卷积神经网络(CNN)代码实现(MNIST)解析

http://blog.csdn.net/fengbingchun/article/details/50814710中给出了CNN的简单实现,这里对每一步的实现作个说明:

共7层:依次为输入层、C1层、S2层、C3层、S4层、C5层、输出层。C代表卷积层(特征提取)。S代表降採样层或池化层(Pooling),输出层为全连接层。

1.        各层权值、偏置(阈值)初始化:

各层权值、偏置个数计算例如以下:

(1)、输入层:预处理后的32*32图像数据。无权值和偏置;

(2)、C1层:卷积窗大小5*5,输出特征图数量6,卷积窗种类1*6=6。输出特征图大小28*28,因此可训练參数(权值+偏置):(5*5*1)*6+6=150+6。

         (3)、S2层:卷积窗大小2*2。输出下採样图数量6,卷积窗种类6,输出下採样图大小14*14,因此可训练參数(权值+偏置):1*6+6=6+6。

         (4)、C3层:卷积窗大小5*5。输出特征图数量16。卷积窗种类6*16=96,输出特征图大小10*10。因此可训练參数(权值+偏置):(5*5*6)*16+16=2400+16。

         (5)、S4层:卷积窗大小2*2。输出下採样图数量16,卷积窗种类16,输出下採样图大小5*5,因此可训练參数(权值+偏置):1*16+16=16+16。

         (6)、C5层:卷积窗大小5*5。输出特征图数量120,卷积窗种类16*120=1920,输出特征图大小1*1,因此可训练參数(权值+偏置):(5*5*16)*120+120=48000+120;

         (7)、输出层:卷积窗大小1*1,输出特征图数量10。卷积窗种类120*10=1200,输出特征图大小1*1,因此可训练參数(权值+偏置):(1*120)*10+10=1200+10.

         代码段例如以下:

#define num_map_input_CNN		1 //输入层map个数
#define num_map_C1_CNN			6 //C1层map个数
#define num_map_S2_CNN			6 //S2层map个数
#define num_map_C3_CNN			16 //C3层map个数
#define num_map_S4_CNN			16 //S4层map个数
#define num_map_C5_CNN			120 //C5层map个数
#define num_map_output_CNN		10 //输出层map个数

#define len_weight_C1_CNN		150 //C1层权值数,(5*5*1)*6=150
#define len_bias_C1_CNN			6 //C1层阈值数,6
#define len_weight_S2_CNN		6 //S2层权值数,1*6=6
#define len_bias_S2_CNN			6 //S2层阈值数,6
#define len_weight_C3_CNN		2400 //C3层权值数,(5*5*6)*16=2400
#define len_bias_C3_CNN			16 //C3层阈值数,16
#define len_weight_S4_CNN		16 //S4层权值数。1*16=16
#define len_bias_S4_CNN			16 //S4层阈值数。16
#define len_weight_C5_CNN		48000 //C5层权值数,(5*5*16)*120=48000
#define len_bias_C5_CNN			120 //C5层阈值数,120
#define len_weight_output_CNN	1200 //输出层权值数。(1*120)*10=1200
#define len_bias_output_CNN		10 //输出层阈值数,10

#define num_neuron_input_CNN	1024 //输入层神经元数,(32*32)*1=1024
#define num_neuron_C1_CNN		4704 //C1层神经元数,(28*28)*6=4704
#define num_neuron_S2_CNN		1176 //S2层神经元数。(14*14)*6=1176
#define num_neuron_C3_CNN		1600 //C3层神经元数。(10*10)*16=1600
#define num_neuron_S4_CNN		400 //S4层神经元数。(5*5)*16=400
#define num_neuron_C5_CNN		120 //C5层神经元数。(1*1)*120=120
#define num_neuron_output_CNN	10 //输出层神经元数,(1*1)*10=10

         权值、偏置初始化:

(1)、权值使用函数uniform_real_distribution均匀分布初始化。tiny-cnn中每次初始化权值数值都同样。这里作了调整,使每次初始化的权值均不同。每层权值初始化大小范围都不一样;

(2)、全部层的偏置均初始化为0.

         代码段例如以下:

double CNN::uniform_rand(double min, double max)
{
	//static std::mt19937 gen(1);
	std::random_device rd;
	std::mt19937 gen(rd());
	std::uniform_real_distribution<double> dst(min, max);
	return dst(gen);
}

bool CNN::uniform_rand(double* src, int len, double min, double max)
{
	for (int i = 0; i < len; i++) {
		src[i] = uniform_rand(min, max);
	}

	return true;
}

bool CNN::initWeightThreshold()
{
	srand(time(0) + rand());
	const double scale = 6.0;

	double min_ = -std::sqrt(scale / (25.0 + 150.0));
	double max_ = std::sqrt(scale / (25.0 + 150.0));
	uniform_rand(weight_C1, len_weight_C1_CNN, min_, max_);
	for (int i = 0; i < len_bias_C1_CNN; i++) {
		bias_C1[i] = 0.0;
	}

	min_ = -std::sqrt(scale / (4.0 + 1.0));
	max_ = std::sqrt(scale / (4.0 + 1.0));
	uniform_rand(weight_S2, len_weight_S2_CNN, min_, max_);
	for (int i = 0; i < len_bias_S2_CNN; i++) {
		bias_S2[i] = 0.0;
	}

	min_ = -std::sqrt(scale / (150.0 + 400.0));
	max_ = std::sqrt(scale / (150.0 + 400.0));
	uniform_rand(weight_C3, len_weight_C3_CNN, min_, max_);
	for (int i = 0; i < len_bias_C3_CNN; i++) {
		bias_C3[i] = 0.0;
	}

	min_ = -std::sqrt(scale / (4.0 + 1.0));
	max_ = std::sqrt(scale / (4.0 + 1.0));
	uniform_rand(weight_S4, len_weight_S4_CNN, min_, max_);
	for (int i = 0; i < len_bias_S4_CNN; i++) {
		bias_S4[i] = 0.0;
	}

	min_ = -std::sqrt(scale / (400.0 + 3000.0));
	max_ = std::sqrt(scale / (400.0 + 3000.0));
	uniform_rand(weight_C5, len_weight_C5_CNN, min_, max_);
	for (int i = 0; i < len_bias_C5_CNN; i++) {
		bias_C5[i] = 0.0;
	}

	min_ = -std::sqrt(scale / (120.0 + 10.0));
	max_ = std::sqrt(scale / (120.0 + 10.0));
	uniform_rand(weight_output, len_weight_output_CNN, min_, max_);
	for (int i = 0; i < len_bias_output_CNN; i++) {
		bias_output[i] = 0.0;
	}

	return true;
}

2.        载入MNIST数据:

关于MNIST的介绍能够參考:http://blog.csdn.net/fengbingchun/article/details/49611549

使用MNIST库作为训练集和測试集。训练样本集为60000个,測试样本集为10000个。

(1)、MNIST库中图像原始大小为28*28,这里缩放为32*32,数据取值范围为[-1,1],扩充值均取-1,作为输入层输入数据。

代码段例如以下:

static void readMnistImages(std::string filename, double* data_dst, int num_image)
{
	const int width_src_image = 28;
	const int height_src_image = 28;
	const int x_padding = 2;
	const int y_padding = 2;
	const double scale_min = -1;
	const double scale_max = 1;

	std::ifstream file(filename, std::ios::binary);
	assert(file.is_open());

	int magic_number = 0;
	int number_of_images = 0;
	int n_rows = 0;
	int n_cols = 0;
	file.read((char*)&magic_number, sizeof(magic_number));
	magic_number = reverseInt(magic_number);
	file.read((char*)&number_of_images, sizeof(number_of_images));
	number_of_images = reverseInt(number_of_images);
	assert(number_of_images == num_image);
	file.read((char*)&n_rows, sizeof(n_rows));
	n_rows = reverseInt(n_rows);
	file.read((char*)&n_cols, sizeof(n_cols));
	n_cols = reverseInt(n_cols);
	assert(n_rows == height_src_image && n_cols == width_src_image);

	int size_single_image = width_image_input_CNN * height_image_input_CNN;

	for (int i = 0; i < number_of_images; ++i) {
		int addr = size_single_image * i;

		for (int r = 0; r < n_rows; ++r) {
			for (int c = 0; c < n_cols; ++c) {
				unsigned char temp = 0;
				file.read((char*)&temp, sizeof(temp));
				data_dst[addr + width_image_input_CNN * (r + y_padding) + c + x_padding] = (temp / 255.0) * (scale_max - scale_min) + scale_min;
			}
		}
	}
}

(2)、对于Label,输出层有10个节点,相应位置的节点值设为0.8。其他节点设为-0.8,作为输出层数据。

代码段例如以下:

static void readMnistLabels(std::string filename, double* data_dst, int num_image)
{
	const double scale_max = 0.8;

	std::ifstream file(filename, std::ios::binary);
	assert(file.is_open());

	int magic_number = 0;
	int number_of_images = 0;
	file.read((char*)&magic_number, sizeof(magic_number));
	magic_number = reverseInt(magic_number);
	file.read((char*)&number_of_images, sizeof(number_of_images));
	number_of_images = reverseInt(number_of_images);
	assert(number_of_images == num_image);

	for (int i = 0; i < number_of_images; ++i) {
		unsigned char temp = 0;
		file.read((char*)&temp, sizeof(temp));
		data_dst[i * num_map_output_CNN + temp] = scale_max;
	}
}static void readMnistLabels(std::string filename, double* data_dst, int num_image)
{
	const double scale_max = 0.8;

	std::ifstream file(filename, std::ios::binary);
	assert(file.is_open());

	int magic_number = 0;
	int number_of_images = 0;
	file.read((char*)&magic_number, sizeof(magic_number));
	magic_number = reverseInt(magic_number);
	file.read((char*)&number_of_images, sizeof(number_of_images));
	number_of_images = reverseInt(number_of_images);
	assert(number_of_images == num_image);

	for (int i = 0; i < number_of_images; ++i) {
		unsigned char temp = 0;
		file.read((char*)&temp, sizeof(temp));
		data_dst[i * num_map_output_CNN + temp] = scale_max;
	}
}

3.        前向传播:主要计算每层的神经元值。当中C1层、C3层、C5层操作过程同样。S2层、S4层操作过程同样。

(1)、输入层:神经元数为(32*32)*1=1024。

(2)、C1层:神经元数为(28*28)*6=4704,分别用每个5*5的卷积图像去乘以32*32的图像,获得一个28*28的图像。即相应位置相加再求和,stride长度为1;一共6个5*5的卷积图像,然后对每个神经元加上一个阈值。最后再通过tanh激活函数对每一神经元进行运算得到终于每个神经元的结果。

激活函数的作用:它是用来增加非线性因素的,解决线性模型所不能解决的问题。提供网络的非线性建模能力。

假设没有激活函数。那么该网络仅能够表达线性映射。此时即便有再多的隐藏层,其整个网络跟单层神经网络也是等价的。因此也能够觉得,唯独增加了激活函数之后,深度神经网络才具备了分层的非线性映射学习能力。

代码段例如以下:

double CNN::activation_function_tanh(double x)
{
	double ep = std::exp(x);
	double em = std::exp(-x);

	return (ep - em) / (ep + em);
}

bool CNN::Forward_C1()
{
	init_variable(neuron_C1, 0.0, num_neuron_C1_CNN);

	for (int o = 0; o < num_map_C1_CNN; o++) {
		for (int inc = 0; inc < num_map_input_CNN; inc++) {
			int addr1 = get_index(0, 0, num_map_input_CNN * o + inc, width_kernel_conv_CNN, height_kernel_conv_CNN, num_map_C1_CNN * num_map_input_CNN);
			int addr2 = get_index(0, 0, inc, width_image_input_CNN, height_image_input_CNN, num_map_input_CNN);
			int addr3 = get_index(0, 0, o, width_image_C1_CNN, height_image_C1_CNN, num_map_C1_CNN);

			const double* pw = &weight_C1[0] + addr1;
			const double* pi = data_single_image + addr2;
			double* pa = &neuron_C1[0] + addr3;

			for (int y = 0; y < height_image_C1_CNN; y++) {
				for (int x = 0; x < width_image_C1_CNN; x++) {
					const double* ppw = pw;
					const double* ppi = pi + y * width_image_input_CNN + x;
					double sum = 0.0;

					for (int wy = 0; wy < height_kernel_conv_CNN; wy++) {
						for (int wx = 0; wx < width_kernel_conv_CNN; wx++) {
							sum += *ppw++ * ppi[wy * width_image_input_CNN + wx];
						}
					}

					pa[y * width_image_C1_CNN + x] += sum;
				}
			}
		}

		int addr3 = get_index(0, 0, o, width_image_C1_CNN, height_image_C1_CNN, num_map_C1_CNN);
		double* pa = &neuron_C1[0] + addr3;
		double b = bias_C1[o];
		for (int y = 0; y < height_image_C1_CNN; y++) {
			for (int x = 0; x < width_image_C1_CNN; x++) {
				pa[y * width_image_C1_CNN + x] += b;
			}
		}
	}

	for (int i = 0; i < num_neuron_C1_CNN; i++) {
		neuron_C1[i] = activation_function_tanh(neuron_C1[i]);
	}

	return true;
}

(3)、S2层:神经元数为(14*14)*6=1176,对C1中6个28*28的特征图生成6个14*14的下採样图,相邻四个神经元分别乘以同一个权值再进行相加求和,再求均值即除以4,然后再加上一个阈值,最后再通过tanh激活函数对每一神经元进行运算得到终于每个神经元的结果。

代码段例如以下:

bool CNN::Forward_S2()
{
	init_variable(neuron_S2, 0.0, num_neuron_S2_CNN);
	double scale_factor = 1.0 / (width_kernel_pooling_CNN * height_kernel_pooling_CNN);

	assert(out2wi_S2.size() == num_neuron_S2_CNN);
	assert(out2bias_S2.size() == num_neuron_S2_CNN);

	for (int i = 0; i < num_neuron_S2_CNN; i++) {
		const wi_connections& connections = out2wi_S2[i];
		neuron_S2[i] = 0;

		for (int index = 0; index < connections.size(); index++) {
			neuron_S2[i] += weight_S2[connections[index].first] * neuron_C1[connections[index].second];
		}

		neuron_S2[i] *= scale_factor;
		neuron_S2[i] += bias_S2[out2bias_S2[i]];
	}

	for (int i = 0; i < num_neuron_S2_CNN; i++) {
		neuron_S2[i] = activation_function_tanh(neuron_S2[i]);
	}

	return true;
}

(4)、C3层:神经元数为(10*10)*16=1600。C3层实现方式与C1层全然同样。由S2中的6个14*14下採样图生成16个10*10特征图,对于生成的每个10*10的特征图,是由6个5*5的卷积图像去乘以6个14*14的下採样图,然后相应位置相加求和,然后对每个神经元加上一个阈值,最后再通过tanh激活函数对每一神经元进行运算得到终于每个神经元的结果。

也可依照Y.Lecun给出的表进行计算。即对于生成的每个10*10的特征图,是由n个5*5的卷积图像去乘以n个14*14的下採样图,当中n是小于6的,即不全然连接。这样做的原因:第一,不全然的连接机制将连接的数量保持在合理的范围内。第二,也是最重要的,其破坏了网络的对称性。因为不同的特征图有不同的输入,所以迫使他们抽取不同的特征。

代码段例如以下:

// connection table [Y.Lecun, 1998 Table.1]
#define O true
#define X false
static const bool tbl[6][16] = {
	O, X, X, X, O, O, O, X, X, O, O, O, O, X, O, O,
	O, O, X, X, X, O, O, O, X, X, O, O, O, O, X, O,
	O, O, O, X, X, X, O, O, O, X, X, O, X, O, O, O,
	X, O, O, O, X, X, O, O, O, O, X, X, O, X, O, O,
	X, X, O, O, O, X, X, O, O, O, O, X, O, O, X, O,
	X, X, X, O, O, O, X, X, O, O, O, O, X, O, O, O
};
#undef O
#undef X

bool CNN::Forward_C3()
{
	init_variable(neuron_C3, 0.0, num_neuron_C3_CNN);

	for (int o = 0; o < num_map_C3_CNN; o++) {
		for (int inc = 0; inc < num_map_S2_CNN; inc++) {
			if (!tbl[inc][o]) continue;

			int addr1 = get_index(0, 0, num_map_S2_CNN * o + inc, width_kernel_conv_CNN, height_kernel_conv_CNN, num_map_C3_CNN * num_map_S2_CNN);
			int addr2 = get_index(0, 0, inc, width_image_S2_CNN, height_image_S2_CNN, num_map_S2_CNN);
			int addr3 = get_index(0, 0, o, width_image_C3_CNN, height_image_C3_CNN, num_map_C3_CNN);

			const double* pw = &weight_C3[0] + addr1;
			const double* pi = &neuron_S2[0] + addr2;
			double* pa = &neuron_C3[0] + addr3;

			for (int y = 0; y < height_image_C3_CNN; y++) {
				for (int x = 0; x < width_image_C3_CNN; x++) {
					const double* ppw = pw;
					const double* ppi = pi + y * width_image_S2_CNN + x;
					double sum = 0.0;

					for (int wy = 0; wy < height_kernel_conv_CNN; wy++) {
						for (int wx = 0; wx < width_kernel_conv_CNN; wx++) {
							sum += *ppw++ * ppi[wy * width_image_S2_CNN + wx];
						}
					}

					pa[y * width_image_C3_CNN + x] += sum;
				}
			}
		}

		int addr3 = get_index(0, 0, o, width_image_C3_CNN, height_image_C3_CNN, num_map_C3_CNN);
		double* pa = &neuron_C3[0] + addr3;
		double b = bias_C3[o];
		for (int y = 0; y < height_image_C3_CNN; y++) {
			for (int x = 0; x < width_image_C3_CNN; x++) {
				pa[y * width_image_C3_CNN + x] += b;
			}
		}
	}

	for (int i = 0; i < num_neuron_C3_CNN; i++) {
		neuron_C3[i] = activation_function_tanh(neuron_C3[i]);
	}

	return true;
}

(5)、S4层:神经元数为(5*5)*16=400,S4层实现方式与S2层全然同样。由C3中16个10*10的特征图生成16个5*5下採样图,相邻四个神经元分别乘以同一个权值再进行相加求和,再求均值即除以4,然后再加上一个阈值。最后再通过tanh激活函数对每一神经元进行运算得到终于每个神经元的结果。

代码段例如以下:

bool CNN::Forward_S4()
{
	double scale_factor = 1.0 / (width_kernel_pooling_CNN * height_kernel_pooling_CNN);
	init_variable(neuron_S4, 0.0, num_neuron_S4_CNN);

	assert(out2wi_S4.size() == num_neuron_S4_CNN);
	assert(out2bias_S4.size() == num_neuron_S4_CNN);

	for (int i = 0; i < num_neuron_S4_CNN; i++) {
		const wi_connections& connections = out2wi_S4[i];
		neuron_S4[i] = 0.0;

		for (int index = 0; index < connections.size(); index++) {
			neuron_S4[i] += weight_S4[connections[index].first] * neuron_C3[connections[index].second];
		}

		neuron_S4[i] *= scale_factor;
		neuron_S4[i] += bias_S4[out2bias_S4[i]];
	}

	for (int i = 0; i < num_neuron_S4_CNN; i++) {
		neuron_S4[i] = activation_function_tanh(neuron_S4[i]);
	}

	return true;
}

(6)、C5层:神经元数为(1*1)*120=120,也可看为全连接层,C5层实现方式与C1、C3层全然同样。由S4中16个5*5下採样图生成120个1*1特征图,对于生成的每个1*1的特征图,是由16个5*5的卷积图像去乘以16个5*5的下採用图,然后相加求和,然后对每个神经元加上一个阈值,最后再通过tanh激活函数对每一神经元进行运算得到终于每个神经元的结果。

代码段例如以下:

bool CNN::Forward_C5()
{
	init_variable(neuron_C5, 0.0, num_neuron_C5_CNN);

	for (int o = 0; o < num_map_C5_CNN; o++) {
		for (int inc = 0; inc < num_map_S4_CNN; inc++) {
			int addr1 = get_index(0, 0, num_map_S4_CNN * o + inc, width_kernel_conv_CNN, height_kernel_conv_CNN, num_map_C5_CNN * num_map_S4_CNN);
			int addr2 = get_index(0, 0, inc, width_image_S4_CNN, height_image_S4_CNN, num_map_S4_CNN);
			int addr3 = get_index(0, 0, o, width_image_C5_CNN, height_image_C5_CNN, num_map_C5_CNN);

			const double *pw = &weight_C5[0] + addr1;
			const double *pi = &neuron_S4[0] + addr2;
			double *pa = &neuron_C5[0] + addr3;

			for (int y = 0; y < height_image_C5_CNN; y++) {
				for (int x = 0; x < width_image_C5_CNN; x++) {
					const double *ppw = pw;
					const double *ppi = pi + y * width_image_S4_CNN + x;
					double sum = 0.0;

					for (int wy = 0; wy < height_kernel_conv_CNN; wy++) {
						for (int wx = 0; wx < width_kernel_conv_CNN; wx++) {
							sum += *ppw++ * ppi[wy * width_image_S4_CNN + wx];
						}
					}

					pa[y * width_image_C5_CNN + x] += sum;
				}
			}
		}

		int addr3 = get_index(0, 0, o, width_image_C5_CNN, height_image_C5_CNN, num_map_C5_CNN);
		double *pa = &neuron_C5[0] + addr3;
		double b = bias_C5[o];
		for (int y = 0; y < height_image_C5_CNN; y++) {
			for (int x = 0; x < width_image_C5_CNN; x++) {
				pa[y * width_image_C5_CNN + x] += b;
			}
		}
	}

	for (int i = 0; i < num_neuron_C5_CNN; i++) {
		neuron_C5[i] = activation_function_tanh(neuron_C5[i]);
	}

	return true;
}

(7)、输出层:神经元数为(1*1)*10=10。为全连接层。输出层中的每个神经元均是由C5层中的120个神经元乘以相相应的权值。然后相加求和;然后对每个神经元加上一个阈值。最后再通过tanh激活函数对每一神经元进行运算得到终于每个神经元的结果。

代码段例如以下:

bool CNN::Forward_output()
{
	init_variable(neuron_output, 0.0, num_neuron_output_CNN);

	for (int i = 0; i < num_neuron_output_CNN; i++) {
		neuron_output[i] = 0.0;

		for (int c = 0; c < num_neuron_C5_CNN; c++) {
			neuron_output[i] += weight_output[c * num_neuron_output_CNN + i] * neuron_C5[c];
		}

		neuron_output[i] += bias_output[i];
	}

	for (int i = 0; i < num_neuron_output_CNN; i++) {
		neuron_output[i] = activation_function_tanh(neuron_output[i]);
	}

	return true;
}

4.        反向传播:主要计算每层权值和偏置的误差以及每层神经元的误差;当中输入层、S2层、S4层操作过程同样。C1层、C3层操作过程同样。

(1)、输出层:计算输出层神经元误差;通过mse损失函数的导数函数和tanh激活函数的导数函数来计算输出层神经元误差,即a、已计算出的输出层神经元值减去相应label值,b、1.0减去输出层神经元值的平方,c、a与c的乘积和。

损失函数作用:在统计学中损失函数是一种衡量损失和错误(这样的损失与”错误地”预计有关)程度的函数。损失函数在实践中最重要的运用。在于协助我们通过过程的改善而持续降低目标值的变异。并不是只追求符合逻辑。

在深度学习中,对于损失函数的收敛特性。我们期望是当误差越大的时候。收敛(学习)速度应该越快。成为损失函数须要满足两点要求:非负性;预測值和期望值接近时,函数值趋于0.

代码段例如以下:

double CNN::loss_function_mse_derivative(double y, double t)
{
	return (y - t);
}

void CNN::loss_function_gradient(const double* y, const double* t, double* dst, int len)
{
	for (int i = 0; i < len; i++) {
		dst[i] = loss_function_mse_derivative(y[i], t[i]);
	}
}

double CNN::activation_function_tanh_derivative(double x)
{
	return (1.0 - x * x);
}

double CNN::dot_product(const double* s1, const double* s2, int len)
{
	double result = 0.0;

	for (int i = 0; i < len; i++) {
		result += s1[i] * s2[i];
	}

	return result;
}

bool CNN::Backward_output()
{
	init_variable(delta_neuron_output, 0.0, num_neuron_output_CNN);

	double dE_dy[num_neuron_output_CNN];
	init_variable(dE_dy, 0.0, num_neuron_output_CNN);
	loss_function_gradient(neuron_output, data_single_label, dE_dy, num_neuron_output_CNN); // 损失函数: mean squared error(均方差)
	
	// delta = dE/da = (dE/dy) * (dy/da)
	for (int i = 0; i < num_neuron_output_CNN; i++) {
		double dy_da[num_neuron_output_CNN];
		init_variable(dy_da, 0.0, num_neuron_output_CNN);

		dy_da[i] = activation_function_tanh_derivative(neuron_output[i]);
		delta_neuron_output[i] = dot_product(dE_dy, dy_da, num_neuron_output_CNN);
	}

	return true;
}

(2)、C5层:计算C5层神经元误差、输出层权值误差、输出层偏置误差;通过输出层神经元误差乘以输出层权值。求和。结果再乘以C5层神经元的tanh激活函数的导数(即1-C5层神经元值的平方)。获得C5层每个神经元误差。通过输出层神经元误差乘以C5层神经元获得输出层权值误差;输出层偏置误差即为输出层神经元误差。

代码段例如以下:

bool CNN::muladd(const double* src, double c, int len, double* dst)
{
	for (int i = 0; i < len; i++) {
		dst[i] += (src[i] * c);
	}

	return true;
}

bool CNN::Backward_C5()
{
	init_variable(delta_neuron_C5, 0.0, num_neuron_C5_CNN);
	init_variable(delta_weight_output, 0.0, len_weight_output_CNN);
	init_variable(delta_bias_output, 0.0, len_bias_output_CNN);

	for (int c = 0; c < num_neuron_C5_CNN; c++) {
		// propagate delta to previous layer
		// prev_delta[c] += current_delta[r] * W_[c * out_size_ + r]
		delta_neuron_C5[c] = dot_product(&delta_neuron_output[0], &weight_output[c * num_neuron_output_CNN], num_neuron_output_CNN);
		delta_neuron_C5[c] *= activation_function_tanh_derivative(neuron_C5[c]);
	}

	// accumulate weight-step using delta
	// dW[c * out_size + i] += current_delta[i] * prev_out[c]
	for (int c = 0; c < num_neuron_C5_CNN; c++) {
		muladd(&delta_neuron_output[0], neuron_C5[c], num_neuron_output_CNN, &delta_weight_output[0] + c * num_neuron_output_CNN);
	}

	for (int i = 0; i < len_bias_output_CNN; i++) {
		delta_bias_output[i] += delta_neuron_output[i];
	}

	return true;
}

(3)、S4层:计算S4层神经元误差、C5层权值误差、C5层偏置误差;通过C5层权值乘以C5层神经元误差。求和。结果再乘以S4层神经元的tanh激活函数的导数(即1-S4神经元的平方),获得S4层每个神经元误差。通过S4层神经元乘以C5层神经元误差,求和,获得C5层权值误差。C5层偏置误差即为C5层神经元误差。

代码段例如以下:

bool CNN::Backward_S4()
{
	init_variable(delta_neuron_S4, 0.0, num_neuron_S4_CNN);
	init_variable(delta_weight_C5, 0.0, len_weight_C5_CNN);
	init_variable(delta_bias_C5, 0.0, len_bias_C5_CNN);

	// propagate delta to previous layer
	for (int inc = 0; inc < num_map_S4_CNN; inc++) {
		for (int outc = 0; outc < num_map_C5_CNN; outc++) {
			int addr1 = get_index(0, 0, num_map_S4_CNN * outc + inc, width_kernel_conv_CNN, height_kernel_conv_CNN, num_map_S4_CNN * num_map_C5_CNN);
			int addr2 = get_index(0, 0, outc, width_image_C5_CNN, height_image_C5_CNN, num_map_C5_CNN);
			int addr3 = get_index(0, 0, inc, width_image_S4_CNN, height_image_S4_CNN, num_map_S4_CNN);

			const double* pw = &weight_C5[0] + addr1;
			const double* pdelta_src = &delta_neuron_C5[0] + addr2;
			double* pdelta_dst = &delta_neuron_S4[0] + addr3;

			for (int y = 0; y < height_image_C5_CNN; y++) {
				for (int x = 0; x < width_image_C5_CNN; x++) {
					const double* ppw = pw;
					const double ppdelta_src = pdelta_src[y * width_image_C5_CNN + x];
					double* ppdelta_dst = pdelta_dst + y * width_image_S4_CNN + x;

					for (int wy = 0; wy < height_kernel_conv_CNN; wy++) {
						for (int wx = 0; wx < width_kernel_conv_CNN; wx++) {
							ppdelta_dst[wy * width_image_S4_CNN + wx] += *ppw++ * ppdelta_src;
						}
					}
				}
			}
		}
	}

	for (int i = 0; i < num_neuron_S4_CNN; i++) {
		delta_neuron_S4[i] *= activation_function_tanh_derivative(neuron_S4[i]);
	}

	// accumulate dw
	for (int inc = 0; inc < num_map_S4_CNN; inc++) {
		for (int outc = 0; outc < num_map_C5_CNN; outc++) {
			for (int wy = 0; wy < height_kernel_conv_CNN; wy++) {
				for (int wx = 0; wx < width_kernel_conv_CNN; wx++) {
					int addr1 = get_index(wx, wy, inc, width_image_S4_CNN, height_image_S4_CNN, num_map_S4_CNN);
					int addr2 = get_index(0, 0, outc, width_image_C5_CNN, height_image_C5_CNN, num_map_C5_CNN);
					int addr3 = get_index(wx, wy, num_map_S4_CNN * outc + inc, width_kernel_conv_CNN, height_kernel_conv_CNN, num_map_S4_CNN * num_map_C5_CNN);

					double dst = 0.0;
					const double* prevo = &neuron_S4[0] + addr1;
					const double* delta = &delta_neuron_C5[0] + addr2;

					for (int y = 0; y < height_image_C5_CNN; y++) {
						dst += dot_product(prevo + y * width_image_S4_CNN, delta + y * width_image_C5_CNN, width_image_C5_CNN);
					}

					delta_weight_C5[addr3] += dst;
				}
			}
		}
	}

	// accumulate db
	for (int outc = 0; outc < num_map_C5_CNN; outc++) {
		int addr2 = get_index(0, 0, outc, width_image_C5_CNN, height_image_C5_CNN, num_map_C5_CNN);
		const double* delta = &delta_neuron_C5[0] + addr2;

		for (int y = 0; y < height_image_C5_CNN; y++) {
			for (int x = 0; x < width_image_C5_CNN; x++) {
				delta_bias_C5[outc] += delta[y * width_image_C5_CNN + x];
			}
		}
	}

	return true;
}

(4)、C3层:计算C3层神经元误差、S4层权值误差、S4层偏置误差。通过S4层权值乘以S4层神经元误差。求和,结果再乘以C3层神经元的tanh激活函数的导数(即1-S4神经元的平方),然后再乘以1/4。获得C3层每个神经元误差;通过C3层神经元乘以S4神经元误差,求和。再乘以1/4。获得S4层权值误差;通过S4层神经元误差求和,来获得S4层偏置误差。

代码段例如以下:

bool CNN::Backward_C3()
{
	init_variable(delta_neuron_C3, 0.0, num_neuron_C3_CNN);
	init_variable(delta_weight_S4, 0.0, len_weight_S4_CNN);
	init_variable(delta_bias_S4, 0.0, len_bias_S4_CNN);

	double scale_factor = 1.0 / (width_kernel_pooling_CNN * height_kernel_pooling_CNN);

	assert(in2wo_C3.size() == num_neuron_C3_CNN);
	assert(weight2io_C3.size() == len_weight_S4_CNN);
	assert(bias2out_C3.size() == len_bias_S4_CNN);

	for (int i = 0; i < num_neuron_C3_CNN; i++) {
		const wo_connections& connections = in2wo_C3[i];
		double delta = 0.0;

		for (int j = 0; j < connections.size(); j++) {
			delta += weight_S4[connections[j].first] * delta_neuron_S4[connections[j].second];
		}

		delta_neuron_C3[i] = delta * scale_factor * activation_function_tanh_derivative(neuron_C3[i]);
	}

	for (int i = 0; i < len_weight_S4_CNN; i++) {
		const io_connections& connections = weight2io_C3[i];
		double diff = 0;

		for (int j = 0; j < connections.size(); j++) {
			diff += neuron_C3[connections[j].first] * delta_neuron_S4[connections[j].second];
		}

		delta_weight_S4[i] += diff * scale_factor;
	}

	for (int i = 0; i < len_bias_S4_CNN; i++) {
		const std::vector<int>& outs = bias2out_C3[i];
		double diff = 0;

		for (int o = 0; o < outs.size(); o++) {
			diff += delta_neuron_S4[outs[o]];
		}

		delta_bias_S4[i] += diff;
	}

	return true;
}

(5)、S2层:计算S2层神经元误差、C3层权值误差、C3层偏置误差。通过C3层权值乘以C3层神经元误差。求和,结果再乘以S2层神经元的tanh激活函数的导数(即1-S2神经元的平方),获得S2层每个神经元误差;通过S2层神经元乘以C3层神经元误差。求和,获得C3层权值误差;C3层偏置误差即为C3层神经元误差和。

代码段例如以下:

bool CNN::Backward_S2()
{
	init_variable(delta_neuron_S2, 0.0, num_neuron_S2_CNN);
	init_variable(delta_weight_C3, 0.0, len_weight_C3_CNN);
	init_variable(delta_bias_C3, 0.0, len_bias_C3_CNN);

	// propagate delta to previous layer
	for (int inc = 0; inc < num_map_S2_CNN; inc++) {
		for (int outc = 0; outc < num_map_C3_CNN; outc++) {
			if (!tbl[inc][outc]) continue;

			int addr1 = get_index(0, 0, num_map_S2_CNN * outc + inc, width_kernel_conv_CNN, height_kernel_conv_CNN, num_map_S2_CNN * num_map_C3_CNN);
			int addr2 = get_index(0, 0, outc, width_image_C3_CNN, height_image_C3_CNN, num_map_C3_CNN);
			int addr3 = get_index(0, 0, inc, width_image_S2_CNN, height_image_S2_CNN, num_map_S2_CNN);

			const double *pw = &weight_C3[0] + addr1;
			const double *pdelta_src = &delta_neuron_C3[0] + addr2;;
			double* pdelta_dst = &delta_neuron_S2[0] + addr3;

			for (int y = 0; y < height_image_C3_CNN; y++) {
				for (int x = 0; x < width_image_C3_CNN; x++) {
					const double* ppw = pw;
					const double ppdelta_src = pdelta_src[y * width_image_C3_CNN + x];
					double* ppdelta_dst = pdelta_dst + y * width_image_S2_CNN + x;

					for (int wy = 0; wy < height_kernel_conv_CNN; wy++) {
						for (int wx = 0; wx < width_kernel_conv_CNN; wx++) {
							ppdelta_dst[wy * width_image_S2_CNN + wx] += *ppw++ * ppdelta_src;
						}
					}
				}
			}
		}
	}

	for (int i = 0; i < num_neuron_S2_CNN; i++) {
		delta_neuron_S2[i] *= activation_function_tanh_derivative(neuron_S2[i]);
	}

	// accumulate dw
	for (int inc = 0; inc < num_map_S2_CNN; inc++) {
		for (int outc = 0; outc < num_map_C3_CNN; outc++) {
			if (!tbl[inc][outc]) continue;

			for (int wy = 0; wy < height_kernel_conv_CNN; wy++) {
				for (int wx = 0; wx < width_kernel_conv_CNN; wx++) {
					int addr1 = get_index(wx, wy, inc, width_image_S2_CNN, height_image_S2_CNN, num_map_S2_CNN);
					int addr2 = get_index(0, 0, outc, width_image_C3_CNN, height_image_C3_CNN, num_map_C3_CNN);
					int addr3 = get_index(wx, wy, num_map_S2_CNN * outc + inc, width_kernel_conv_CNN, height_kernel_conv_CNN, num_map_S2_CNN * num_map_C3_CNN);
					
					double dst = 0.0;
					const double* prevo = &neuron_S2[0] + addr1;
					const double* delta = &delta_neuron_C3[0] + addr2;

					for (int y = 0; y < height_image_C3_CNN; y++) {
						dst += dot_product(prevo + y * width_image_S2_CNN, delta + y * width_image_C3_CNN, width_image_C3_CNN);
					}

					delta_weight_C3[addr3] += dst;
				}
			}
		}
	}

	// accumulate db
	for (int outc = 0; outc < len_bias_C3_CNN; outc++) {
		int addr1 = get_index(0, 0, outc, width_image_C3_CNN, height_image_C3_CNN, num_map_C3_CNN);
		const double* delta = &delta_neuron_C3[0] + addr1;

		for (int y = 0; y < height_image_C3_CNN; y++) {
			for (int x = 0; x < width_image_C3_CNN; x++) {
				delta_bias_C3[outc] += delta[y * width_image_C3_CNN + x];
			}
		}
	}

	return true;
}

(6)、C1层:计算C1层神经元误差、S2层权值误差、S2层偏置误差;通过S2层权值乘以S2层神经元误差,求和。结果再乘以C1层神经元的tanh激活函数的导数(即1-C1神经元的平方),然后再乘以1/4,获得C1层每个神经元误差;通过C1层神经元乘以S2神经元误差,求和。再乘以1/4,获得S2层权值误差;通过S2层神经元误差求和,来获得S4层偏置误差。

代码段例如以下:

bool CNN::Backward_C1()
{
	init_variable(delta_neuron_C1, 0.0, num_neuron_C1_CNN);
	init_variable(delta_weight_S2, 0.0, len_weight_S2_CNN);
	init_variable(delta_bias_S2, 0.0, len_bias_S2_CNN);

	double scale_factor = 1.0 / (width_kernel_pooling_CNN * height_kernel_pooling_CNN);

	assert(in2wo_C1.size() == num_neuron_C1_CNN);
	assert(weight2io_C1.size() == len_weight_S2_CNN);
	assert(bias2out_C1.size() == len_bias_S2_CNN);

	for (int i = 0; i < num_neuron_C1_CNN; i++) {
		const wo_connections& connections = in2wo_C1[i];
		double delta = 0.0;

		for (int j = 0; j < connections.size(); j++) {
			delta += weight_S2[connections[j].first] * delta_neuron_S2[connections[j].second];
		}

		delta_neuron_C1[i] = delta * scale_factor * activation_function_tanh_derivative(neuron_C1[i]);
	}

	for (int i = 0; i < len_weight_S2_CNN; i++) {
		const io_connections& connections = weight2io_C1[i];
		double diff = 0.0;

		for (int j = 0; j < connections.size(); j++) {
			diff += neuron_C1[connections[j].first] * delta_neuron_S2[connections[j].second];
		}

		delta_weight_S2[i] += diff * scale_factor;
	}

	for (int i = 0; i < len_bias_S2_CNN; i++) {
		const std::vector<int>& outs = bias2out_C1[i];
		double diff = 0;

		for (int o = 0; o < outs.size(); o++) {
			diff += delta_neuron_S2[outs[o]];
		}

		delta_bias_S2[i] += diff;
	}

	return true;
}

(7)、输入层:计算输入层神经元误差、C1层权值误差、C1层偏置误差;通过C1层权值乘以C1层神经元误差。求和。结果再乘以输入层神经元的tanh激活函数的导数(即1-输入层神经元的平方),获得输入层每个神经元误差;通过输入层层神经元乘以C1层神经元误差,求和。获得C1层权值误差;C1层偏置误差即为C1层神经元误差和。

bool CNN::Backward_input()
{
	init_variable(delta_neuron_input, 0.0, num_neuron_input_CNN);
	init_variable(delta_weight_C1, 0.0, len_weight_C1_CNN);
	init_variable(delta_bias_C1, 0.0, len_bias_C1_CNN);

	// propagate delta to previous layer
	for (int inc = 0; inc < num_map_input_CNN; inc++) {
		for (int outc = 0; outc < num_map_C1_CNN; outc++) {
			int addr1 = get_index(0, 0, num_map_input_CNN * outc + inc, width_kernel_conv_CNN, height_kernel_conv_CNN, num_map_C1_CNN);
			int addr2 = get_index(0, 0, outc, width_image_C1_CNN, height_image_C1_CNN, num_map_C1_CNN);
			int addr3 = get_index(0, 0, inc, width_image_input_CNN, height_image_input_CNN, num_map_input_CNN);

			const double* pw = &weight_C1[0] + addr1;
			const double* pdelta_src = &delta_neuron_C1[0] + addr2;
			double* pdelta_dst = &delta_neuron_input[0] + addr3;

			for (int y = 0; y < height_image_C1_CNN; y++) {
				for (int x = 0; x < width_image_C1_CNN; x++) {
					const double* ppw = pw;
					const double ppdelta_src = pdelta_src[y * width_image_C1_CNN + x];
					double* ppdelta_dst = pdelta_dst + y * width_image_input_CNN + x;

					for (int wy = 0; wy < height_kernel_conv_CNN; wy++) {
						for (int wx = 0; wx < width_kernel_conv_CNN; wx++) {
							ppdelta_dst[wy * width_image_input_CNN + wx] += *ppw++ * ppdelta_src;
						}
					}
				}
			}
		}
	}

	for (int i = 0; i < num_neuron_input_CNN; i++) {
		delta_neuron_input[i] *= activation_function_identity_derivative(data_single_image[i]/*neuron_input[i]*/);
	}

	// accumulate dw
	for (int inc = 0; inc < num_map_input_CNN; inc++) {
		for (int outc = 0; outc < num_map_C1_CNN; outc++) {
			for (int wy = 0; wy < height_kernel_conv_CNN; wy++) {
				for (int wx = 0; wx < width_kernel_conv_CNN; wx++) {
					int addr1 = get_index(wx, wy, inc, width_image_input_CNN, height_image_input_CNN, num_map_input_CNN);
					int addr2 = get_index(0, 0, outc, width_image_C1_CNN, height_image_C1_CNN, num_map_C1_CNN);
					int addr3 = get_index(wx, wy, num_map_input_CNN * outc + inc, width_kernel_conv_CNN, height_kernel_conv_CNN, num_map_C1_CNN);

					double dst = 0.0;
					const double* prevo = data_single_image + addr1;//&neuron_input[0]
					const double* delta = &delta_neuron_C1[0] + addr2;

					for (int y = 0; y < height_image_C1_CNN; y++) {
						dst += dot_product(prevo + y * width_image_input_CNN, delta + y * width_image_C1_CNN, width_image_C1_CNN);
					}

					delta_weight_C1[addr3] += dst;
				}
			}
		}
	}

	// accumulate db
	for (int outc = 0; outc < len_bias_C1_CNN; outc++) {
		int addr1 = get_index(0, 0, outc, width_image_C1_CNN, height_image_C1_CNN, num_map_C1_CNN);
		const double* delta = &delta_neuron_C1[0] + addr1;

		for (int y = 0; y < height_image_C1_CNN; y++) {
			for (int x = 0; x < width_image_C1_CNN; x++) {
				delta_bias_C1[outc] += delta[y * width_image_C1_CNN + x];
			}
		}
	}

	return true;
}

5.        更新各层权值、偏置:通过之前计算的各层权值、各层权值误差。各层偏置、各层偏置误差以及学习率来更新各层权值和偏置。

代码段例如以下:

void CNN::update_weights_bias(const double* delta, double* e_weight, double* weight, int len)
{
	for (int i = 0; i < len; i++) {
		e_weight[i] += delta[i] * delta[i];
		weight[i] -= learning_rate_CNN * delta[i] / (std::sqrt(e_weight[i]) + eps_CNN);
	}
}

bool CNN::UpdateWeights()
{
	update_weights_bias(delta_weight_C1, E_weight_C1, weight_C1, len_weight_C1_CNN);
	update_weights_bias(delta_bias_C1, E_bias_C1, bias_C1, len_bias_C1_CNN);

	update_weights_bias(delta_weight_S2, E_weight_S2, weight_S2, len_weight_S2_CNN);
	update_weights_bias(delta_bias_S2, E_bias_S2, bias_S2, len_bias_S2_CNN);

	update_weights_bias(delta_weight_C3, E_weight_C3, weight_C3, len_weight_C3_CNN);
	update_weights_bias(delta_bias_C3, E_bias_C3, bias_C3, len_bias_C3_CNN);

	update_weights_bias(delta_weight_S4, E_weight_S4, weight_S4, len_weight_S4_CNN);
	update_weights_bias(delta_bias_S4, E_bias_S4, bias_S4, len_bias_S4_CNN);

	update_weights_bias(delta_weight_C5, E_weight_C5, weight_C5, len_weight_C5_CNN);
	update_weights_bias(delta_bias_C5, E_bias_C5, bias_C5, len_bias_C5_CNN);

	update_weights_bias(delta_weight_output, E_weight_output, weight_output, len_weight_output_CNN);
	update_weights_bias(delta_bias_output, E_bias_output, bias_output, len_bias_output_CNN);

	return true;
}

6.        測试准确率是否达到要求或已达到循环次数:依次循环3至5中操作,依据训练集数量。每循环60000次时,通过计算的权值和偏置。来对10000个測试集进行測试,假设准确率达到0.985或者达到迭代次数上限100次时。保存权值和偏置。

代码段例如以下:

bool CNN::train()
{
	out2wi_S2.clear();
	out2bias_S2.clear();
	out2wi_S4.clear();
	out2bias_S4.clear();
	in2wo_C3.clear();
	weight2io_C3.clear();
	bias2out_C3.clear();
	in2wo_C1.clear();
	weight2io_C1.clear();
	bias2out_C1.clear();

	calc_out2wi(width_image_C1_CNN, height_image_C1_CNN, width_image_S2_CNN, height_image_S2_CNN, num_map_S2_CNN, out2wi_S2);
	calc_out2bias(width_image_S2_CNN, height_image_S2_CNN, num_map_S2_CNN, out2bias_S2);
	calc_out2wi(width_image_C3_CNN, height_image_C3_CNN, width_image_S4_CNN, height_image_S4_CNN, num_map_S4_CNN, out2wi_S4);
	calc_out2bias(width_image_S4_CNN, height_image_S4_CNN, num_map_S4_CNN, out2bias_S4);
	calc_in2wo(width_image_C3_CNN, height_image_C3_CNN, width_image_S4_CNN, height_image_S4_CNN, num_map_C3_CNN, num_map_S4_CNN, in2wo_C3);
	calc_weight2io(width_image_C3_CNN, height_image_C3_CNN, width_image_S4_CNN, height_image_S4_CNN, num_map_C3_CNN, num_map_S4_CNN, weight2io_C3);
	calc_bias2out(width_image_C3_CNN, height_image_C3_CNN, width_image_S4_CNN, height_image_S4_CNN, num_map_C3_CNN, num_map_S4_CNN, bias2out_C3);
	calc_in2wo(width_image_C1_CNN, height_image_C1_CNN, width_image_S2_CNN, height_image_S2_CNN, num_map_C1_CNN, num_map_C3_CNN, in2wo_C1);
	calc_weight2io(width_image_C1_CNN, height_image_C1_CNN, width_image_S2_CNN, height_image_S2_CNN, num_map_C1_CNN, num_map_C3_CNN, weight2io_C1);
	calc_bias2out(width_image_C1_CNN, height_image_C1_CNN, width_image_S2_CNN, height_image_S2_CNN, num_map_C1_CNN, num_map_C3_CNN, bias2out_C1);

	int iter = 0;
	for (iter = 0; iter < num_epochs_CNN; iter++) {
		std::cout << "epoch: " << iter + 1;

		for (int i = 0; i < num_patterns_train_CNN; i++) {
			data_single_image = data_input_train + i * num_neuron_input_CNN;
			data_single_label = data_output_train + i * num_neuron_output_CNN;

			Forward_C1();
			Forward_S2();
			Forward_C3();
			Forward_S4();
			Forward_C5();
			Forward_output();

			Backward_output();
			Backward_C5();
			Backward_S4();
			Backward_C3();
			Backward_S2();
			Backward_C1();
			Backward_input();

			UpdateWeights();
		}

		double accuracyRate = test();
		std::cout << ",    accuray rate: " << accuracyRate << std::endl;
		if (accuracyRate > accuracy_rate_CNN) {
			saveModelFile("E:/GitCode/NN_Test/data/cnn.model");
			std::cout << "generate cnn model" << std::endl;
			break;
		}
	}

	if (iter == num_epochs_CNN) {
		saveModelFile("E:/GitCode/NN_Test/data/cnn.model");
		std::cout << "generate cnn model" << std::endl;
	}

	return true;
}

double CNN::test()
{
	int count_accuracy = 0;

	for (int num = 0; num < num_patterns_test_CNN; num++) {
		data_single_image = data_input_test + num * num_neuron_input_CNN;
		data_single_label = data_output_test + num * num_neuron_output_CNN;

		Forward_C1();
		Forward_S2();
		Forward_C3();
		Forward_S4();
		Forward_C5();
		Forward_output();

		int pos_t = -1;
		int pos_y = -2;
		double max_value_t = -9999.0;
		double max_value_y = -9999.0;

		for (int i = 0; i < num_neuron_output_CNN; i++) {
			if (neuron_output[i] > max_value_y) {
				max_value_y = neuron_output[i];
				pos_y = i;
			}

			if (data_single_label[i] > max_value_t) {
				max_value_t = data_single_label[i];
				pos_t = i;
			}
		}

		if (pos_y == pos_t) {
			++count_accuracy;
		}

		Sleep(1);
	}

	return (count_accuracy * 1.0 / num_patterns_test_CNN);
}

7.        对输入的图像数据进行识别:载入已保存的权值和偏置,对输入的数据进行识别。过程相当于前向传播。

代码段例如以下:

int CNN::predict(const unsigned char* data, int width, int height)
{
	assert(data && width == width_image_input_CNN && height == height_image_input_CNN);

	const double scale_min = -1;
	const double scale_max = 1;

	double tmp[width_image_input_CNN * height_image_input_CNN];
	for (int y = 0; y < height; y++) {
		for (int x = 0; x < width; x++) {
			tmp[y * width + x] = (data[y * width + x] / 255.0) * (scale_max - scale_min) + scale_min;
		}
	}

	data_single_image = &tmp[0];

	Forward_C1();
	Forward_S2();
	Forward_C3();
	Forward_S4();
	Forward_C5();
	Forward_output();

	int pos = -1;
	double max_value = -9999.0;

	for (int i = 0; i < num_neuron_output_CNN; i++) {
		if (neuron_output[i] > max_value) {
			max_value = neuron_output[i];
			pos = i;
		}
	}

	return pos;
}

GitHub:
https://github.com/fengbingchun/NN_Test

    原文作者:神经网络
    原文地址: https://www.cnblogs.com/cxchanpin/p/7401188.html
    本文转自网络文章,转载此文章仅为分享知识,如有侵权,请联系博主进行删除。
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