神经网络二（Neural Network）

#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
__title__ = ''
__author__ = 'wlc'
__mtime__ = '2017/9/04'
"""
import numpy as np
import randomclass Network(object):def __init__(self,sizes):#size神经元个数list[3,2,4]self.num_layers = len(sizes)#几层self.sizes = sizesself.biases = [np.random.randn(y,1) for y in sizes[1:]]#randn生成指定参数的矩阵 高斯分布正态分布均值为0方差为1 zip生成数对，zip([1,2],[2,3,4]) = [(1,2),(2,3)self.weights = [np.random.randn(y,x) for x,y in zip(sizes[:-1],sizes[1:])]#[1:]从第一个元素开始到最后一个元素，[:1]从开始元素到第一个结束不包含第一个元素def feedforward(self, a):  # y=Wx + bfor b, w in zip(self.biases, self.weights):a = sigmoid(np.dot(w, a) + b)return a  # 向量def cost_derivative(self, output_activations, y):return (output_activations - y)# """Return the vector of partial derivatives \partial C_x /# \partial a for the output activations."""def SGD(self, training_data, epoch, mini_batch_size, eta, test_data=None):if test_data: n_test = len(test_data)n = len(training_data)for j in xrange(epoch):random.shuffle(training_data)  # 洗牌打乱mini_batches = [training_data[k:k + mini_batch_size]for k in xrange(0, n, mini_batch_size)]  # 按照batch_size 大小依次将实例取出for mini_batch in mini_batches:self.update_mini_batch(mini_batch, eta)if test_data:print "Epoch {0}:{1} / {2}".format(j, self.evaluate(test_data), n_test)else:print "Epoch {0} complete".format(j)def update_mini_batch(self, mini_batch, eta):nabla_b = [np.zeors(b.shape) for b in self.biases]nabla_w = [np.zeros(w.shape) for w in self.weights]for x, y in mini_batch:delta_nabla_b, delta_nabla_w = self.backprop(x, y)  # 求出权重和偏置的偏导数nabla_b = [nb + dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]  # 随机梯度下降使用mini_batch 的所有梯度累加然后求均值代替求导nabla_w = [nw + dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]  # 累加mini_batch 数量的biases的偏导数代替逐个求导self.weights = [  # 随机梯度下降更新权重公式w - (eta / len(mini_batch)) * nwfor w, nw in zip(self.weights, nabla_w)]self.biases = [  # 更新偏置公式b - (eta / len(mini_batch)) * nbfor b, nb in zip(self.biases, nabla_b)]def evaluate(self, test_data):test_results = [(np.argmax(self.feedforward(x)), y)  # 对于手写体识别而言返回的是10维的向量，因此返回最大值得那一维的索引便是类别for (x, y) in test_data]return sum(int(x == y) for (x, y) in test_results)  # 统计测试集中预测正确的个数def backprop(self, x, y):nabla_b = [np.zeros(b.shape) for b in self.biases]nabla_w = [np.zeros(w.shape) for w in self.weights]# 正向 feedforwardactivation = xactivations = [x]  # 所有的activationszs = []  # 储存所有的Zfor b, w in zip(self.biases, self.weights):  # b w 一行一行的读取z = np.dot(w, activation) + bzs.append(z)activation = sigmoid(z)activations.append(activation)# 反向 backward pass#（对于y = x**2 而言delta y = 2x * delta x）因此对于最后的输出层delta x 就是预测值与真实值的差，2x就是对激活函数求导delta = self.cost_derivative(activations[-1], y) * sigmoid_prime(zs[-1])#对于输出层的deltanabla_b[-1] = deltanabla_w[-1] = np.dot(delta, activations[-2].transpose())for l in xrange(2, self.num_layers):z = zs[-1]sp = sigmoid_prime(z)delta = np.dot(self.weights[-l + 1].transpose(), delta)* spnabla_b[-l] = deltanabla_w[-l] = np.dot(delta, activations[-l +1].transpose())return (nabla_b, nabla_w)nn = Network([2,3,1])
print("#第一层到第二层的链接权重[2,3,1]")
print nn.weights#每个array行代表当前层所有神经元连接下一层某一个神经元的权重
print("#Biases")
print nn.biases#### Miscellaneous functions
def sigmoid(z):"""The sigmoid function."""return 1.0 / (1.0 + np.exp(-z))def sigmoid_prime(z):"""Derivative of the sigmoid function."""return sigmoid(z) * (1 - sigmoid(z))