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 random class 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 = sizes self.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 + b for 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)) * nw for w, nw in zip(self.weights, nabla_w) ] self.biases = [ # 更新偏置公式 b - (eta / len(mini_batch)) * nb for 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 feedforward activation = x activations = [x] # 所有的activations zs = [] # 储存所有的Z for b, w in zip(self.biases, self.weights): # b w 一行一行的读取 z = np.dot(w, activation) + b zs.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delta nabla_b[-1] = delta nabla_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)* sp nabla_b[-l] = delta nabla_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))