头文件

 1 #pragma once
 2 
 3 #include <iostream>
 4 #include <cmath>
 5 #include <vector>
 6 #include <stdlib.h>
 7 #include <time.h>
 8 
 9 using namespace std;
10 
11 #define innode 2        //输入结点数
12 #define hidenode 4      //隐含结点数
13 #define hidelayer 1     //隐含层数
14 #define outnode 1       //输出结点数
15 #define learningRate 0.9//学习速率，alpha
16 
17 // --- -1~1 随机数产生器 --- 
18 inline double get_11Random()    // -1 ~ 1
19 {
20     return ((2.0*(double)rand()/RAND_MAX) - 1);
21 }
22 
23 // --- sigmoid 函数 --- 
24 inline double sigmoid(double x)
25 {
26     double ans = 1 / (1+exp(-x));
27     return ans;
28 }
29 
30 // --- 输入层节点。包含以下分量：--- 
31 // 1.value:     固定输入值； 
32 // 2.weight:    面对第一层隐含层每个节点都有权值； 
33 // 3.wDeltaSum: 面对第一层隐含层每个节点权值的delta值累积
34 typedef struct inputNode
35 {
36     double value;
37     vector<double> weight, wDeltaSum;
38 }inputNode;
39 
40 // --- 输出层节点。包含以下数值：--- 
41 // 1.value:     节点当前值； 
42 // 2.delta:     与正确输出值之间的delta值； 
43 // 3.rightout:  正确输出值
44 // 4.bias:      偏移量
45 // 5.bDeltaSum: bias的delta值的累积，每个节点一个
46 typedef struct outputNode   // 输出层节点
47 {
48     double value, delta, rightout, bias, bDeltaSum;
49 }outputNode;
50 
51 // --- 隐含层节点。包含以下数值：--- 
52 // 1.value:     节点当前值； 
53 // 2.delta:     BP推导出的delta值；
54 // 3.bias:      偏移量
55 // 4.bDeltaSum: bias的delta值的累积，每个节点一个
56 // 5.weight:    面对下一层（隐含层/输出层）每个节点都有权值； 
57 // 6.wDeltaSum： weight的delta值的累积，面对下一层（隐含层/输出层）每个节点各自积累
58 typedef struct hiddenNode   // 隐含层节点
59 {
60     double value, delta, bias, bDeltaSum;
61     vector<double> weight, wDeltaSum;
62 }hiddenNode;
63 
64 // --- 单个样本 --- 
65 typedef struct sample
66 {
67     vector<double> in, out;
68 }sample;
69 
70 // --- BP神经网络 --- 
71 class BpNet
72 {
73 public:
74     BpNet();    //构造函数
75     void forwardPropagationEpoc();  // 单个样本前向传播
76     void backPropagationEpoc();     // 单个样本后向传播
77     // 更新 weight, bias
78     void training (static vector<sample> sampleGroup, double threshold);
79     // 神经网络预测
80     void predict  (vector<sample>& testGroup);                          
81     // 设置学习样本输入
82     void setInput (static vector<double> sampleIn); 
83     // 设置学习样本输出        
84     void setOutput(static vector<double> sampleOut);    
85 
86 public:
87     double error;
88     inputNode* inputLayer[innode];// 输入层（仅一层）
89     outputNode* outputLayer[outnode];// 输出层（仅一层）
90     // 隐含层（可能有多层）
91     hiddenNode* hiddenLayer[hidelayer][hidenode];
92 };

主程序：main

 1 #include "BP.h"
 2 
 3 int main()
 4 {
 5     BpNet testNet;
 6 
 7     // 学习样本
 8     vector<double> samplein[4];
 9     vector<double> sampleout[4];
10     samplein[0].push_back(0); samplein[0].push_back(0); sampleout[0].push_back(0); 
11     samplein[1].push_back(0); samplein[1].push_back(1); sampleout[1].push_back(1); 
12     samplein[2].push_back(1); samplein[2].push_back(0); sampleout[2].push_back(1); 
13     samplein[3].push_back(1); samplein[3].push_back(1); sampleout[3].push_back(0); 
14     sample sampleInOut[4];
15     for (int i = 0; i < 4; i++)
16     {
17         sampleInOut[i].in = samplein[i];
18         sampleInOut[i].out = sampleout[i];
19     }
20     vector<sample> sampleGroup(sampleInOut, sampleInOut + 4);
21     testNet.training(sampleGroup, 0.0001);
22 
23     // 测试数据
24     vector<double> testin[4];
25     vector<double> testout[4];
26     testin[0].push_back(0.1);   testin[0].push_back(0.2);
27     testin[1].push_back(0.15);  testin[1].push_back(0.9);
28     testin[2].push_back(1.1);   testin[2].push_back(0.01);
29     testin[3].push_back(0.88);  testin[3].push_back(1.03);
30     sample testInOut[4];
31     for (int i = 0; i < 4; i++) testInOut[i].in = testin[i];
32     vector<sample> testGroup(testInOut, testInOut + 4);
33 
34     // 预测测试数据，并输出结果
35     testNet.predict(testGroup);
36     for (int i = 0; i < testGroup.size(); i++)
37     {
38         for (int j = 0; j < testGroup[i].in.size(); j++) 
39         cout << testGroup[i].in[j] << "\t";
40         cout << "-- prediction :";
41         for (int j = 0; j < testGroup[i].out.size(); j++) 
42         cout << testGroup[i].out[j] << "\t";
43         cout << endl;
44     }
45 
46     system("pause");
47     return 0;
48 }

源程序：bp.cpp

  1 #include "BP.h"
  2 
  3 using namespace std;
  4 
  5 BpNet::BpNet()
  6 {
  7     srand((unsigned)time(NULL)); // 随机数种子    
  8     error = 100.f;      // error初始值，极大值即可
  9 
 10     // 初始化输入层
 11     for (int i = 0; i < innode; i++)
 12     {
 13         inputLayer[i] = new inputNode();
 14         for (int j = 0; j < hidenode; j++) 
 15         {
 16             inputLayer[i]->weight.push_back(get_11Random());
 17             inputLayer[i]->wDeltaSum.push_back(0.f);
 18         }
 19     }
 20 
 21     // 初始化隐藏层
 22     for (int i = 0; i < hidelayer; i++)
 23     {
 24         if (i == hidelayer - 1)
 25         {
 26             for (int j = 0; j < hidenode; j++)
 27             {
 28                 hiddenLayer[i][j] = new hiddenNode();
 29                 hiddenLayer[i][j]->bias = get_11Random();
 30                 for (int k = 0; k < outnode; k++) 
 31                 {
 32                     hiddenLayer[i][j]->weight.push_back(get_11Random());
 33                     hiddenLayer[i][j]->wDeltaSum.push_back(0.f);
 34                 }
 35             }
 36         }
 37         else
 38         {
 39             for (int j = 0; j < hidenode; j++)
 40             {
 41                 hiddenLayer[i][j] = new hiddenNode();
 42                 hiddenLayer[i][j]->bias = get_11Random();
 43                 for (int k = 0; k < hidenode; k++) 
 44                 {
 45                     hiddenLayer[i][j]->weight.push_back(get_11Random());
 46                 }
 47             }
 48         }
 49     }
 50 
 51     // 初始化输出层
 52     for (int i = 0; i < outnode; i++)
 53     {
 54         outputLayer[i] = new outputNode();
 55         outputLayer[i]->bias = get_11Random();
 56     }
 57 }
 58 
 59 void BpNet::forwardPropagationEpoc()
 60 {
 61     // forward propagation on hidden layer
 62     for (int i = 0; i < hidelayer; i++)
 63     {
 64         if (i == 0)
 65         {
 66             for (int j = 0; j < hidenode; j++)
 67             {
 68                 double sum = 0.f;
 69                 for (int k = 0; k < innode; k++) 
 70                 {
 71                     sum += inputLayer[k]->value * inputLayer[k]->weight[j];
 72                 }
 73                 sum += hiddenLayer[i][j]->bias;
 74                 hiddenLayer[i][j]->value = sigmoid(sum);
 75             }
 76         }
 77         else
 78         {
 79             for (int j = 0; j < hidenode; j++)
 80             {
 81                 double sum = 0.f;
 82                 for (int k = 0; k < hidenode; k++) 
 83                 {
 84                     sum += hiddenLayer[i-1][k]->value * hiddenLayer[i-1][k]->weight[j];
 85                 }
 86                 sum += hiddenLayer[i][j]->bias;
 87                 hiddenLayer[i][j]->value = sigmoid(sum);
 88             }
 89         }
 90     }
 91 
 92     // forward propagation on output layer
 93     for (int i = 0; i < outnode; i++)
 94     {
 95         double sum = 0.f;
 96         for (int j = 0; j < hidenode; j++)
 97         {
 98             sum += hiddenLayer[hidelayer-1][j]->value * hiddenLayer[hidelayer-1][j]->weight[i];
 99         }
100         sum += outputLayer[i]->bias;
101         outputLayer[i]->value = sigmoid(sum);
102     }
103 }
104 
105 void BpNet::backPropagationEpoc()
106 {
107     // backward propagation on output layer
108     // -- compute delta
109     for (int i = 0; i < outnode; i++)
110     {
111         double tmpe = fabs(outputLayer[i]->value-outputLayer[i]->rightout);
112         error += tmpe * tmpe / 2;
113 
114         outputLayer[i]->delta 
115             = (outputLayer[i]->value-outputLayer[i]->rightout)*(1-outputLayer[i]->value)*outputLayer[i]->value;
116     }
117 
118     // backward propagation on hidden layer
119     // -- compute delta
120     for (int i = hidelayer - 1; i >= 0; i--)    // 反向计算
121     {
122         if (i == hidelayer - 1)
123         {
124             for (int j = 0; j < hidenode; j++)
125             {
126                 double sum = 0.f;
127                 for (int k=0; k<outnode; k++)
128                 {
129                     sum += outputLayer[k]->delta * hiddenLayer[i][j]->weight[k];
130                 }
131                 hiddenLayer[i][j]->delta
132                     = sum * (1 - hiddenLayer[i][j]->value) * hiddenLayer[i][j]->value;
133             }
134         }
135         else
136         {
137             for (int j = 0; j < hidenode; j++)
138             {
139                 double sum = 0.f;
140                 for (int k=0; k<hidenode; k++)
141                 {
142                     sum += hiddenLayer[i + 1][k]->delta * hiddenLayer[i][j]->weight[k];
143                 }
144                 hiddenLayer[i][j]->delta 
145                     = sum * (1 - hiddenLayer[i][j]->value) * hiddenLayer[i][j]->value;
146             }
147         }
148     }
149 
150     // backward propagation on input layer
151     // -- update weight delta sum
152     for (int i = 0; i < innode; i++)
153     {
154         for (int j = 0; j < hidenode; j++)
155         {
156             inputLayer[i]->wDeltaSum[j] += inputLayer[i]->value * hiddenLayer[0][j]->delta;
157         }
158     }
159 
160     // backward propagation on hidden layer
161     // -- update weight delta sum & bias delta sum
162     for (int i = 0; i < hidelayer; i++)
163     {
164         if (i == hidelayer - 1)
165         {
166             for (int j = 0; j < hidenode; j++)
167             {
168                 hiddenLayer[i][j]->bDeltaSum += hiddenLayer[i][j]->delta;
169                 for (int k = 0; k < outnode; k++)
170                 { 
171                     hiddenLayer[i][j]->wDeltaSum[k] += hiddenLayer[i][j]->value * outputLayer[k]->delta; 
172                 }
173             }
174         }
175         else
176         {
177             for (int j = 0; j < hidenode; j++)
178             {
179                 hiddenLayer[i][j]->bDeltaSum += hiddenLayer[i][j]->delta;
180                 for (int k = 0; k < hidenode; k++)
181                 { 
182                     hiddenLayer[i][j]->wDeltaSum[k] += hiddenLayer[i][j]->value * hiddenLayer[i+1][k]->delta; 
183                 }
184             }
185         }
186     }
187 
188     // backward propagation on output layer
189     // -- update bias delta sum
190     for (int i = 0; i < outnode; i++) outputLayer[i]->bDeltaSum += outputLayer[i]->delta;
191 }
192 
193 void BpNet::training(static vector<sample> sampleGroup, double threshold)
194 {
195     int sampleNum = sampleGroup.size();
196 
197     while(error > threshold)
198     //for (int curTrainingTime = 0; curTrainingTime < trainingTime; curTrainingTime++)
199     {
200         cout << "training error: " << error << endl;
201         error = 0.f;
202         // initialize delta sum
203         for (int i = 0; i < innode; i++) inputLayer[i]->wDeltaSum.assign(inputLayer[i]->wDeltaSum.size(), 0.f);
204         for (int i = 0; i < hidelayer; i++){
205             for (int j = 0; j < hidenode; j++) 
206             {
207                 hiddenLayer[i][j]->wDeltaSum.assign(hiddenLayer[i][j]->wDeltaSum.size(), 0.f);
208                 hiddenLayer[i][j]->bDeltaSum = 0.f;
209             }
210         }
211         for (int i = 0; i < outnode; i++) outputLayer[i]->bDeltaSum = 0.f;
212 
213         for (int iter = 0; iter < sampleNum; iter++)
214         {
215             setInput(sampleGroup[iter].in);
216             setOutput(sampleGroup[iter].out);
217 
218             forwardPropagationEpoc();
219             backPropagationEpoc();
220         }
221 
222         // backward propagation on input layer
223         // -- update weight
224         for (int i = 0; i < innode; i++)
225         {
226             for (int j = 0; j < hidenode; j++) 
227             {
228                 inputLayer[i]->weight[j] -= learningRate * inputLayer[i]->wDeltaSum[j] / sampleNum;
229             }
230         }
231 
232         // backward propagation on hidden layer
233         // -- update weight & bias
234         for (int i = 0; i < hidelayer; i++)
235         {
236             if (i == hidelayer - 1)
237             {
238                 for (int j = 0; j < hidenode; j++)
239                 { 
240                     // bias
241                     hiddenLayer[i][j]->bias -= learningRate * hiddenLayer[i][j]->bDeltaSum / sampleNum;
242 
243                     // weight
244                     for (int k = 0; k < outnode; k++) 
245                     { hiddenLayer[i][j]->weight[k] -= learningRate * hiddenLayer[i][j]->wDeltaSum[k] / sampleNum; }
246                 }
247             }
248             else
249             {
250                 for (int j = 0; j < hidenode; j++)
251                 {
252                     // bias
253                     hiddenLayer[i][j]->bias -= learningRate * hiddenLayer[i][j]->bDeltaSum / sampleNum;
254 
255                     // weight
256                     for (int k = 0; k < hidenode; k++) 
257                     { hiddenLayer[i][j]->weight[k] -= learningRate * hiddenLayer[i][j]->wDeltaSum[k] / sampleNum; }
258                 }
259             }
260         }
261 
262         // backward propagation on output layer
263         // -- update bias
264         for (int i = 0; i < outnode; i++)
265         { outputLayer[i]->bias -= learningRate * outputLayer[i]->bDeltaSum / sampleNum; }
266     }
267 }
268 
269 void BpNet::predict(vector<sample>& testGroup)
270 {
271     int testNum = testGroup.size();
272 
273     for (int iter = 0; iter < testNum; iter++)
274     {
275         testGroup[iter].out.clear();
276         setInput(testGroup[iter].in);
277 
278         // forward propagation on hidden layer
279         for (int i = 0; i < hidelayer; i++)
280         {
281             if (i == 0)
282             {
283                 for (int j = 0; j < hidenode; j++)
284                 {
285                     double sum = 0.f;
286                     for (int k = 0; k < innode; k++) 
287                     {
288                         sum += inputLayer[k]->value * inputLayer[k]->weight[j];
289                     }
290                     sum += hiddenLayer[i][j]->bias;
291                     hiddenLayer[i][j]->value = sigmoid(sum);
292                 }
293             }
294             else
295             {
296                 for (int j = 0; j < hidenode; j++)
297                 {
298                     double sum = 0.f;
299                     for (int k = 0; k < hidenode; k++) 
300                     {
301                         sum += hiddenLayer[i-1][k]->value * hiddenLayer[i-1][k]->weight[j];
302                     }
303                     sum += hiddenLayer[i][j]->bias;
304                     hiddenLayer[i][j]->value = sigmoid(sum);
305                 }
306             }
307         }
308 
309         // forward propagation on output layer
310         for (int i = 0; i < outnode; i++)
311         {
312             double sum = 0.f;
313             for (int j = 0; j < hidenode; j++)
314             {
315                 sum += hiddenLayer[hidelayer-1][j]->value * hiddenLayer[hidelayer-1][j]->weight[i];
316             }
317             sum += outputLayer[i]->bias;
318             outputLayer[i]->value = sigmoid(sum);
319             testGroup[iter].out.push_back(outputLayer[i]->value);
320         }
321     }
322 }
323 
324 void BpNet::setInput(static vector<double> sampleIn)
325 {
326     for (int i = 0; i < innode; i++)
327     inputLayer[i]->value = sampleIn[i];
328 }
329 
330 void BpNet::setOutput(static vector<double> sampleOut)
331 {
332     for (int i = 0; i < outnode; i++) 
333     outputLayer[i]->rightout = sampleOut[i];
334 }