参考彭亮老师的视频教程：转载请注明出处及彭亮老师原创
视频教程： http://pan.baidu.com/s/1kVNe5EJ

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 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))

class NeuralNetwork:        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              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  # adding the bias unit to the input layer                  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)):  #going forward network, for each layer                 a.append(self.activation(np.dot(a[l], self.weights[l])))  #Computer the node value for each layer (O_i) using activation function             error = y[i] – a[-1]  #Computer the error at the top layer             deltas = [error * self.activation_deriv(a[-1])] #For output layer, Err calculation (delta is updated error)                          #Staring backprobagation             for l in range(len(a) – 2, 0, -1): # we need to begin at the second to last layer                  #Compute the updated error (i,e, deltas) for each node going from top layer to input 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)                                       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