NMF(非负矩阵分解)的SGD（随机梯度下降）实现

NMF把一个矩阵分解为两个矩阵的乘积，可以用来解决很多问题，例如：用户聚类、item聚类、预测（补全）用户对item的评分、个性化推荐等问题。NMF的过程可以转化为最小化损失函数（即误差函数）的过程，其实整个问题也就是一个最优化的问题。详细实现过程如下：（其中，输入矩阵很多时候会比较稀疏，即很多元素都是缺失项，故数据存储采用的是libsvm的格式，这个类在此忽略）

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1. package NMF_danji; 
2.  
3. import java.io.File; 
4. import java.util.ArrayList; 
5.  
6. /**
7. * @author 玉心sober： http://weibo.com/karensober
8. * @date 2013-05-19
9. *
10. * */ 
11. public class NMF { 
12.     private Dataset dataset = null; 
13.     private int M = -1;// 行数 
14.     private int V = -1;// 列数 
15.     private int K = -1;// 隐含主题数 
16.     double[][] P; 
17.     double[][] Q; 
18.  
19.     public NMF(String datafileName,int topics) { 
20.         File datafile = new File(datafileName); 
21.         if (datafile.exists()) { 
22.             if ((this.dataset =new Dataset(datafile)) == null) { 
23.                 System.out.println(datafileName + " is null"); 
24.             } 
25.             this.M = this.dataset.size(); 
26.             this.V = this.dataset.getFeatureNum(); 
27.             this.K = topics; 
28.         } else { 
29.             System.out.println(datafileName + " doesn't exist"); 
30.         } 
31.     } 
32.  
33.     public void initPQ() { 
34.         P = new double[this.M][this.K]; 
35.         Q = new double[this.K][this.V]; 
36.  
37.         for (int k =0; k < K; k++) { 
38.             for (int i =0; i < M; i++) { 
39.                 P[i][k] = Math.random(); 
40.             } 
41.             for (int j =0; j < V; j++) { 
42.                 Q[k][j] = Math.random(); 
43.             } 
44.         } 
45.     } 
46.  
47.     // 随机梯度下降，更新参数 
48.     public void updatePQ(double alpha,double beta) { 
49.         for (int i =0; i < M; i++) { 
50.             ArrayList<Feature> Ri = this.dataset.getDataAt(i).getAllFeature(); 
51.             for (Feature Rij : Ri) { 
52.                 // eij=Rij.weight-PQ for updating P and Q 
53.                 double PQ =0; 
54.                 for (int k =0; k < K; k++) { 
55.                     PQ += P[i][k] * Q[k][Rij.dim]; 
56.                 } 
57.                 double eij = Rij.weight - PQ; 
58.  
59.                 // update Pik and Qkj 
60.                 for (int k =0; k < K; k++) { 
61.                     double oldPik = P[i][k]; 
62.                     P[i][k] += alpha 
63.                             * (2 * eij * Q[k][Rij.dim] - beta * P[i][k]); 
64.                     Q[k][Rij.dim] += alpha 
65.                             * (2 * eij * oldPik - beta * Q[k][Rij.dim]); 
66.                 } 
67.             } 
68.         } 
69.     } 
70.  
71.     // 每步迭代后计算SSE 
72.     public double getSSE(double beta) { 
73.         double sse = 0; 
74.         for (int i =0; i < M; i++) { 
75.             ArrayList<Feature> Ri = this.dataset.getDataAt(i).getAllFeature(); 
76.             for (Feature Rij : Ri) { 
77.                 double PQ =0; 
78.                 for (int k =0; k < K; k++) { 
79.                     PQ += P[i][k] * Q[k][Rij.dim]; 
80.                 } 
81.                 sse += Math.pow((Rij.weight - PQ), 2); 
82.             } 
83.         } 
84.  
85.         for (int i =0; i < M; i++) { 
86.             for (int k =0; k < K; k++) { 
87.                 sse += ((beta / 2) * (Math.pow(P[i][k],2))); 
88.             } 
89.         } 
90.  
91.         for (int i =0; i < V; i++) { 
92.             for (int k =0; k < K; k++) { 
93.                 sse += ((beta / 2) * (Math.pow(Q[k][i],2))); 
94.             } 
95.         } 
96.  
97.         return sse; 
98.     } 
99.  
100.     // 采用随机梯度下降方法迭代求解参数，即求解最终分解后的矩阵 
101.     public boolean doNMF(int iters,double alpha, double beta) { 
102.         for (int step =0; step < iters; step++) { 
103.             updatePQ(alpha, beta); 
104.             double sse = getSSE(beta); 
105.             if (step % 100 == 0) 
106.                 System.out.println("step " + step +" SSE = " + sse); 
107.         } 
108.         return true; 
109.     } 
110.  
111.     public void printMatrix() { 
112.         System.out.println("===========原始矩阵=============="); 
113.         for (int i =0; i < this.dataset.size(); i++) { 
114.             for (Feature feature : this.dataset.getDataAt(i).getAllFeature()) { 
115.                 System.out.print(feature.dim + ":" + feature.weight + " "); 
116.             } 
117.             System.out.println(); 
118.         } 
119.     } 
120.  
121.     public void printFacMatrxi() { 
122.         System.out.println("===========分解矩阵=============="); 
123.         for (int i =0; i < P.length; i++) { 
124.             for (int j =0; j < Q[0].length; j++) { 
125.                 double cell =0; 
126.                 for (int k =0; k < K; k++) { 
127.                     cell += P[i][k] * Q[k][j]; 
128.                 } 
129.                 System.out.print(baoliu(cell, 3) + " "); 
130.             } 
131.             System.out.println(); 
132.         } 
133.     } 
134.  
135.     // 为double类型变量保留有效数字 
136.     public staticdouble baoliu(double d,int n) { 
137.         double p = Math.pow(10, n); 
138.         return Math.round(d * p) / p; 
139.     } 
140.  
141.     public staticvoid main(String[] args) { 
142.         double alpha = 0.002; 
143.         double beta = 0.02; 
144.  
145.         NMF nmf = new NMF("D:\\myEclipse\\graphModel\\data\\nmfinput.txt",10); 
146.         nmf.initPQ(); 
147.         nmf.doNMF(3000, alpha, beta); 
148.  
149.         // 输出原始矩阵 
150.         nmf.printMatrix(); 
151.  
152.         // 输出分解后矩阵 
153.         nmf.printFacMatrxi(); 
154.     } 
155. } 

package NMF_danji;import java.io.File;import java.util.ArrayList;/** * @author 玉心sober： http://weibo.com/karensober * @date 2013-05-19 *  * */public class NMF {private Dataset dataset = null;private int M = -1; // 行数private int V = -1; // 列数private int K = -1; // 隐含主题数double[][] P;double[][] Q;public NMF(String datafileName, int topics) {File datafile = new File(datafileName);if (datafile.exists()) {if ((this.dataset = new Dataset(datafile)) == null) {System.out.println(datafileName + " is null");}this.M = this.dataset.size();this.V = this.dataset.getFeatureNum();this.K = topics;} else {System.out.println(datafileName + " doesn't exist");}}public void initPQ() {P = new double[this.M][this.K];Q = new double[this.K][this.V];for (int k = 0; k < K; k++) {for (int i = 0; i < M; i++) {P[i][k] = Math.random();}for (int j = 0; j < V; j++) {Q[k][j] = Math.random();}}}// 随机梯度下降，更新参数public void updatePQ(double alpha, double beta) {for (int i = 0; i < M; i++) {ArrayList<Feature> Ri = this.dataset.getDataAt(i).getAllFeature();for (Feature Rij : Ri) {// eij=Rij.weight-PQ for updating P and Qdouble PQ = 0;for (int k = 0; k < K; k++) {PQ += P[i][k] * Q[k][Rij.dim];}double eij = Rij.weight - PQ;// update Pik and Qkjfor (int k = 0; k < K; k++) {double oldPik = P[i][k];P[i][k] += alpha* (2 * eij * Q[k][Rij.dim] - beta * P[i][k]);Q[k][Rij.dim] += alpha* (2 * eij * oldPik - beta * Q[k][Rij.dim]);}}}}// 每步迭代后计算SSEpublic double getSSE(double beta) {double sse = 0;for (int i = 0; i < M; i++) {ArrayList<Feature> Ri = this.dataset.getDataAt(i).getAllFeature();for (Feature Rij : Ri) {double PQ = 0;for (int k = 0; k < K; k++) {PQ += P[i][k] * Q[k][Rij.dim];}sse += Math.pow((Rij.weight - PQ), 2);}}for (int i = 0; i < M; i++) {for (int k = 0; k < K; k++) {sse += ((beta / 2) * (Math.pow(P[i][k], 2)));}}for (int i = 0; i < V; i++) {for (int k = 0; k < K; k++) {sse += ((beta / 2) * (Math.pow(Q[k][i], 2)));}}return sse;}// 采用随机梯度下降方法迭代求解参数，即求解最终分解后的矩阵public boolean doNMF(int iters, double alpha, double beta) {for (int step = 0; step < iters; step++) {updatePQ(alpha, beta);double sse = getSSE(beta);if (step % 100 == 0)System.out.println("step " + step + " SSE = " + sse);}return true;}public void printMatrix() {System.out.println("===========原始矩阵==============");for (int i = 0; i < this.dataset.size(); i++) {for (Feature feature : this.dataset.getDataAt(i).getAllFeature()) {System.out.print(feature.dim + ":" + feature.weight + " ");}System.out.println();}}public void printFacMatrxi() {System.out.println("===========分解矩阵==============");for (int i = 0; i < P.length; i++) {for (int j = 0; j < Q[0].length; j++) {double cell = 0;for (int k = 0; k < K; k++) {cell += P[i][k] * Q[k][j];}System.out.print(baoliu(cell, 3) + " ");}System.out.println();}}// 为double类型变量保留有效数字public static double baoliu(double d, int n) {double p = Math.pow(10, n);return Math.round(d * p) / p;}public static void main(String[] args) {double alpha = 0.002;double beta = 0.02;NMF nmf = new NMF("D:\\myEclipse\\graphModel\\data\\nmfinput.txt", 10);nmf.initPQ();nmf.doNMF(3000, alpha, beta);// 输出原始矩阵nmf.printMatrix();// 输出分解后矩阵nmf.printFacMatrxi();}}

结果：
...

step 2900 SSE = 0.5878774074369989
===========原始矩阵==============
0:9.0 1:2.0 2:1.0 3:1.0 4:1.0
0:8.0 1:3.0 2:2.0 3:1.0
0:3.0 3:1.0 4:2.0 5:8.0
1:1.0 3:2.0 4:4.0 5:7.0
0:2.0 1:1.0 2:1.0 4:1.0 5:3.0
===========分解矩阵==============
8.959 2.007 1.007 0.996 1.007 6.293
7.981 2.972 1.989 1.005 2.046 7.076
3.01 1.601 1.773 1.003 2.005 7.968
4.821 1.009 2.209 1.984 3.968 6.988
2.0 0.991 0.984 0.51 1.0 2.994