BP.rar_BP_BP神经网络_bp python_mixo1q_python

#!/usr/bin/env python # -*- coding: UTF-8 -*- """ network.py ~~~~~~~~~~ A module to implement the stochastic gradient descent learning algorithm for a feedforward neural network. Gradients are calculated using backpropagation. Note that I have focused on making the code simple, easily readable, and easily modifiable. It is not optimized, and omits many desirable features. """ #### Libraries # Standard library import random # Third-party libraries import numpy as np class Network(object): def __init__(self, sizes): """ :param sizes: list类型，储存每层神经网络的神经元数目 譬如说：sizes = [2, 3, 2] 表示输入层有两个神经元、 隐藏层有3个神经元以及输出层有2个神经元 """ # 有几层神经网络 self.num_layers = len(sizes) self.sizes = sizes # 除去输入层，随机产生每层中 y 个神经元的 biase 值（0 - 1） self.biases = [np.random.randn(y, 1) for y in sizes[1:]] # 随机产生每条连接线的 weight 值（0 - 1） self.weights = [np.random.randn(y, x) for x, y in zip(sizes[:-1], sizes[1:])] def feedforward(self, a): """ 前向传输计算每个神经元的值 :param a: 输入值 :return: 计算后每个神经元的值 """ for b, w in zip(self.biases, self.weights): # 加权求和以及加上 biase a = sigmoid(np.dot(w, a) + b) return a def SGD(self, training_data, epochs, mini_batch_size, eta, test_data=None): """ 随机梯度下降 :param training_data: 输入的训练集 :param epochs: 迭代次数 :param mini_batch_size: 小样本数量 :param eta: 学习率 :param test_data: 测试数据集 """ test_data = list(test_data) training_data = list(training_data) if test_data: n_test = len(test_data) n = len(training_data) for j in range(epochs): # 搅乱训练集，让其排序顺序发生变化 random.shuffle(training_data) # 按照小样本数量划分训练集 mini_batches = [ training_data[k:k+mini_batch_size] for k in range(0, n, mini_batch_size)] for mini_batch in mini_batches: # 根据每个小样本来更新 w 和 b，代码在下一段 self.update_mini_batch(mini_batch, eta) # 输出测试每轮结束后，神经网络的准确度 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): """ 更新 w 和 b 的值 :param mini_batch: 一部分的样本 :param eta: 学习率 """ # 根据 biases 和 weights 的行列数创建对应的全部元素值为 0 的空矩阵 nabla_b = [np.zeros(b.shape) for b in self.biases] nabla_w = [np.zeros(w.shape) for w in self.weights] for x, y in mini_batch: # 根据样本中的每一个输入 x 的其输出 y，计算 w 和 b 的偏导数 delta_nabla_b, delta_nabla_w = self.backprop(x, y) # 累加储存偏导值 delta_nabla_b 和 delta_nabla_w nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)] nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)] # 更新根据累加的偏导值更新 w 和 b，这里因为用了小样本， # 所以 eta 要除于小样本的长度 self.weights = [w-(eta/len(mini_batch))*nw for w, nw in zip(self.weights, nabla_w)] self.biases = [b-(eta/len(mini_batch))*nb for b, nb in zip(self.biases, nabla_b)] def backprop(self, x, y): """ :param x: :param y: :return: """ nabla_b = [np.zeros(b.shape) for b in self.biases] nabla_w = [np.zeros(w.shape) for w in self.weights] # 前向传输 activation = x # 储存每层的神经元的值的矩阵，下面循环会 append 每层的神经元的值 activations = [x] # 储存每个未经过 sigmoid 计算的神经元的值 zs = [] for b, w in zip(self.biases, self.weights): z = np.dot(w, activation)+b zs.append(z) activation = sigmoid(z) activations.append(activation) # 求 δ 的值 delta = self.cost_derivative(activations[-1], y) * \ sigmoid_prime(zs[-1]) nabla_b[-1] = delta # 乘于前一层的输出值 nabla_w[-1] = np.dot(delta, activations[-2].transpose()) for l in range(2, self.num_layers): # 从倒数第 **l** 层开始更新，**-l** 是 python 中特有的语法表示从倒数第 l 层开始计算 # 下面这里利用 **l+1** 层的 δ 值来计算 **l** 的 δ 值 z = zs[-l] 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) def evaluate(self, test_data): # 获得预测结果 test_results = [(np.argmax(self.feedforward(x)), y) for (x, y) in test_data] # 返回正确识别的个数 return sum(int(x == y) for (x, y) in test_results) def cost_derivative(self, output_activations, y): """ 二次损失函数 :param output_activations: :param y: :return: """ return (output_activations-y) #### Miscellaneous functions def sigmoid(z): """ 求 sigmoid 函数的值 :param z: :return: """ return 1.0/(1.0+np.exp(-z)) def sigmoid_prime(z): """ 求 sigmoid 函数的导数 :param z: :return: """ return sigmoid(z)*(1-sigmoid(z))