][rank];
for (int i = 0; i < numUsers; i++) {
for (int j = 0; j < rank; j++) {
userSubspace[i][j] = rand.nextDouble();
} // Of for j
} // Of for i
itemSubspace = new double[numItems][rank];
for (int i = 0; i < numItems; i++) {
for (int j = 0; j < rank; j++) {
itemSubspace[i][j] = rand.nextDouble();
} // Of for j
} // Of for i
}// Of initializeSubspaces
/**
************************
* Predict the rating of the user to the item
*
* @param paraUser
* The user index.
************************
*/
public double predict(int paraUser, int paraItem) {
double resultValue = 0;
for (int i = 0; i < rank; i++) {
// The row vector of a user and the column vector of an item
resultValue += userSubspace[paraUser][i] * itemSubspace[paraItem][i];
} // Of for i
return resultValue;
}// Of predict
/**
************************
* Train.
*
* @param paraRounds
* The number of rounds.
************************
*/
public void train(int paraRounds) {
initializeSubspaces();
for (int i = 0; i < paraRounds; i++) {
updateNoRegular();
if (i % 50 == 0) {
// Show the process
System.out.println("Round " + i);
System.out.println("MAE: " + mae());
} // Of if
} // Of for i
}// Of train
/**
************************
* Update sub-spaces using the training data.
************************
*/
public void updateNoRegular() {
for (int i = 0; i < numRatings; i++) {
int tempUserId = dataset[i].user;
int tempItemId = dataset[i].item;
double tempRate = dataset[i].rating;
double tempResidual = tempRate - predict(tempUserId, tempItemId); // Residual
// Update user subspace
double tempValue = 0;
for (int j = 0; j < rank; j++) {
tempValue = 2 * tempResidual * itemSubspace[tempItemId][j];
userSubspace[tempUserId][j] += alpha * tempValue;
} // Of for j
// Update item subspace
for (int j = 0; j < rank; j++) {
tempValue = 2 * tempResidual * userSubspace[tempUserId][j];
itemSubspace[tempItemId][j] += alpha * tempValue;
} // Of for j
} // Of for i
}// Of updateNoRegular
/**
************************
* Compute the RSME.
*
* @return RSME of the current factorization.
************************
*/
public double rsme() {
double resultRsme = 0;
int tempTestCount = 0;
for (int i = 0; i < numRatings; i++) {
int tempUserIndex = dataset[i].user;
int tempItemIndex = dataset[i].item;
double tempRate = dataset[i].rating;
double tempPrediction = predict(tempUserIndex, tempItemIndex);// +
// DataInfo.mean_rating;
if (tempPrediction < ratingLowerBound) {
tempPrediction = ratingLowerBound;
} else if (tempPrediction > ratingUpperBound) {
tempPrediction = ratingUpperBound;
} // Of if
double tempError = tempRate - tempPrediction;
resultRsme += tempError * tempError;
tempTestCount++;
} // Of for i
return Math.sqrt(resultRsme / tempTestCount);
}// Of rsme
/**
************************
* Compute the MAE.
*
* @return MAE of the current factorization.
************************
*/
public double mae() {
double resultMae = 0;
int tempTestCount = 0;
for (int i = 0; i < numRatings; i++) {
int tempUserIndex = dataset[i].user;
int tempItemIndex = dataset[i].item;
double tempRate = dataset[i].rating;
double tempPrediction = predict(tempUserIndex, tempItemIndex);
if (tempPrediction < ratingLowerBound) {
tempPrediction = ratingLowerBound;
} // Of if
if (tempPrediction > ratingUpperBound) {
tempPrediction = ratingUpperBound;
} // Of if
double tempError = tempRate - tempPrediction;
resultMae += Math.abs(tempError);
// System.out.println("resultMae: " + resultMae);
tempTestCount++;
} // Of for i
return (resultMae / tempTestCount);
}// Of mae
/**
************************
* Compute the MAE.
*
* @return MAE of the current factorization.
************************
*/
public static void testTrainingTesting(String paraFilename, int paraNumUsers, int paraNumItems,
int paraNumRatings, double paraRatingLowerBound, double paraRatingUpperBound,
int paraRounds) {
try {
// Step 1. read the training and testing data
MatrixFactorization tempMF = new MatrixFactorization(paraFilename, paraNumUsers,
paraNumItems, paraNumRatings, paraRatingLowerBound, paraRatingUpperBound);
tempMF.setParameters(5, 0.0001, 0.005);
// Step 3. update and predict
System.out.println("Begin Training ! ! !");
tempMF.train(paraRounds);
double tempMAE = tempMF.mae();
double tempRSME = tempMF.rsme();
System.out.println("Finally, MAE = " + tempMAE + ", RSME = " + tempRSME);
} catch (Exception e) {
e.printStackTrace();
} // Of try
}// Of testTrainingTesting
/**
************************
* @param args
************************
*/
public static void main(String args[]) {
testTrainingTesting("D:/data/movielens-943u1682m.txt", 943, 1682, 10000, 1, 5, 2000);
}// Of main
public class Triple {
public int user;
public int item;
public double rating;
/**
*********************
* The constructor.
*********************
*/
public Triple() {
user = -1;
item = -1;
rating = -1;
}// Of the first constructor
/**
*********************
* The constructor.
*********************
*/
public Triple(int paraUser, int paraItem, double paraRating) {
user = paraUser;
item = paraItem;
rating = paraRating;
}// Of the first constructor
/**
*********************
* Show me.
*********************
*/
public String toString() {
return "" + user + ", " + item + ", " + rating;
}// Of toString
}// Of class Triple
}// Of class MatrixFactorization
运行结果
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