第14节--神经网络算法（python实现）

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1. 关于非线性转化方程(non-linear transformation function)

sigmoid函数(S 曲线)用来作为activation function:
1.1 双曲函数(tanh)
1.2 逻辑函数(logistic function)

2. 实现一个简单的神经网络算法

import numpy as npdef 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))class NeuralNetwork:    def __init__(self,layers,activation='tanh'):        if activation == 'logistic':            self.activation = logistic            self.activation_deriv = logistic_derivative        elif activation == 'tanh':            self.activation = tanh            self.activation_deriv = tanh_deriv        self.weights = []        for i in range(1,len(layers)-1):            self.weights.append((2*np.random.random((layers[i-1]+1,layers[i]+1))-1)*0.25)            self.weights.append((2*np.random.random((layers[i]+1,layers[i+1]))-1)*0.25)    def fit(self,X,y,learning_rate=0.2,epochs=10000):        X = np.atleast_2d(X)        temp = np.ones([X.shape[0],X.shape[1]+1])        temp[:,0:-1] = X        X = temp        y = np.array(y)        for k in range(epochs):            i = np.random.randint(X.shape[0])            a = [X[i]]            for l in range(len(self.weights)):                a.append(self.activation(np.dot(a[l],self.weights[l])))            error = y[i] - a[-1]            deltas = [error*self.activation_deriv(a[-1])]            for l in range(len(a)-2,0,-1):                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)    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

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