bpnn.rar_0_101.bmp_BP神经网络；_python3_手写体识别_手写数字bp

# -*- coding: utf-8 -*- import numpy as np def tanh(x): return np.tanh(x) def tanh_deriv(x): return 1.0 - np.tanh(x) * np.tanh(x) def logistic(x): return 1 / (1 + np.exp(-x)) def logistic_derivative(x): return logistic(x) * (1 - logistic(x)) ''' ClassName：NeuralNetwork Author：kTWO Time：2017-8-10 ''' class NeuralNetwork: #构造函数 def __init__(self, layers, activation='tanh'): ''' :param layers: list类型,比如[2,2.1]代表输入层有两个神经元,隐藏层有两个，输出层有一个 :param activation: 激活函数 ''' self.layers = layers #选择后面用到的激活函数 if activation == 'logistic': self.activation = logistic self.activation_deriv = logistic_derivative elif activation == 'tanh': self.activation = tanh self.activation_deriv = tanh_deriv #定义网络的层数 self.num_layers = len(layers) ''' 生成除输入层外的每层中神经元的biase值，在（-1，-1）之间，每一层都是一行一维数组数据 randn函数执行一次生成x行y列的数据 ''' self.biases = [np.random.randn(x) for x in layers[1:]] # print "偏向：",self.biases ''' 随机生成每条连接线的权重，在（-1,1）之间 weights[i-1]代表第i层和第i-1层之间的权重，元素个数等于i层神经元个数 weights[i-1][0]表示第i层中第一个神经单元和第i-1层每个神经元的权重，元素个数等于i-1层神经元个数 ''' self.weights = [np.random.randn(y, x) for x, y in zip(layers[:-1], layers[1:])] # print "权重：",self.weights #训练模型，进行建模 def fit(self, X, y, learning_rate=0.2, epochs=1): ''' :param self: 当前对象指针 :param X: 训练集 :param y: 训练标记 :param learning_rate: 学习率 :param epochs: 训练次数 :return: void ''' for k in range(epochs): print("epochs:", k) #每次迭代都循环一次训练集 for i in range(len(X)): i = np.random.randint(X.shape[0]) #存储本次的输入和后几层的输出 activations = [X[i]] #向前一层一层的走 for b, w in zip(self.biases, self.weights): # print "w:",w # print "activations[-1]:",activations[-1] # print "b:", b #计算激活函数的参数,计算公式：权重.dot(输入)+偏向 z = np.dot(w, activations[-1])+b #计算输出值 output = self.activation(z) #将本次输出放进输入列表，后面更新权重的时候备用 activations.append(output) # print "计算结果",activations #计算误差值 error = y[i]-activations[-1] #print "实际y值:",y[i] #print "预测值：",activations[-1] # print "误差值",error #计算输出层误差率 deltas = [error * self.activation_deriv(activations[-1])] #循环计算隐藏层的误差率,从倒数第2层开始 for l in range(self.num_layers-2, 0, -1): # print "第l层的权重",self.weights[l] # print "l+1层的误差率",deltas[-1] deltas.append(self.activation_deriv(activations[l]) * np.dot( deltas[-1],self.weights[l])) #将各层误差率顺序颠倒，准备逐层更新权重和偏向 deltas.reverse() # print "每层的误差率：",deltas #更新权重和偏向 for j in range(self.num_layers-1): #本层结点的输出值 layers = np.array(activations[j]) # print "本层输出：",layers # print "错误率：",deltas[j] # 权重的增长量，计算公式，增长量 = 学习率 * (错误率.dot(输出值)) delta = learning_rate * ((np.atleast_2d(deltas[j]).T).dot(np.atleast_2d(layers))) #更新权重 self.weights[j] += delta #print "本层偏向：",self.biases[j] #偏向增加量，计算公式：学习率 * 错误率 delta = learning_rate * deltas[j] #print np.atleast_2d(delta).T #更新偏向 self.biases[j] += delta #print self.weights def predict(self, x): ''' :param x: 测试集 :return: 各类型的预测值 ''' for b, w in zip(self.biases, self.weights): # 计算权重相加再加上偏向的结果 z = np.dot(w, x) + b # 计算输出值 x = self.activation(z) return x if __name__ == '__main__' : nn = NeuralNetwork([2,4,3,1], 'tanh') #训练集 X = np.array([[0, 0], [0, 1], [1, 0],[1, 1]]) #lanbel标记 y = np.array([0, 1, 1, 0]) #建模 nn.fit(X, y, epochs=1000) #预测 for i in [[0, 0], [0, 1], [1, 0], [1,1]]: print(i, nn.predict(i))