不用框架，python实现卷积神经网络

最近学习了卷积神经网络，推荐一些比较好的学习资源

1: https://www.zybuluo.com/hanbingtao/note/485480

2: http://blog.csdn.net/u010540396/article/details/52895074

对于网址，我大部分学习的资源和数学公式都是来源于此，强烈推荐学习。

对于网址2，我下面的代码就是在其基础上改写的，作者是用matlab实现的，这对于不会matlab的同学而言，会比较费时，毕竟，

我们要做的是搞懂卷积神经网络，而不是某一个编程语言。

而且最重要的是，我自己想弄明白CNN的前向网络和误差反向传播算法，自己亲自实现一遍，更有助于理解和记忆，哪怕是看着别人的代码学会的。

A:下面代码实现是LenNet-5的代码，但是只有一个卷积层，一个mean-pooling层，和一个全连接层，出来经过softmax层。

B:使用的数据集是MNIST,你可以到http://yann.lecun.com/exdb/mnist/

C:MNIST的数据解析，可以从我下面的analysisMNIST.py中修改路径，谢谢(http://blog.csdn.net/u014046170/article/details/47445919)然后取得到数据如下情况:

D:在C解析完之后，我把label文件的内容转置了，开始的时候是一行，我改成了一列。

注:代码里面的TODO是很多公式推导，我有空会敲出来，然后也作为超链接给弄出来，怕自己下次又给忘了。

我的总共有三个文件:

这是我定义的全局变量的文件 gParam.py

#! /usr/bin/env python# -*- coding: utf-8 -*-TOP_PATH = '/media/autumn/Work/data/MNIST/mnist-png/'LAB_PATH = '/media/autumn/Work/data/MNIST/mnist-png/label1.txt'C_SIZE = 5F_NUM = 12P_SIZE = 2FILE_TYPE = '.png'MAX_ITER_NUM = 50

这是我测试的文件myCnnTest.py

#! /usr/bin/env python# -*- coding: utf-8 -*-from numpy import *import numpy as npfrom myCnn import Ccnnimport mathimport gParam# codecLyNum = 20pLyNum = 20fLyNum = 100oLyNum = 10train_num = 800myCnn = Ccnn(cLyNum, pLyNum, fLyNum, oLyNum)ylabel = myCnn.read_label(gParam.LAB_PATH)for iter0 in range(gParam.MAX_ITER_NUM):for i in range(train_num):data = myCnn.read_pic_data(gParam.TOP_PATH, i)#print shape(data)ylab = int(ylabel[i])d_m, d_n = shape(data)m_c = d_m - gParam.C_SIZE + 1n_c = d_n - gParam.C_SIZE + 1m_p = m_c/myCnn.pSizen_p = n_c/myCnn.pSizestate_c = zeros((m_c, n_c,myCnn.cLyNum))state_p = zeros((m_p, n_p, myCnn.pLyNum))for n in range(myCnn.cLyNum):state_c[:,:,n] = myCnn.convolution(data, myCnn.kernel_c[:,:,n])#print shape(myCnn.cLyNum)tmp_bias = ones((m_c,n_c)) * myCnn.cLyBias[:,n]state_c[:,:,n] = np.tanh(state_c[:,:,n] + tmp_bias)# 加上偏置项然后过激活函数state_p[:,:,n] = myCnn.pooling(state_c[:,:,n],myCnn.pooling_a)state_f, state_f_pre = myCnn.convolution_f1(state_p,myCnn.kernel_f, myCnn.weight_f)#print shape(state_f), shape(state_f_pre)#进入激活函数state_fo = zeros((1,myCnn.fLyNum))#全连接层经过激活函数的结果for n in range(myCnn.fLyNum):state_fo[:,n] = np.tanh(state_f[:,:,n] + myCnn.fLyBias[:,n])#进入softmax层output = myCnn.softmax_layer(state_fo)err = -output[:,ylab]#计算误差y_pre = output.argmax(axis=1)#print output#计算误差#print err myCnn.cnn_upweight(err,ylab,data,state_c,state_p,\state_fo, state_f_pre, output)# print myCnn.kernel_c# print myCnn.cLyBias# print myCnn.weight_f# print myCnn.kernel_f# print myCnn.fLyBias# print myCnn.weight_output# predicttest_num = []for i in range(100):test_num.append(train_num+i+1)for i in test_num:data = myCnn.read_pic_data(gParam.TOP_PATH, i)#print shape(data)ylab = int(ylabel[i])d_m, d_n = shape(data)m_c = d_m - gParam.C_SIZE + 1n_c = d_n - gParam.C_SIZE + 1m_p = m_c/myCnn.pSizen_p = n_c/myCnn.pSizestate_c = zeros((m_c, n_c,myCnn.cLyNum))state_p = zeros((m_p, n_p, myCnn.pLyNum))for n in range(myCnn.cLyNum):state_c[:,:,n] = myCnn.convolution(data, myCnn.kernel_c[:,:,n])#print shape(myCnn.cLyNum)tmp_bias = ones((m_c,n_c)) * myCnn.cLyBias[:,n]state_c[:,:,n] = np.tanh(state_c[:,:,n] + tmp_bias)# 加上偏置项然后过激活函数state_p[:,:,n] = myCnn.pooling(state_c[:,:,n],myCnn.pooling_a)state_f, state_f_pre = myCnn.convolution_f1(state_p,myCnn.kernel_f, myCnn.weight_f)#print shape(state_f), shape(state_f_pre)#进入激活函数state_fo = zeros((1,myCnn.fLyNum))#全连接层经过激活函数的结果for n in range(myCnn.fLyNum):state_fo[:,n] = np.tanh(state_f[:,:,n] + myCnn.fLyBias[:,n])#进入softmax层output = myCnn.softmax_layer(state_fo)#计算误差y_pre = output.argmax(axis=1)print '真实数字为%d',ylab, '预测数字是%d', y_pre

接下来是CNN的核心代码，里面有中文注释，文件名是myCnn.py

#! /usr/bin/env python# -*- coding: utf-8 -*-from numpy import *import numpy as npimport matplotlib.pyplot as pltimport matplotlib.image as mgimgimport mathimport gParamimport copyimport scipy.signal as signal# createst uniform random array w/ values in [a,b) and shape args# return value type is ndarraydef rand_arr(a, b, *args):     np.random.seed(0)     return np.random.rand(*args) * (b - a) + a# Class Cnn     class Ccnn:def __init__(self, cLyNum, pLyNum,fLyNum,oLyNum):self.cLyNum = cLyNumself.pLyNum = pLyNumself.fLyNum = fLyNumself.oLyNum = oLyNumself.pSize = gParam.P_SIZEself.yita = 0.01self.cLyBias = rand_arr(-0.1, 0.1, 1,cLyNum)self.fLyBias = rand_arr(-0.1, 0.1, 1,fLyNum)self.kernel_c = zeros((gParam.C_SIZE,gParam.C_SIZE,cLyNum))self.kernel_f = zeros((gParam.F_NUM,gParam.F_NUM,fLyNum))for i in range(cLyNum):self.kernel_c[:,:,i] = rand_arr(-0.1,0.1,gParam.C_SIZE,gParam.C_SIZE)for i in range(fLyNum):self.kernel_f[:,:,i] = rand_arr(-0.1,0.1,gParam.F_NUM,gParam.F_NUM)self.pooling_a = ones((self.pSize,self.pSize))/(self.pSize**2)self.weight_f = rand_arr(-0.1,0.1, pLyNum, fLyNum)self.weight_output = rand_arr(-0.1,0.1,fLyNum,oLyNum)def read_pic_data(self, path, i):#print 'read_pic_data'data = np.array([])full_path = path + '%d'%i + gParam.FILE_TYPEtry:data = mgimg.imread(full_path) #data is np.arraydata = (double)(data)except IOError:raise Exception('open file error in read_pic_data():', full_path)return datadef read_label(self, path):#print 'read_label'ylab = []try:fobj = open(path, 'r')for line in fobj:ylab.append(line.strip())fobj.close()except IOError:raise Exception('open file error in read_label():', path)return ylab#卷积层def convolution(self, data, kernel):data_row, data_col = shape(data)kernel_row, kernel_col = shape(kernel)n = data_col - kernel_colm = data_row - kernel_rowstate = zeros((m+1, n+1))for i in range(m+1):for j in range(n+1):temp = multiply(data[i:i+kernel_row,j:j+kernel_col], kernel)state[i][j] = temp.sum()return state# 池化层def pooling(self, data, pooling_a):data_r, data_c = shape(data)p_r, p_c = shape(pooling_a)r0 = data_r/p_rc0 = data_c/p_cstate = zeros((r0,c0))for i in range(c0):for j in range(r0):temp = multiply(data[p_r*i:p_r*i+1,p_c*j:p_c*j+1],pooling_a)state[i][j] = temp.sum()return state#全连接层def convolution_f1(self, state_p1, kernel_f1, weight_f1):#池化层出来的20个特征矩阵乘以池化层与全连接层的连接权重进行相加#wx(这里的偏置项=0),这个结果然后再和全连接层中的神经元的核#进行卷积,返回值:#1：全连接层卷积前,只和weight_f1相加之后的矩阵#2：和全连接层卷积完之后的矩阵n_p0, n_f = shape(weight_f1)#n_p0=20(是Feature Map的个数);n_f是100(全连接层神经元个数)m_p, n_p, pCnt = shape(state_p1)#这个矩阵是三维的m_k_f1, n_k_f1,fCnt = shape(kernel_f1)#12*12*100state_f1_temp = zeros((m_p,n_p,n_f))state_f1 = zeros((m_p - m_k_f1 + 1,n_p - n_k_f1 + 1,n_f))for n in range(n_f):count = 0for m in range(n_p0):temp = state_p1[:,:,m] * weight_f1[m][n] count = count + tempstate_f1_temp[:,:,n] = countstate_f1[:,:,n] = self.convolution(state_f1_temp[:,:,n], kernel_f1[:,:,n])return state_f1, state_f1_temp# softmax 层def softmax_layer(self,state_f1):# print 'softmax_layer'output = zeros((1,self.oLyNum))t1 = (exp(np.dot(state_f1,self.weight_output))).sum()for i in range(self.oLyNum):t0 = exp(np.dot(state_f1,self.weight_output[:,i]))output[:,i]=t0/t1return output#误差反向传播更新权值def cnn_upweight(self,err_cost, ylab, train_data,state_c1, \state_s1, state_f1, state_f1_temp, output):#print 'cnn_upweight'm_data, n_data = shape(train_data)# softmax的资料请查看 (TODO)label = zeros((1,self.oLyNum))label[:,ylab]= 1 delta_layer_output = output - labelweight_output_temp = copy.deepcopy(self.weight_output)delta_weight_output_temp = zeros((self.fLyNum, self.oLyNum))#print shape(state_f1)#更新weight_outputfor n in range(self.oLyNum):delta_weight_output_temp[:,n] = delta_layer_output[:,n] * state_f1weight_output_temp = weight_output_temp - self.yita * delta_weight_output_temp#更新bais_f和kernel_f (推导公式请查看 TODO)delta_layer_f1 = zeros((1, self.fLyNum))delta_bias_f1 = zeros((1,self.fLyNum))delta_kernel_f1_temp = zeros(shape(state_f1_temp))kernel_f_temp = copy.deepcopy(self.kernel_f)for n in range(self.fLyNum):count = 0for m in range(self.oLyNum):count = count + delta_layer_output[:,m] * self.weight_output[n,m]delta_layer_f1[:,n] = np.dot(count, (1 - np.tanh(state_f1[:,n])**2))delta_bias_f1[:,n] = delta_layer_f1[:,n]delta_kernel_f1_temp[:,:,n] = delta_layer_f1[:,n] * state_f1_temp[:,:,n]# 1self.fLyBias = self.fLyBias - self.yita * delta_bias_f1kernel_f_temp = kernel_f_temp - self.yita * delta_kernel_f1_temp #更新weight_f1delta_layer_f1_temp = zeros((gParam.F_NUM,gParam.F_NUM,self.fLyNum))delta_weight_f1_temp = zeros(shape(self.weight_f))weight_f1_temp = copy.deepcopy(self.weight_f)for n in range(self.fLyNum):delta_layer_f1_temp[:,:,n] = delta_layer_f1[:,n] * self.kernel_f[:,:,n]for n in range(self.pLyNum):for m in range(self.fLyNum):temp = delta_layer_f1_temp[:,:,m] * state_s1[:,:,n]delta_weight_f1_temp[n,m] = temp.sum()weight_f1_temp = weight_f1_temp - self.yita * delta_weight_f1_temp# 更新bias_c1n_delta_c = m_data - gParam.C_SIZE + 1delta_layer_p = zeros((gParam.F_NUM,gParam.F_NUM,self.pLyNum))delta_layer_c = zeros((n_delta_c,n_delta_c,self.pLyNum))delta_bias_c = zeros((1,self.cLyNum))for n in range(self.pLyNum):count = 0for m in range(self.fLyNum):count = count + delta_layer_f1_temp[:,:,m] * self.weight_f[n,m]delta_layer_p[:,:,n] = count#print shape(np.kron(delta_layer_p[:,:,n], ones((2,2))/4))delta_layer_c[:,:,n] = np.kron(delta_layer_p[:,:,n], ones((2,2))/4) \  * (1 - np.tanh(state_c1[:,:,n])**2)delta_bias_c[:,n] = delta_layer_c[:,:,n].sum()# 2self.cLyBias = self.cLyBias - self.yita * delta_bias_c#更新 kernel_c1delta_kernel_c1_temp = zeros(shape(self.kernel_c))for n in range(self.cLyNum):temp = delta_layer_c[:,:,n]r1 = map(list,zip(*temp[::1]))#逆时针旋转90度r2 = map(list,zip(*r1[::1]))#再逆时针旋转90度temp = signal.convolve2d(train_data, r2,'valid')temp1 = map(list,zip(*temp[::1]))delta_kernel_c1_temp[:,:,n] = map(list,zip(*temp1[::1]))self.kernel_c = self.kernel_c - self.yita * delta_kernel_c1_temp  self.weight_f = weight_f1_tempself.kernel_f = kernel_f_tempself.weight_output = weight_output_temp# predictdef cnn_predict(self,data):return 

这是单独解析MNIST的脚本,analysisMNIST.py，修改相应的路径后，运行能成功

#!/usr/bin/env python# -*- coding: utf-8 -*-from PIL import Imageimport structdef read_image(filename):  f = open(filename, 'rb')  index = 0  buf = f.read()  f.close()  magic, images, rows, columns = struct.unpack_from('>IIII' , buf , index)  index += struct.calcsize('>IIII')  for i in xrange(images):  #for i in xrange(2000):    image = Image.new('L', (columns, rows))    for x in xrange(rows):      for y in xrange(columns):        image.putpixel((y, x), int(struct.unpack_from('>B', buf, index)[0]))        index += struct.calcsize('>B')    print 'save ' + str(i) + 'image'    image.save('/media/autumn/Work/data/MNIST/mnist-png/' + str(i) + '.png')def read_label(filename, saveFilename):  f = open(filename, 'rb')  index = 0  buf = f.read()  f.close()  magic, labels = struct.unpack_from('>II' , buf , index)  index += struct.calcsize('>II')    labelArr = [0] * labels  #labelArr = [0] * 2000  for x in xrange(labels):  #for x in xrange(2000):    labelArr[x] = int(struct.unpack_from('>B', buf, index)[0])    index += struct.calcsize('>B')  save = open(saveFilename, 'w')  save.write(','.join(map(lambda x: str(x), labelArr)))  save.write('\n')  save.close()  print 'save labels success'if __name__ == '__main__':  read_image('/media/autumn/Work/data/MNIST/mnist/t10k-images.idx3-ubyte')  read_label('/media/autumn/Work/data/MNIST/mnist/t10k-labels.idx1-ubyte', '/media/autumn/Work/data/MNIST/mnist-png/label.txt')

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