都说《机器学习》是学计算机的人必须要看的一本书，确实不是浪得虚名。看了一章人工神经网络(ANN)中关于反向传播算法的内容，相比单个感知器而言，采用多层网络的反向传播算法能表示出更多种类的非线性曲面，下面总结下它基本的处理框架。
ANN核心数据结构:
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typedef struct
{
int input_n; /* number of input units */
int hidden_n; /* number of hidden units */
int output_n; /* number of output units */
double *input_units; /* the input units */
double *hidden_units; /* the hidden units */
double *output_units; /* the output units */
double *hidden_delta; /* storage for hidden unit error */
double *output_delta; /* storage for output unit error */
double *target; /* storage for target vector */
double **input_weights; /* weights from input to hidden layer */
double **hidden_weights; /* weights from hidden to output layer */
/*** The next two are for momentum ***/
double **input_prev_weights; /* previous change on input to hidden wgt */
double **hidden_prev_weights; /* previous change on hidden to output wgt */
} BPNN;
整个神经网络可以分成三层：输入层，隐藏层，输出层，通过加权线性变换，层与层之间的传递，最终得到输入层的实数值。
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BPNN *bpnn_internal_create(int n_in, int n_hidden,int n_out;)
{//创建人工网络，参数分别指定输入层，隐藏层和输出层大小
BPNN *newnet;
newnet = (BPNN *) malloc (sizeof (BPNN));
if (newnet == NULL)
{
printf("BPNN_CREATE: Couldn't allocate neural network\n");
return (NULL);
}
newnet->input_n = n_in;//输入层
newnet->hidden_n = n_hidden;//隐藏层
newnet->output_n = n_out;//输出层
newnet->input_units = alloc_1d_dbl(n_in + 1);
newnet->hidden_units = alloc_1d_dbl(n_hidden + 1);
newnet->output_units = alloc_1d_dbl(n_out + 1);
newnet->hidden_delta = alloc_1d_dbl(n_hidden + 1);
newnet->output_delta = alloc_1d_dbl(n_out + 1);
newnet->target = alloc_1d_dbl(n_out + 1);//目标向量
newnet->input_weights = alloc_2d_dbl(n_in + 1, n_hidden + 1);//输入层到隐藏层的权值
newnet->hidden_weights = alloc_2d_dbl(n_hidden + 1, n_out + 1);//隐藏层到输出层的权值
newnet->input_prev_weights = alloc_2d_dbl(n_in + 1, n_hidden + 1);
newnet->hidden_prev_weights = alloc_2d_dbl(n_hidden + 1, n_out + 1);
return (newnet);
}
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下面代码段是ANN运行的核心部分：
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if (train_n > 0)
{//提供了训练集
printf("Creating new network '%s'\n", netname);
iimg = trainlist->list[0];//指向训练集第一张图片
imgsize = ROWS(iimg) * COLS(iimg);
/* bthom ===========================
make a net with:
imgsize inputs, 4 hiden units, and 1 output unit
*/
//输入层为图片大小，隐藏层为，输出层为
net = bpnn_create(imgsize, 4, 1);
}
// 训练
/************** Train it *****************************/
for (epoch = 1; epoch <= epochs; epoch++)
{
printf("%d ", epoch); fflush(stdout);
sumerr = 0.0;
for (i = 0; i < train_n; i++)
{
/** Set up input units on net with image i **/
//为图像i在网络上建立输入单元
load_input_with_image(trainlist->list[i], net);
/** Set up target vector for image i **/
//为图像i建立目标向量
load_target(trainlist->list[i], net);
/** Run backprop, learning rate 0.3, momentum 0.3 **/
//学习速率.3，冲量.3
bpnn_train(net, 0.3, 0.3, &out_err, &hid_err);
sumerr += (out_err + hid_err);
}
进行性能评估：
for (i = 0; i < n; i++)
{
/*** Load the image into the input layer. **/
load_input_with_image(il->list[i], net);//加载图片到输入层中
/*** Run the net on this input. **/
bpnn_feedforward(net);//在当前输入上运行神经网络
/*** Set up the target vector for this image. **/
load_target(il->list[i], net);//为此图片建立目标向量
/*** See if it got it right. ***/
if (evaluate_performance(net, &val, 0))
{//判断是否正确识别,
correct++;
}
else if (list_errors)
{
printf("%s - outputs ", NAME(il->list[i]));
for (j = 1; j <= net->output_n; j++)
{
printf("%.3f ", net->output_units[j]);
}
putchar('\n');
}
err += val;
}
err = err / (double) n;
if (!list_errors)
/* bthom==================================
this line prints part of the ouput line
discussed in section 3.1.2 of homework
*/
printf("%g %g ", ((double) correct / (double) n) * 100.0, err);
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用到的性能评估函数：
evaluate_performance(BPNN *net, double *err)
{//性能评估
double delta;
delta = net->target[1] - net->output_units[1];
*err = (0.5 * delta * delta);
/*** If the target unit is on... ***/
if (net->target[1] > 0.5)
{
/*** If the output unit is on, then we correctly recognized me! ***/
if (net->output_units[1] > 0.5)
{
return (1);
}
else
{
return (0);
}
/*** Else, the target unit is off... ***/
}
else
{
/*** If the output unit is on, then we mistakenly thought it was me ***/
if (net->output_units[1] > 0.5)
{
return (0);
/*** else, we correctly realized that it wasn't me ***/
}
else
{
return (1);
}
}
}
辅助处理函数区：
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load_input_with_image(IMAGE *img, BPNN *net)
{//输入图像
double *units;
int nr, nc, imgsize, i, j, k;
nr = ROWS(img);// 行大小
nc = COLS(img);//列大小
imgsize = nr * nc;;
if (imgsize != net->input_n)
{//确保输入单元数目设置为图片大小
printf("LOAD_INPUT_WITH_IMAGE: This image has %d pixels,\n", imgsize);
printf(" but your net has %d input units. I give up.\n", net->input_n);
exit (-1);
}
//取图片的每个像素为输入单元
units = net->input_units;
k = 1;
for (i = 0; i < nr; i++)
{
for (j = 0; j < nc; j++)
{
units[k] = ((double) img_getpixel(img, i, j)) / 255.0;
k++;
}
}
}
load_target(IMAGE *img, BPNN *net)
{//加载目标值
int scale;
char userid[40], head[40], expression[40], eyes[40], photo[40];
userid[0] = head[0] = expression[0] = eyes[0] = photo[0] = '\0';
/*** scan in the image features ***/
sscanf(NAME(img), "%[^_]_%[^_]_%[^_]_%[^_]_%d.%[^_]",
userid, head, expression, eyes, &scale, photo);
if (!strcmp(userid, "glickman"))
{
net->target[1] = TARGET_HIGH; /* it's me, set target to HIGH */
}
else
{
net->target[1] = TARGET_LOW; /* not me, set it to LOW */
}
}
void bpnn_train(BPNN *net, double eta, momentum *eo, momentum *eh)
{//人工神经网络训练
int in, hid, out;
double out_err, hid_err;
in = net->input_n;
hid = net->hidden_n;
out = net->output_n;
/*** Feed forward input activations. ***/
bpnn_layerforward(net->input_units, net->hidden_units,
net->input_weights, in, hid);
bpnn_layerforward(net->hidden_units, net->output_units,
net->hidden_weights, hid, out);
/*** Compute error on output and hidden units. ***/
bpnn_output_error(net->output_delta, net->target, net->output_units,out, &out_err);
bpnn_hidden_error(net->hidden_delta, hid, net->output_delta, out,net->hidden_weights, net->hidden_units, &hid_err);
*eo = out_err;
*eh = hid_err;
/*** Adjust input and hidden weights. ***/
bpnn_adjust_weights(net->output_delta, out, net->hidden_units, hid,net->hidden_weights, net->hidden_prev_weights, eta, momentum);
bpnn_adjust_weights(net->hidden_delta, hid, net->input_units, in,net->input_weights, net->input_prev_weights, eta, momentum);
}
void bpnn_feedforward(BPNN *net)
{//前向反馈
int in, hid, out;
in = net->input_n;//输入层大小
hid = net->hidden_n;//隐藏层大小
out = net->output_n;//输出层大小
/*** Feed forward input activations. ***/
bpnn_layerforward(net->input_units, net->hidden_units,net->input_weights, in, hid);
bpnn_layerforward(net->hidden_units, net->output_units,net->hidden_weights, hid, out);
}
void bpnn_adjust_weights(double *delta, double *ly,double **w, double **oldw, double eta, double momentum)
{//调整权值
double new_dw;
int k, j;
ly[0] = 1.0;
for (j = 1; j <= ndelta; j++)
{
for (k = 0; k <= nly; k++)
{
new_dw = ((eta * delta[j] * ly[k]) + (momentum * oldw[k][j]));
w[k][j] += new_dw;
oldw[k][j] = new_dw;
}
}
}
void bpnn_layerforward(double *l1, double *l2, double **conn,int n1,int n2)
{//层次前向输入
double sum;
int j, k;
/*** Set up thresholding unit ***/
l1[0] = 1.0;
//加权线性变换
/*** For each unit in second layer ***/
for (j = 1; j <= n2; j++)
{
/*** Compute weighted sum of its inputs ***/
sum = 0.0;
for (k = 0; k <= n1; k++)
{
sum += conn[k][j] * l1[k];
}
l2[j] = squash(sum);
}
}
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本文转自Phinecos(洞庭散人)博客园博客，原文链接：http://www.cnblogs.com/phinecos/archive/2008/10/18/1314181.html，如需转载请自行联系原作者
