python构建深度神经网络（DNN）

本文学习Neural Networks and Deep Learning 在线免费书籍（http://neuralnetworksanddeeplearning.com/index.html），用python构建神经网络识别手写体的一个总结。

代码主要包括两三部分：

1） 数据调用和预处理

2） 神经网络类构建和方法建立

3） 代码测试文件

1)  数据调用：

#!/usr/bin/env python
# -*- coding: utf-8 -*-
# @Time    : 2017-03-12 15:11
# @Author  : CC
# @File    : net_load_data.py
# @Software: PyCharm Community Edition

from numpy import *
import numpy as np
import cPickle
def load_data():
    """载入解压后的数据，并读取"""
    with open('data/mnist_pkl/mnist.pkl','rb') as f:
        try:
            train_data,validation_data,test_data = cPickle.load(f)
            print " the file open sucessfully"
            # print train_data[0].shape  #(50000,784)
            # print train_data[1].shape   #(50000,)
            return (train_data,validation_data,test_data)
        except EOFError:
            print 'the file open error'
            return None

def data_transform():
    """将数据转化为计算格式"""
    t_d,va_d,te_d = load_data()
    # print t_d[0].shape  # (50000,784)
    # print te_d[0].shape  # (10000,784)
    # print va_d[0].shape  # (10000,784)
    # n1 = [np.reshape(x,784,1) for x in t_d[0]] # 将5万个数据分别逐个取出化成（784,1），逐个排列
    n = [np.reshape(x, (784, 1)) for x in t_d[0]]  # 将5万个数据分别逐个取出化成（784,1），逐个排列
    # print 'n1',n1[0].shape
    # print 'n',n[0].shape
    m = [vectors(y) for y in t_d[1]] # 将5万标签（50000,1）化为（10,50000）
    train_data = zip(n,m)  # 将数据与标签打包成元组形式
    n = [np.reshape(x, (784, 1)) for x in va_d[0]]  # 将5万个数据分别逐个取出化成（784,1），排列
    validation_data = zip(n,va_d[1])   # 没有将标签数据矢量化
    n = [np.reshape(x, (784, 1)) for x in te_d[0]]  # 将5万个数据分别逐个取出化成（784,1），排列
    test_data = zip(n, te_d[1])  # 没有将标签数据矢量化
    # print train_data[0][0].shape  #(784,）
    # print "len(train_data[0])",len(train_data[0]) #2
    # print "len(train_data[100])",len(train_data[100]) #2
    # print "len(train_data[0][0])", len(train_data[0][0]) #784
    # print "train_data[0][0].shape", train_data[0][0].shape #（784,1）
    # print "len(train_data)", len(train_data)  #50000
    # print train_data[0][1].shape  #(10,1)
    # print test_data[0][1] # 7
    return (train_data,validation_data,test_data)
def vectors(y):
    """赋予标签"""
    label = np.zeros((10,1))
    label[y] = 1.0 #浮点计算
    return label

2）网络构建

#!/usr/bin/env python
# -*- coding: utf-8 -*-
# @Time    : 2017-03-12 16:07
# @Author  : CC
# @File    : net_network.py

import numpy as np
import random
class Network(object):   #默认为基类?用于继承：print isinstance(network,object)
    def __init__(self,sizes):
        self.num_layers = len(sizes)
        self.sizes = sizes
        # print 'num_layers', self.num_layers
        self.weight = [np.random.randn(a1, a2) for (a1, a2) in zip(sizes[1:], sizes[:-1])] #产生一个个数组
        self.bias = [np.random.randn(a3,1) for a3 in sizes[1:]]
        # print self.weight[0].shape  #(20,10)

    def SGD(self,train_data,min_batch_size,epoches,eta,test_data=False):
        """ 1) 打乱样本，将训练数据划分成小批次
            2）计算出反向传播梯度
            3） 获得权重更新"""
        if test_data: n_test = len(test_data)
        n = len(train_data)   #50000
        random.shuffle(train_data)  # 打乱
        min_batches = [train_data[k:k+min_batch_size] for k in xrange(0,n,min_batch_size)] #提取批次数据
        for k in xrange(0,epoches):   #利用更新后的权值继续更新
            random.shuffle(train_data)  # 打乱
            for min_batch in min_batches:  #逐个传入，效率很低
                self.updata_parameter(min_batch,eta)
            if test_data:
                num = self.evaluate(test_data)
                print "the {0}th epoches: {1}/{2}".format(k,num,len(test_data))
            else:
                print 'epoches {0} completed'.format(k)

    def forward(self,x):
        """获得各层激活值"""
        for w,b in zip(self.weight,self.bias):
            x = sigmoid(np.dot(w, x)+b)
        return x

    def updata_parameter(self,min_batch,eta):
        """1) 反向传播计算每个样本梯度值
           2） 累加每个批次样本的梯度值
           3） 权值更新"""
        ndeltab = [np.zeros(b.shape) for b in self.bias]
        ndeltaw = [np.zeros(w.shape) for w in self.weight]
        for x,y in min_batch:
            deltab,deltaw = self.backprop(x,y)
            ndeltab = [nb +db for nb,db in zip(ndeltab,deltab)]
            ndeltaw = [nw + dw for nw,dw in zip(ndeltaw,deltaw)]
        self.bias = [b - eta * ndb/len(min_batch) for ndb,b in zip(ndeltab,self.bias)]
        self.weight = [w - eta * ndw/len(min_batch) for ndw,w in zip(ndeltaw,self.weight)]


    def backprop(self,x,y):
        """执行前向计算，再进行反向传播，返回deltaw,deltab"""
        # [w for w in self.weight]
        # print 'len',len(w)
        # print "self.weight",self.weight[0].shape
        # print w[0].shape
        # print w[1].shape
        # print w.shape
        activation = x
        activations = [x]
        zs = []
        # feedforward
        for w, b in zip(self.weight, self.bias):
            # print w.shape,activation.shape,b.shape
            z = np.dot(w, activation) +b
            zs.append(z)   #用于计算f(z)导数
            activation = sigmoid(z)
            # print 'activation',activation.shape
            activations.append(activation)  # 每层的输出结果
        delta = self.top_subtract(activations[-1],y) * dsigmoid(zs[-1]) #最后一层的delta,np.array乘,相同维度乘
        deltaw = [np.zeros(w1.shape) for w1 in self.weight]  #每一次将获得的值作为列表形式赋给deltaw
        deltab = [np.zeros(b1.shape) for b1 in self.bias]
        # print 'deltab[0]',deltab[-1].shape
        deltab[-1] = delta
        deltaw[-1] = np.dot(delta,activations[-2].transpose())
        for k in xrange(2,self.num_layers):
            delta = np.dot(self.weight[-k+1].transpose(),delta) * dsigmoid(zs[-k])
            deltab[-k] = delta
            deltaw[-k] = np.dot(delta,activations[-k-1].transpose())
        return (deltab,deltaw)

    def evaluate(self,test_data):
        """评估验证集和测试集的精度,标签直接一个数作为比较"""
        z = [(np.argmax(self.forward(x)),y) for x,y in test_data]
        zs = np.sum(int(a == b) for a,b in z)
        # zk = sum(int(a == b) for a,b in z)
        # print "zs/zk:",zs,zk
        return zs

    def top_subtract(self,x,y):
        return (x - y)

def sigmoid(x):
    return 1.0/(1.0+np.exp(-x))

def dsigmoid(x):
    z = sigmoid(x)
    return z*(1-z)

3） 网络测试

#!/usr/bin/env python
# -*- coding: utf-8 -*-
# @Time    : 2017-03-12 15:24
# @Author  : CC
# @File    : net_test.py

import net_load_data
# net_load_data.load_data()
train_data,validation_data,test_data = net_load_data.data_transform()

import net_network as net
net1 = net.Network([784,30,10])
min_batch_size = 10
eta = 3.0
epoches = 30
net1.SGD(train_data,min_batch_size,epoches,eta,test_data)
print "complete"

4） 结果

the 9th epoches: 9405/10000
the 10th epoches: 9420/10000
the 11th epoches: 9385/10000
the 12th epoches: 9404/10000
the 13th epoches: 9398/10000
the 14th epoches: 9406/10000
the 15th epoches: 9396/10000
the 16th epoches: 9413/10000
the 17th epoches: 9405/10000
the 18th epoches: 9425/10000
the 19th epoches: 9420/10000