Numpy 实现神经网络

#coding:utf-8

import numpy as np  
  
#定义激活函数和他们的导数  
def tanh(x):  
    return np.tanh(x)  
  
def tanh_deriv(x):  
    return 1.0 - np.tanh(x)**2  
  
def logistic(x):  
    return 1/(1 + np.exp(-x))  
  
def logistic_derivative(x):  
    return logistic(x)*(1-logistic(x))  

#定义NeuralNetwork 神经网络算法  
class NeuralNetwork:  
    #初始化，layes表示的是一个list，eg[10,10,3]表示第一层10个神经元，第二层10个神经元，第三层3个神经元  
    def __init__(self, layers, activation='tanh'):  
        """ 
        :param layers: A list containing the number of units in each layer. 
        Should be at least two values 
        :param activation: The activation function to be used. Can be 
        "logistic" or "tanh" 
        """  
        if activation == 'logistic':  
            self.activation = logistic  
            self.activation_deriv = logistic_derivative  
        elif activation == 'tanh':  
            self.activation = tanh  
            self.activation_deriv = tanh_deriv  
        
        # 随机初始化权重
        self.weights = []  
        #循环从1开始，相当于以第二层为基准，进行权重的初始化  
        for i in range(1, len(layers) - 1):  
            #对当前神经节点的前驱赋值  
            self.weights.append((2*np.random.random((layers[i - 1] + 1, layers[i] + 1))-1)*0.25)  
            #对当前神经节点的后继赋值  
            self.weights.append((2*np.random.random((layers[i] + 1, layers[i + 1]))-1)*0.25)  
      
    #训练函数，X矩阵，每行是一个实例 ，y是每个实例对应的结果，learning_rate 学习率，   
    # epochs，表示抽样的方法对神经网络进行更新的最大次数  
    def fit(self, X, y, learning_rate=0.1, epochs=10000):  
        X = np.atleast_2d(X) #确定X至少是二维的数据  
        temp = np.ones([X.shape[0], X.shape[1]+1]) #初始化矩阵  
        temp[:, 0:-1] = X  # adding the bias unit to the input layer  
        X = temp  
        y = np.array(y) #把list转换成array的形式  
  
        for k in range(epochs):  
            #随机选取一行，对神经网络进行更新  
            i = np.random.randint(X.shape[0])   
            a = [X[i]]  
  
            #完成所有正向的更新  
            for l in range(len(self.weights)):  
                a.append(self.activation(np.dot(a[l], self.weights[l])))  
            #误差反向传播
            error = y[i] - a[-1]  
            deltas = [error * self.activation_deriv(a[-1])]  
            if  k%1000 == 0:
                print(k,'...',error*error*100)
            #开始反向计算误差，更新权重  
            for l in range(len(a) - 2, 0, -1): # we need to begin at the second to last layer  
                deltas.append(deltas[-1].dot(self.weights[l].T)*self.activation_deriv(a[l]))  
            deltas.reverse()  
            for i in range(len(self.weights)):  
                layer = np.atleast_2d(a[i])  
                delta = np.atleast_2d(deltas[i])  
                self.weights[i] += learning_rate * layer.T.dot(delta)  
      
    #预测函数              
    def predict(self, x):  
        x = np.array(x)  
        temp = np.ones(x.shape[0]+1)  
        temp[0:-1] = x  
        a = temp  
        for l in range(0, len(self.weights)):  
            a = self.activation(np.dot(a, self.weights[l]))  
        return a  

以上代码仅仅是对 BP 做一个简单地演示，离可用的神经网络还有千里之遥，下面用它来演示 XOR 的学习：

nn = NeuralNetwork([2,2,1], 'tanh')  
X = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])  
y = np.array([0, 1, 1, 0])  
nn.fit(X, y)  
for i in [[0, 0], [0, 1], [1, 0], [1,1]]:  
    print(i,nn.predict(i)) 

output：

0 ... [99.46125954]
1000 ... [13.75662528]
2000 ... [0.89069164]
3000 ... [0.04930435]
4000 ... [0.02505558]
5000 ... [0.00486738]
6000 ... [0.00715196]
7000 ... [0.00313886]
8000 ... [0.0028314]
9000 ... [4.51779469e-05]
[0, 0] [0.00068042]
[0, 1] [0.9962246]
[1, 0] [0.99607674]
[1, 1] [-0.00014186]

该代码可能有问题