ChocolateBlack
C语言实现LSTM算法

C语言实现LSTM算法

2020年10月06日 6.6k 字 大概 36 分钟

1.算法介绍

LSTM，长短期记忆网络，全称为Long Short Term Memory networks。它是基于RNN的一种时间循环神经网络。

在理解LSTM之前，首先需要了解循环神经网络（RNN）的原理。

1.1 RNN与LSTM

人的思维是连续的，思考问题并不会从头开始，而是会“结合上下文”。传统的神经网络并不能做到这点，而RNN正是这一问题的解决方案。

循环神经网络（RNN）中的神经元，可以把输出值作为下一个神经元的输入值的一部分，进而保证神经网络能够连续“思考”。

然而RNN并不完美，它存在“长依赖”的问题。比方说，假设想让RNN根据一段不完整的句子来预测缺失的单词，例如“I grew up in France… I speak fluent ________.”（缺失的单词为French)，则有用的信息主要集中在前半句。然而要预测的单词却和前面有用的信息距离较远，这会导致RNN很难学习到有用的信息。

而LSTM解决了RNN的长依赖问题。如图所示，LSTM也是链状结构，但它和RNN的不同之处在于中间的神经元变成了一个较为复杂的细胞，其主要由遗忘门、输入门、输出门和记忆部分组成。而这个模块正是LSTM的核心。

img

2.算法实现步骤

2.1 读取csv

该步骤代码与前面代码一致，不再重复给出。

2.2 划分数据为k折

该步骤代码与前面代码一致，不再重复给出。

2.3 核心算法

2.3.1 初始化

首先我们需要确定LSTM的细胞数、输入结点数（$x_t$的维度）和隐藏结点数（$h_t$的维度）。以本节为例，设置输入结点数为2，隐藏结点数为12，细胞数为8。代码如下：

1
2
3
#define innode  2       //输入结点数
#define hidenode  2   //隐藏结点数
#define cell_num 8  //LSTM细胞数

依照定义，我们可以初始化LSTM网络的权重矩阵：

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
double W_I[innode][hidenode];     //连接输入与细胞输入门的权值矩阵
double U_I[hidenode][hidenode];   //连接上一细胞输出与本细胞单元中输入门的权值矩阵
double W_F[innode][hidenode];     //连接输入与细胞遗忘门的权值矩阵
double U_F[hidenode][hidenode];   //连接上一细胞与本细胞中遗忘门的权值矩阵
double W_O[innode][hidenode];     //连接输入与细胞输出门的权值矩阵
double U_O[hidenode][hidenode];   //连接上一细胞与现在时刻的细胞的权值矩阵
double W_G[innode][hidenode];     //用于产生新记忆的权值矩阵
double U_G[hidenode][hidenode];   //用于产生新记忆的权值矩阵
double W_out[hidenode];  //连接隐含层与输出层的权值矩阵

int i,j;

// 初始化
for(i=0;i<innode;i++){
 for(j=0;j<hidenode;j++){
     W_I[i][j] = 1;
     W_F[i][j] = 1;
     W_O[i][j] = 1;
     W_G[i][j] = 1;
  printf("W_I[%d][%d] = %f,",i,j,W_I[i][j]);
     printf("W_F[%d][%d] = %f,",i,j,W_F[i][j]);
     printf("W_O[%d][%d] = %f,",i,j,W_O[i][j]);
     printf("W_G[%d][%d] = %f\n",i,j,W_G[i][j]);
 }
}
for(i=0;i<hidenode;i++){
 for(j=0;j<hidenode;j++){
  U_I[i][j] = 1;
  U_F[i][j] = 1;
  U_O[i][j] = 1;
  U_G[i][j] = 1;
        printf("U_I[%d][%d] = %f,",i,j,U_I[i][j]);
     printf("U_F[%d][%d] = %f,",i,j,U_F[i][j]);
     printf("U_O[%d][%d] = %f,",i,j,U_O[i][j]);
     printf("U_G[%d][%d] = %f\n",i,j,U_G[i][j]);
 }
 W_out[i] = 1;
    printf("W_out[%d] = %f\n",i,W_out[i]);
}

将权重矩阵的值打印出来结果如下：

1
2
3
4
5
6
7
8
9
10
W_I[0][0] = 1.000000,W_F[0][0] = 1.000000,W_O[0][0] = 1.000000,W_G[0][0] = 1.000000
W_I[0][1] = 1.000000,W_F[0][1] = 1.000000,W_O[0][1] = 1.000000,W_G[0][1] = 1.000000
W_I[1][0] = 1.000000,W_F[1][0] = 1.000000,W_O[1][0] = 1.000000,W_G[1][0] = 1.000000
W_I[1][1] = 1.000000,W_F[1][1] = 1.000000,W_O[1][1] = 1.000000,W_G[1][1] = 1.000000
U_I[0][0] = 1.000000,U_F[0][0] = 1.000000,U_O[0][0] = 1.000000,U_G[0][0] = 1.000000
U_I[0][1] = 1.000000,U_F[0][1] = 1.000000,U_O[0][1] = 1.000000,U_G[0][1] = 1.000000
W_out[0] = 1.000000
U_I[1][0] = 1.000000,U_F[1][0] = 1.000000,U_O[1][0] = 1.000000,U_G[1][0] = 1.000000
U_I[1][1] = 1.000000,U_F[1][1] = 1.000000,U_O[1][1] = 1.000000,U_G[1][1] = 1.000000
W_out[1] = 1.000000

之后，在训练过程中，我们需要定义二维数组来保存各个门和记忆的数组：

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
double **I_vector = (double **)malloc((cell_num)*sizeof(double *)); //保存输入门信息
double **F_vector = (double **)malloc((cell_num)*sizeof(double *)); //保存遗忘门信息
double **O_vector = (double **)malloc((cell_num)*sizeof(double *)); //保存输出门信息
double **G_vector = (double **)malloc((cell_num)*sizeof(double *)); //保存记忆信息(C`t)    
double **S_vector = (double **)malloc((cell_num+1)*sizeof(double *)); //保存记忆信息(Ct) 
double **h_vector = (double **)malloc((cell_num+1)*sizeof(double *)); //保存细胞输出信息
  
for(j=0;j<cell_num;j++){
 S_vector[j] = (double *)malloc(hidenode*sizeof(double));
 h_vector[j] = (double *)malloc(hidenode*sizeof(double));
 I_vector[j] = (double *)malloc(hidenode*sizeof(double));
 F_vector[j] = (double *)malloc(hidenode*sizeof(double));
 O_vector[j] = (double *)malloc(hidenode*sizeof(double));
 G_vector[j] = (double *)malloc(hidenode*sizeof(double));
}
 S_vector[cell_num] = (double *)malloc(hidenode*sizeof(double));
 h_vector[cell_num] = (double *)malloc(hidenode*sizeof(double));

2.3.2 构建细胞

LSTM的细胞主要由以下四个部分组成：

  • 遗忘门
  • 输入门
  • 输出门
  • 记忆部分

2.3.2.1 遗忘门

遗忘门主要负责接受并筛选上一个细胞的信息。设为遗忘门输出值，为细胞输出值，为输入值，表示激活函数，和代表遗忘门的权重和偏差，其计算公式为：

img

2.3.2.2 输入门

输入门主要负责控制新信息的传入，并将新信息传入记忆中。设和为输入门输出值，、和、代表输入门的权重和偏差，其计算公式为：

img

2.3.2.3 记忆部分

记忆主要负责记录该细胞里的信息，并影响后续的细胞。设为记忆值，则公式如下：

img

2.3.2.4 输出门

输出门主要负责输出值，同时输出值也将作为下一个细胞输入的一部分。设为细胞输出值，和代表输出门的权重和偏差，则公式如下：

img

2.3.2.5 代码

将以上四个部分结合起来，便可以构成LSTM的细胞。以本文为例，将LSTM前向传播过程写成代码片段如下：

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
#include "math.h"
#include "stdlib.h"
#include "time.h"
#include "assert.h"
#include "string.h"
#include "stdio.h" 


#define innode  2       //输入结点数
#define hidenode  2   //隐藏结点数
#define cell_num 8  //LSTM细胞数 

double sigmoid(double x) 
{
    return 1.0 / (1.0 + exp(-x));
}

void main(void){
 double W_I[innode][hidenode];     //连接输入与细胞输入门的权值矩阵
 double U_I[hidenode][hidenode];   //连接上一细胞输出与本细胞单元中输入门的权值矩阵
 double W_F[innode][hidenode];     //连接输入与细胞遗忘门的权值矩阵
 double U_F[hidenode][hidenode];   //连接上一细胞与本细胞中遗忘门的权值矩阵
 double W_O[innode][hidenode];     //连接输入与细胞输出门的权值矩阵
 double U_O[hidenode][hidenode];   //连接上一细胞与现在时刻的细胞的权值矩阵
 double W_G[innode][hidenode];     //用于产生新记忆的权值矩阵
 double U_G[hidenode][hidenode];   //用于产生新记忆的权值矩阵
 double W_out[hidenode];  //连接隐含层与输出层的权值矩阵
 
 int i,j;
 // 初始化
 for(i=0;i<innode;i++){
  for(j=0;j<hidenode;j++){
      W_I[i][j] = 1;
      W_F[i][j] = 1;
      W_O[i][j] = 1;
      W_G[i][j] = 1;
  }
 }
 for(i=0;i<hidenode;i++){
  for(j=0;j<hidenode;j++){
   U_I[i][j] = 1;
   U_F[i][j] = 1;
   U_O[i][j] = 1;
   U_G[i][j] = 1; 
  }
  W_out[i] = 1;
 }
 double **I_vector = (double **)malloc((cell_num)*sizeof(double *));
 double **F_vector = (double **)malloc((cell_num)*sizeof(double *));
 double **O_vector = (double **)malloc((cell_num)*sizeof(double *));    
 double **G_vector = (double **)malloc((cell_num)*sizeof(double *));      
 double **M_vector = (double **)malloc((cell_num+1)*sizeof(double *));     
 double **h_vector = (double **)malloc((cell_num+1)*sizeof(double *));     
 double y_delta[cell_num];    //保存误差关于输出层的偏导
  
 for(j=0;j<cell_num;j++){
  M_vector[j] = (double *)malloc(hidenode*sizeof(double));
  h_vector[j] = (double *)malloc(hidenode*sizeof(double));
  I_vector[j] = (double *)malloc(hidenode*sizeof(double));
  F_vector[j] = (double *)malloc(hidenode*sizeof(double));
  O_vector[j] = (double *)malloc(hidenode*sizeof(double));
  G_vector[j] = (double *)malloc(hidenode*sizeof(double));
 }
 M_vector[cell_num] = (double *)malloc(hidenode*sizeof(double));
 h_vector[cell_num] = (double *)malloc(hidenode*sizeof(double));
 
    int predict[cell_num];     //保存每次生成的预测值
 
        
    double M[hidenode];     //记忆值
    double h[hidenode];     //输出值
        
 for(j=0; j<hidenode; j++)  
    {
        M[j] = 0;
        h[j] = 0;
        M_vector[0][j] = 0;
        h_vector[0][j] = 0;
    }
    
 int a[8] = {0,0,0,0,1,1,0,0}; //设a为12
 int b[8] = {0,0,0,0,1,1,1,1}; //设b为15
 int p;
 int x[2];
 for(p=0;p<cell_num;p++){
  x[0]=a[p]; //输入值
  x[1]=b[p]; //输入值
  double in_gate[hidenode];     //输入门
  double out_gate[hidenode];    //输出门
  double forget_gate[hidenode]; //遗忘门
  double g_gate[hidenode];      //C`t 
  double memory[hidenode];       //记忆值
  double h[hidenode];           //隐层输出值
              
  double *h_pre = h_vector[p];
  double *memory_pre = M_vector[p];
  
  int k;     
  for(k=0; k<hidenode; k++)
  {   //输入层转播到隐层
   double inGate = 0.0;
      double outGate = 0.0;
      double forgetGate = 0.0;
      double gGate = 0.0;
      double s = 0.0;
      
   int m;            
      for(m=0; m<innode; m++) 
      {
          inGate += x[m] * W_I[m][k]; 
          outGate += x[m] * W_O[m][k];
          forgetGate += x[m] * W_F[m][k];
          gGate += x[m] * W_G[m][k];
      }
                  
      for(m=0; m<hidenode; m++)
         {
             inGate += h_pre[m] * U_I[m][k];
             outGate += h_pre[m] * U_O[m][k];
             forgetGate += h_pre[m] * U_F[m][k];
             gGate += h_pre[m] * U_G[m][k];
         }
   
      
      in_gate[k] = sigmoid(inGate);
      out_gate[k] = sigmoid(outGate);
      forget_gate[k] = sigmoid(forgetGate);
      g_gate[k] = sigmoid(gGate);
   
      double m_pre = memory_pre[k];
      memory[k] = forget_gate[k] * m_pre + g_gate[k] * in_gate[k];
                  
      h[k] = out_gate[k] * tanh(memory[k]);
                  
   I_vector[p][k] = in_gate[k];
   F_vector[p][k] = forget_gate[k];
   O_vector[p][k] = out_gate[k];
   M_vector[p+1][k] = memory[k];
   G_vector[p][k] = g_gate[k];
   h_vector[p+1][k] = h[k];
   }
   
   //隐藏层传播到输出层
   double out = 0.0;
   for(j=0; j<hidenode; j++){
      out += h[j] * W_out[j]; 
   }
      
   double y;        
   y = sigmoid(out);               //输出层各单元输出
   predict[p] = floor(y + 0.5);   //记录预测值
   printf("predict[%d] = %f\n",p,predict[p]);
 }
}

输出的结果如下：

1
2
3
4
5
6
7
8
predict[0] = 0.000000
predict[1] = 0.000000
predict[2] = 0.000000
predict[3] = 0.000000
predict[4] = 0.000000
predict[5] = 0.000000
predict[6] = 0.000000
predict[7] = 0.000000

2.3.3 反向传播

首先，我们先求预测值和实际值的误差：

1
2
3
4
5
6
7
double y_delta[cell_num];
for(p=0;p<cell_num;p++){
 //前向传播部分略
 //保存标准误差关于输出层的偏导
 y_delta[p] = (t - y) * dsigmoid(y);
    printf("y_delta[%d] = %f\n",p,y_delta[p]);
}

得到误差如下：

1
2
3
4
5
6
7
8
y_delta[0] = -0.138149
y_delta[1] = -0.145825
y_delta[2] = -0.148124
y_delta[3] = 0.055493
y_delta[4] = 0.017513
y_delta[5] = -0.096220
y_delta[6] = 0.014835
y_delta[7] = 0.014861

之后进行反向传播，更新权值矩阵：

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
//误差反向传播
 
//隐含层偏差，通过当前之后一个时间点的隐含层误差和当前输出层的误差计算
double h_delta[hidenode];  
double O_delta[hidenode];
double I_delta[hidenode];
double F_delta[hidenode];
double G_delta[hidenode];
double memory_delta[hidenode];
//当前时间之后的一个隐藏层误差
double O_future_delta[hidenode]; 
double I_future_delta[hidenode];
double F_future_delta[hidenode];
double G_future_delta[hidenode];
double memory_future_delta[hidenode];
double forget_gate_future[hidenode];
int l_rate = 0.1;
for(j=0; j<hidenode; j++)
{
 O_future_delta[j] = 0.0;
 I_future_delta[j] = 0.0;
 F_future_delta[j] = 0.0;
 G_future_delta[j] = 0.0;
 memory_future_delta[j] = 0.0;
 forget_gate_future[j] = 0.0;
}
         
for(p=cell_num-1; p>=0 ; p--)
{
    x[0] = a[p];
 x[1] = b[p];
  
 //当前隐藏层
 double in_gate[hidenode];     //输入门
 double out_gate[hidenode];    //输出门
 double forget_gate[hidenode]; //遗忘门
 double g_gate[hidenode];      //C`t
 double memory[hidenode];     //记忆值
 double h[hidenode];         //隐层输出值
 for(k=0;k<hidenode;k++){
  in_gate[k] = I_vector[p][k];
  out_gate[k] = O_vector[p][k];
  forget_gate[k] = F_vector[p][k]; //遗忘门
     g_gate[k] = G_vector[p][k];      //C`t 
     memory[k] = M_vector[p+1][k];     //记忆值
     h[k] = h_vector[p+1][k];         //隐层输出值
 }
 //前一个隐藏层
 double *h_pre = h_vector[p];   
 double *memory_pre = M_vector[p];
  
 //更新隐含层和输出层之间的连接权
 for(j=0; j<hidenode; j++){
     W_out[j] += l_rate * y_delta[p] * h[j];  
 }
                 
 //对于网络中每个隐藏单元，计算误差项，并更新权值
 for(j=0; j<hidenode; j++) 
 {
  h_delta[j] = y_delta[p] * W_out[j];
     for(k=0; k<hidenode; k++)
     {
      h_delta[j] += I_future_delta[k] * U_I[j][k];
         h_delta[j] += F_future_delta[k] * U_F[j][k];
         h_delta[j] += O_future_delta[k] * U_O[j][k];
         h_delta[j] += G_future_delta[k] * U_G[j][k];
     }
  
     O_delta[j] = 0.0;
     I_delta[j] = 0.0;
     F_delta[j] = 0.0;
     G_delta[j] = 0.0;
     memory_delta[j] = 0.0;
  
     //隐含层的校正误差
     O_delta[j] = h_delta[j] * tanh(memory[j]) * dsigmoid(out_gate[j]);
     memory_delta[j] = h_delta[j] * out_gate[j] * dtanh(memory[j]) +
                                  memory_future_delta[j] * forget_gate_future[j];
                 F_delta[j] = memory_delta[j] * memory_pre[j] * dsigmoid(forget_gate[j]);
     I_delta[j] = memory_delta[j] * g_gate[j] * dsigmoid(in_gate[j]);
     G_delta[j] = memory_delta[j] * in_gate[j] * dsigmoid(g_gate[j]);
                 
     O_future_delta[j] = O_delta[j];
     F_future_delta[j] = F_delta[j];
     I_future_delta[j] = I_delta[j];
     G_future_delta[j] = G_delta[j];
     memory_future_delta[j] = memory_delta[j];
     forget_gate_future[j] = forget_gate[j]; 
  
     //更新前一个隐含层和现在隐含层之间的权值
     for(k=0; k<hidenode; k++)
     {
      U_I[k][j] += l_rate * I_delta[j] * h_pre[k];
         U_F[k][j] += l_rate * F_delta[j] * h_pre[k];
         U_O[k][j] += l_rate * O_delta[j] * h_pre[k];
         U_G[k][j] += l_rate * G_delta[j] * h_pre[k];
            printf("U_I[%d][%d] = %f,",k,j,U_I[k][j]);
      printf("U_F[%d][%d] = %f,",k,j,U_F[k][j]);
      printf("U_O[%d][%d] = %f,",k,j,U_O[k][j]);
      printf("U_G[%d][%d] = %f\n",k,j,U_G[k][j]);
     }
  
     //更新输入层和隐含层之间的连接权
     for(k=0; k<innode; k++)
     {
      W_I[k][j] += l_rate * I_delta[j] * x[k];
         W_F[k][j] += l_rate * F_delta[j] * x[k];
         W_O[k][j] += l_rate * O_delta[j] * x[k];
         W_G[k][j] += l_rate * G_delta[j] * x[k];
            printf("W_I[%d][%d] = %f,",k,j,W_I[k][j]);
      printf("W_F[%d][%d] = %f,",k,j,W_F[k][j]);
      printf("W_O[%d][%d] = %f,",k,j,W_O[k][j]);
      printf("W_G[%d][%d] = %f\n",k,j,W_G[k][j]);
     }
 }
}

结合上述代码，把全新的权重矩阵打印如下：

1
2
3
4
5
6
7
8
U_I[0][0] = 0.999978,U_F[0][0] = 0.999992,U_O[0][0] = 0.999968,U_G[0][0] = 0.999978
U_I[1][0] = 0.999978,U_F[1][0] = 0.999992,U_O[1][0] = 0.999968,U_G[1][0] = 0.999978
W_I[0][0] = 1.000000,W_F[0][0] = 1.000000,W_O[0][0] = 1.000000,W_G[0][0] = 1.000000
W_I[1][0] = 0.999574,W_F[1][0] = 0.999919,W_O[1][0] = 0.999550,W_G[1][0] = 0.999574
U_I[0][1] = 0.999972,U_F[0][1] = 0.999989,U_O[0][1] = 0.999959,U_G[0][1] = 0.999972
U_I[1][1] = 0.999972,U_F[1][1] = 0.999989,U_O[1][1] = 0.999959,U_G[1][1] = 0.999972
W_I[0][1] = 1.000000,W_F[0][1] = 1.000000,W_O[0][1] = 1.000000,W_G[0][1] = 1.000000
W_I[1][1] = 0.999507,W_F[1][1] = 0.999897,W_O[1][1] = 0.999477,W_G[1][1] = 0.999507

2.3.4 预测

训练完成后，就可以利用训练好的权重矩阵进行预测。其过程和前向传播大致相同。代码如下：

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
int *predictions=(int*)malloc(test_size*sizeof(int));
// 预测
for(i=0;i<test_size;i++){
 double **M_vector = (double **)malloc((cell_num+1)*sizeof(double *));     
 double **h_vector = (double **)malloc((cell_num+1)*sizeof(double *));
 for(j=0;j<cell_num+1;j++){
  M_vector[j] = (double *)malloc(hidenode*sizeof(double));
  h_vector[j] = (double *)malloc(hidenode*sizeof(double));
 }
  
 int predict[cell_num];               //保存每次生成的预测值
    memset(predict, 0, sizeof(predict));
        
 double M[hidenode];     //记忆值
    double h[hidenode];     //输出值
        
    for(j=0; j<hidenode; j++)  
    {
     M[j] = 0;
        h[j] = 0;
        M_vector[0][j] = 0;
        h_vector[0][j] = 0;
    }

    int a_int = test[i][0];
    int a[cell_num];
    int b_int = test[i][1];
    int b[cell_num];
    int c_int = test[i][2];
    int c[cell_num];

    int2binary(a_int, a); //把输入值变成二进制
    int2binary(b_int, b);
    int2binary(c_int, c);
        
         
    for(p=0;p<cell_num;p++){
  x[0]=a[p];
     x[1]=b[p];
     double in_gate[hidenode];     //输入门
     double out_gate[hidenode];    //输出门
     double forget_gate[hidenode]; //遗忘门
     double g_gate[hidenode];      //C`t 
     double memory[hidenode];       //记忆值
     double h[hidenode];           //隐层输出值
       
     for(k=0; k<hidenode; k++)
     {   
         //输入层转播到隐层
      double inGate = 0.0;
         double outGate = 0.0;
         double forgetGate = 0.0;
         double gGate = 0.0;
         double s = 0.0;
  
         double *h_pre = h_vector[p];
         double *memory_pre = M_vector[p];
                 
         for(m=0; m<innode; m++) 
         {
          inGate += x[m] * W_I[m][k]; 
             outGate += x[m] * W_O[m][k];
             forgetGate += x[m] * W_F[m][k];
             gGate += x[m] * W_G[m][k];
         }
                 
         for(m=0; m<hidenode; m++)
            {
             inGate += h_pre[m] * U_I[m][k];
                outGate += h_pre[m] * U_O[m][k];
                forgetGate += h_pre[m] * U_F[m][k];
                gGate += h_pre[m] * U_G[m][k];
            }
  
 
         in_gate[k] = sigmoid(inGate);   
         out_gate[k] = sigmoid(outGate);
         forget_gate[k] = sigmoid(forgetGate);
         g_gate[k] = sigmoid(gGate);
  
         double m_pre = memory_pre[k];
         memory[k] = forget_gate[k] * m_pre + g_gate[k] * in_gate[k];
         h[k] = out_gate[k] * tanh(memory[k]);
             
         M_vector[p+1][k] = memory[k];
   h_vector[p+1][k] = h[k];
     }

     //隐藏层传播到输出层
     double out = 0.0;
     for(j=0; j<hidenode; j++){
      out += h[j] * W_out[j];
  }
     y = sigmoid(out);               //输出层各单元输出
     predict[p] = (int)floor(y + 0.5);
 }
 free(M_vector);
 free(h_vector);
     
 double out = 0;
 for(k=cell_num-1; k>=0; k--){
     out += predict[k] * pow(2, k);
 }  
 predictions[i] = out;
}

2.4 计算RMSE

该步骤代码与前面代码一致，不再重复给出。

2.5 按划分的k折交叉验证计算预测所得平均RMSE

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
#include <stdlib.h>
#include <stdio.h>
extern double  ***cross_validation_split(double **dataset, int row, int n_folds, int fold_size,int col);
extern double* get_test_prediction(double **train, double **test, double l_rate, int n_epoch, int train_size,int test_size,int col);
extern double accuracy_metric(double *actual, double *predicted, int fold_size);

double* evaluate_algorithm(double **dataset, int n_folds, int fold_size, double l_rate, int n_epoch,int col,int row) 
{
 double*** split =  cross_validation_split(dataset, row, n_folds, fold_size,col);
 int i, j, k, l;
 int test_size = fold_size;
 int train_size = fold_size * (n_folds - 1);//train_size个一维数组
 double* score = (double*)malloc(n_folds * sizeof(double));
 for (i = 0; i < n_folds; i++) 
    {  //因为要遍历删除，所以拷贝一份split
  double*** split_copy = (double***)malloc(n_folds * sizeof(double**));
  for (j = 0; j < n_folds; j++) {
   split_copy[j] = (double**)malloc(fold_size * sizeof(double*));
   for (k = 0; k < fold_size; k++) {
    split_copy[j][k] = (double*)malloc(col * sizeof(double));
   }
  }
  for (j = 0; j < n_folds; j++)
  {
   for (k = 0; k < fold_size; k++)
   {
    for (l = 0; l < col; l++)
    {
     split_copy[j][k][l] = split[j][k][l];
    }
   }
  }
  double** test_set = (double**)malloc(test_size * sizeof(double*));
  for (j = 0; j < test_size; j++) {//对test_size中的每一行
   test_set[j] = (double*)malloc(col * sizeof(double));
   for (k = 0; k < col; k++) {
    test_set[j][k] = split_copy[i][j][k];
   }
  }
  for (j = i; j < n_folds - 1; j++) {
   split_copy[j] = split_copy[j + 1];
  }
  double** train_set = (double**)malloc(train_size * sizeof(double*));
  for (k = 0; k < n_folds - 1; k++) {
   for (l = 0; l < fold_size; l++) {
    train_set[k*fold_size + l] = (double*)malloc(col * sizeof(double));
    train_set[k*fold_size + l] = split_copy[k][l];
   }
  }
  double *predicted_2;
  predicted_2 = get_test_prediction(train_set, test_set, l_rate, n_epoch, train_size,test_size,col);
  double predicted[test_size];
  double* actual = (double*)malloc(test_size * sizeof(double));
  for(l=0;l<test_size;l++){
   predicted[l] = (double) *(predicted_2+l);
   actual[l] = test_set[l][col - 1];
  }
  double accuracy = accuracy_metric(actual, predicted, test_size);
  score[i] = accuracy;
  printf("score[%d]=%f\n", i, score[i]);
  free(split_copy);
 }
 double total = 0.0;
 for (l = 0; l < n_folds; l++) {
  total += score[l];
 }
 printf("mean_accuracy=%f\n", total / n_folds);
 return score;
}

3.完整算法及应用

本节将用LSTM网络让模型学习加法，其过程如下：

  • 读取数据
  • 把数据转换为二进制格式（输入与实际值）
  • 训练模型
  • 预测

下面给出完整的主函数以及训练函数代码：

main.c:

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
#include "math.h"
#include "stdlib.h"
#include "time.h"
#include "assert.h"
#include "string.h"
#include "stdio.h" 
 

extern int get_row(char *filename);
extern int get_col(char *filename);
extern void get_two_dimension(char *line, double **dataset, char *filename);

void main(){
 char filename[] = "data.csv";
    char line[1024];
    int row = get_row(filename);
    int col = get_col(filename);
    printf("row = %d\n",row);
    printf("col = %d\n",col);
    double **dataset = (double **)malloc(row*sizeof(int *));
    int i;
 for (i = 0; i < row; ++i){
  dataset[i] = (double *)malloc(col*sizeof(double));
 }//动态申请二维数组 
 get_two_dimension(line, dataset, filename);
    double l_rate = 0.01;
 int n_epoch = 100;
 int n_folds = 4;
 int fold_size;
    fold_size=(int)(row/n_folds);
 evaluate_algorithm(dataset, n_folds, fold_size, l_rate, n_epoch,col,row);
}

test_prediction.c:

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
#define innode  2       //输入结点数
#define hidenode  12   //隐藏结点数
#define cell_num 8  //LMTM细胞数 

#define uniform_plus_minus_one ( (double)( 2.0 * rand() ) / ((double)RAND_MAX + 1.0) - 1.0 )  //均匀随机分布 

#include "math.h"
#include "stdlib.h"
#include "time.h"
#include "assert.h"
#include "string.h"
#include "stdio.h" 
//激活函数
double sigmoid(double x) 
{
    return 1.0 / (1.0 + exp(-x));
}
 
//激活函数的导数，y为激活函数值
double dsigmoid(double y)
{
    return y * (1.0 - y);  
}           
 
//tanh的导数，y为tanh值
double dtanh(double y)
{
    y = tanh(y);
    return 1.0 - y * y;  
}
 
//将一个10进制整数转换为2进制数
void int2binary(int n, int *arr)
{
    int i = 0;
    while(n)
    {
        arr[i++] = n % 2;
        n /= 2;
    }
    while(i < cell_num)
        arr[i++] = 0;
}

//训练模型并获得预测值 
int* get_test_prediction(double **train, double **test, double l_rate, int n_epoch, int train_size,int test_size,int col){
 int epoch,i, j, k, m, p;
 int x[innode];
 double y;
 
 double W_I[innode][hidenode];     //连接输入与隐含层单元中输入门的权值矩阵
    double U_I[hidenode][hidenode];   //连接上一隐层输出与本隐含层单元中输入门的权值矩阵
    double W_F[innode][hidenode];     //连接输入与隐含层单元中遗忘门的权值矩阵
    double U_F[hidenode][hidenode];   //连接上一隐含层与本隐含层单元中遗忘门的权值矩阵
    double W_O[innode][hidenode];     //连接输入与隐含层单元中遗忘门的权值矩阵
    double U_O[hidenode][hidenode];   //连接上一隐含层与现在时刻的隐含层的权值矩阵
    double W_G[innode][hidenode];     //用于产生新记忆的权值矩阵
    double U_G[hidenode][hidenode];   //用于产生新记忆的权值矩阵
    double W_out[hidenode];  //连接隐层与输出层的权值矩阵
    
    // 初始化 
    for(i=0;i<innode;i++){
     for(j=0;j<hidenode;j++){
      W_I[i][j] = uniform_plus_minus_one;
      W_F[i][j] = uniform_plus_minus_one;
      W_O[i][j] = uniform_plus_minus_one;
      W_G[i][j] = uniform_plus_minus_one;
  }
 }
 for(i=0;i<hidenode;i++){
  for(j=0;j<hidenode;j++){
   U_I[i][j] = uniform_plus_minus_one;
   U_F[i][j] = uniform_plus_minus_one;
   U_O[i][j] = uniform_plus_minus_one;
   U_G[i][j] = uniform_plus_minus_one;
  }
  W_out[i] = uniform_plus_minus_one;
 }
 
    for(epoch=0;epoch<n_epoch;epoch++){
     for(i=0;i<train_size;i++){
      double **I_vector = (double **)malloc((cell_num)*sizeof(double *));
   double **F_vector = (double **)malloc((cell_num)*sizeof(double *));
   double **O_vector = (double **)malloc((cell_num)*sizeof(double *));    
      double **G_vector = (double **)malloc((cell_num)*sizeof(double *));      
      double **M_vector = (double **)malloc((cell_num+1)*sizeof(double *));     
      double **h_vector = (double **)malloc((cell_num+1)*sizeof(double *));     
      double y_delta[cell_num];    //保存误差关于输出层的偏导
  
   for(j=0;j<cell_num;j++){
          M_vector[j] = (double *)malloc(hidenode*sizeof(double));
          h_vector[j] = (double *)malloc(hidenode*sizeof(double));
          I_vector[j] = (double *)malloc(hidenode*sizeof(double));
          F_vector[j] = (double *)malloc(hidenode*sizeof(double));
          O_vector[j] = (double *)malloc(hidenode*sizeof(double));
          G_vector[j] = (double *)malloc(hidenode*sizeof(double));
   }
   M_vector[cell_num] = (double *)malloc(hidenode*sizeof(double));
      h_vector[cell_num] = (double *)malloc(hidenode*sizeof(double));
 
         int predict[cell_num];     //保存每次生成的预测值
 
        
         double M[hidenode];     //记忆值
         double h[hidenode];     //输出值
        
         for(j=0; j<hidenode; j++)  
         {
             M[j] = 0;
             h[j] = 0;
             M_vector[0][j] = 0;
          h_vector[0][j] = 0;
         }
         
         double a_int = train[i][0];
         int a[cell_num];
         double b_int = train[i][1];
         int b[cell_num];
         double c_int = train[i][2];
         int c[cell_num];
         int2binary(a_int, a);
   int2binary(b_int, b);
   int2binary(c_int, c);
         
         for(p=0;p<cell_num;p++){
       x[0]=a[p];
       x[1]=b[p];
       double t = (double)c[p];      //实际值
       double in_gate[hidenode];     //输入门
             double out_gate[hidenode];    //输出门
             double forget_gate[hidenode]; //遗忘门
             double g_gate[hidenode];      //C`t 
             double memory[hidenode];       //记忆值
             double h[hidenode];           //隐层输出值
             
             double *h_pre = h_vector[p];
             double *memory_pre = M_vector[p];
       
       for(k=0; k<hidenode; k++)
             {   
                 //输入层转播到隐层
                 double inGate = 0.0;
                 double outGate = 0.0;
                 double forgetGate = 0.0;
                 double gGate = 0.0;
                 double s = 0.0;
                 

  
                 for(m=0; m<innode; m++) 
                 {
                     inGate += x[m] * W_I[m][k]; 
                     outGate += x[m] * W_O[m][k];
                     forgetGate += x[m] * W_F[m][k];
                     gGate += x[m] * W_G[m][k];
                 }
                 
                 for(m=0; m<hidenode; m++)
                 {
                     inGate += h_pre[m] * U_I[m][k];
                     outGate += h_pre[m] * U_O[m][k];
                     forgetGate += h_pre[m] * U_F[m][k];
                     gGate += h_pre[m] * U_G[m][k];
                 }
  
     
                 in_gate[k] = sigmoid(inGate);
                 out_gate[k] = sigmoid(outGate);
                 forget_gate[k] = sigmoid(forgetGate);
                 g_gate[k] = sigmoid(gGate);
  
                 double m_pre = memory_pre[k];
                 memory[k] = forget_gate[k] * m_pre + g_gate[k] * in_gate[k];
                 
                 h[k] = out_gate[k] * tanh(memory[k]);
                 
     I_vector[p][k] = in_gate[k];
     F_vector[p][k] = forget_gate[k];
     O_vector[p][k] = out_gate[k];
     M_vector[p+1][k] = memory[k];
     G_vector[p][k] = g_gate[k];
     h_vector[p+1][k] = h[k];
             }

             //隐藏层传播到输出层
             double out = 0.0;
             for(j=0; j<hidenode; j++){
                 out += h[j] * W_out[j]; 
    }
             
             y = sigmoid(out);               //输出层各单元输出
             predict[p] = floor(y + 0.5);   //记录预测值
             
    //保存标准误差关于输出层的偏导
             y_delta[p] = (t - y) * dsigmoid(y);

   }
   //误差反向传播
 
         //隐含层偏差，通过当前之后一个时间点的隐含层误差和当前输出层的误差计算
         double h_delta[hidenode];  
         double O_delta[hidenode];
         double I_delta[hidenode];
         double F_delta[hidenode];
         double G_delta[hidenode];
         double memory_delta[hidenode];
         //当前时间之后的一个隐藏层误差
         double O_future_delta[hidenode]; 
         double I_future_delta[hidenode];
         double F_future_delta[hidenode];
         double G_future_delta[hidenode];
         double memory_future_delta[hidenode];
         double forget_gate_future[hidenode];
         for(j=0; j<hidenode; j++)
         {
             O_future_delta[j] = 0.0;
             I_future_delta[j] = 0.0;
             F_future_delta[j] = 0.0;
             G_future_delta[j] = 0.0;
             memory_future_delta[j] = 0.0;
             forget_gate_future[j] = 0.0;
         }
         
         for(p=cell_num-1; p>=0 ; p--)
         {
             x[0] = a[p];
             x[1] = b[p];
  
             //当前隐藏层

    double in_gate[hidenode];     //输入门
             double out_gate[hidenode];    //输出门
             double forget_gate[hidenode]; //遗忘门
             double g_gate[hidenode];      //C`t
             double memory[hidenode];     //记忆值
             double h[hidenode];         //隐层输出值
    for(k=0;k<hidenode;k++){
     in_gate[k] = I_vector[p][k];
     out_gate[k] = O_vector[p][k];
     forget_gate[k] = F_vector[p][k]; //遗忘门
              g_gate[k] = G_vector[p][k];      //C`t 
              memory[k] = M_vector[p+1][k];     //记忆值
              h[k] = h_vector[p+1][k];         //隐层输出值
    }
             //前一个隐藏层
             double *h_pre = h_vector[p];   
             double *memory_pre = M_vector[p];
  
             //更新隐含层和输出层之间的连接权
             for(j=0; j<hidenode; j++){
              W_out[j] += l_rate * y_delta[p] * h[j];  
    }
                 
             //对于网络中每个隐藏单元，计算误差项，并更新权值
             for(j=0; j<hidenode; j++) 
             {
                 h_delta[j] = y_delta[p] * W_out[j];
                 for(k=0; k<hidenode; k++)
                 {
                     h_delta[j] += I_future_delta[k] * U_I[j][k];
                     h_delta[j] += F_future_delta[k] * U_F[j][k];
                     h_delta[j] += O_future_delta[k] * U_O[j][k];
                     h_delta[j] += G_future_delta[k] * U_G[j][k];
                 }
  
                 O_delta[j] = 0.0;
                 I_delta[j] = 0.0;
                 F_delta[j] = 0.0;
                 G_delta[j] = 0.0;
                 memory_delta[j] = 0.0;
  
                 //隐含层的校正误差
                 O_delta[j] = h_delta[j] * tanh(memory[j]) * dsigmoid(out_gate[j]);
                 memory_delta[j] = h_delta[j] * out_gate[j] * dtanh(memory[j]) +
                                  memory_future_delta[j] * forget_gate_future[j];
                 F_delta[j] = memory_delta[j] * memory_pre[j] * dsigmoid(forget_gate[j]);
                 I_delta[j] = memory_delta[j] * g_gate[j] * dsigmoid(in_gate[j]);
                 G_delta[j] = memory_delta[j] * in_gate[j] * dsigmoid(g_gate[j]);
                 
                 O_future_delta[j] = O_delta[j];
              F_future_delta[j] = F_delta[j];
              I_future_delta[j] = I_delta[j];
              G_future_delta[j] = G_delta[j];
              memory_future_delta[j] = memory_delta[j];
              forget_gate_future[j] = forget_gate[j]; 
  
                 //更新前一个隐含层和现在隐含层之间的权值
                 for(k=0; k<hidenode; k++)
                 {
                  U_I[k][j] += l_rate * I_delta[j] * h_pre[k];
                     U_F[k][j] += l_rate * F_delta[j] * h_pre[k];
                     U_O[k][j] += l_rate * O_delta[j] * h_pre[k];
                     U_G[k][j] += l_rate * G_delta[j] * h_pre[k];
                 }
  
                 //更新输入层和隐含层之间的连接权
                 for(k=0; k<innode; k++)
                 {
                     W_I[k][j] += l_rate * I_delta[j] * x[k];
                     W_F[k][j] += l_rate * F_delta[j] * x[k];
                     W_O[k][j] += l_rate * O_delta[j] * x[k];
                     W_G[k][j] += l_rate * G_delta[j] * x[k];
                 }
             }
         }
   free(I_vector);
         free(F_vector);
         free(O_vector);
         free(G_vector);
         free(M_vector);
         free(h_vector);
  }
 }
 int *predictions=(int*)malloc(test_size*sizeof(int));
 // 预测
 for(i=0;i<test_size;i++){
  double **M_vector = (double **)malloc((cell_num+1)*sizeof(double *));     
  double **h_vector = (double **)malloc((cell_num+1)*sizeof(double *));
  for(j=0;j<cell_num+1;j++){
      M_vector[j] = (double *)malloc(hidenode*sizeof(double));
      h_vector[j] = (double *)malloc(hidenode*sizeof(double));
  }
  
  
  int predict[cell_num];               //保存每次生成的预测值
        // memset(predict, 0, sizeof(predict));
        
  double M[hidenode];     //记忆值
        double h[hidenode];     //输出值
        
        for(j=0; j<hidenode; j++)  
        {
            M[j] = 0;
            h[j] = 0;
            M_vector[0][j] = 0;
         h_vector[0][j] = 0;
        }

         
        double a_int = test[i][0];
        int a[cell_num];
        double b_int = test[i][1];
        int b[cell_num];
        double c_int = test[i][2];
        int c[cell_num];

  int2binary(a_int, a);
  int2binary(b_int, b);
  int2binary(c_int, c);
        
         
        for(p=0;p<cell_num;p++){
      x[0]=a[p];
      x[1]=b[p];
      double in_gate[hidenode];     //输入门
         double out_gate[hidenode];    //输出门
         double forget_gate[hidenode]; //遗忘门
         double g_gate[hidenode];      //C`t 
         double memory[hidenode];       //记忆值
         double h[hidenode];           //隐层输出值
       
      for(k=0; k<hidenode; k++)
         {   
             //输入层转播到隐层
             double inGate = 0.0;
             double outGate = 0.0;
             double forgetGate = 0.0;
             double gGate = 0.0;
             double s = 0.0;
  
  
             double *h_pre = h_vector[p];
             double *memory_pre = M_vector[p];
                 
             for(m=0; m<innode; m++) 
             {
                 inGate += x[m] * W_I[m][k]; 
                 outGate += x[m] * W_O[m][k];
                 forgetGate += x[m] * W_F[m][k];
                 gGate += x[m] * W_G[m][k];
             }
                 
             for(m=0; m<hidenode; m++)
                {
                    inGate += h_pre[m] * U_I[m][k];
                    outGate += h_pre[m] * U_O[m][k];
                    forgetGate += h_pre[m] * U_F[m][k];
                    gGate += h_pre[m] * U_G[m][k];
                }
  
 
             in_gate[k] = sigmoid(inGate);   
             out_gate[k] = sigmoid(outGate);
             forget_gate[k] = sigmoid(forgetGate);
             g_gate[k] = sigmoid(gGate);
  
             double m_pre = memory_pre[k];
             memory[k] = forget_gate[k] * m_pre + g_gate[k] * in_gate[k];
             h[k] = out_gate[k] * tanh(memory[k]);
             
             M_vector[p+1][k] = memory[k];
    h_vector[p+1][k] = h[k];
         }

         //隐藏层传播到输出层
         double out = 0.0;
         for(j=0; j<hidenode; j++){
             out += h[j] * W_out[j];
   }
         y = sigmoid(out);     //输出层各单元输出
         predict[p] = floor(y + 0.5);
         
     }
     free(M_vector);
     free(h_vector);
     
     int out=0;
  for(k=cell_num-1; k>=0; k--){
            out += predict[k] * pow(2, k);
  }  
  predictions[i] = out;
 }

 return predictions;
}

最终输出结果如下：

1
2
3
4
5
6
7
row = 910
col = 3
score[0]=80.176211%
score[1]=100.000000%
score[2]=32.599119%
score[3]=100.000000%
mean_accuracy=78.193833%

B站视频链接：C语言实现机器学习系列教程_哔哩哔哩 (゜-゜)つロ 干杯~-bilibili P22

github链接：Gao-Jianxiong-SDUWH/C-machine-learning

本文作者：ChocolateBlack
本文链接：http://chocolateblack.club/2020/10/06/C语言实现LSTM算法/
版权声明：本文采用 CC BY-NC-SA 3.0 CN 协议进行许可
技术教程