概述

本文完全利用numpy实现一个简单的BP神经网络，由于是做regression而不是classification，因此在这里输出层选取的激励函数就是f(x)=x。BP神经网络的具体原理此处不再介绍。

import numpy as np 
 
class NeuralNetwork(object): 
  def __init__(self,input_nodes,hidden_nodes,output_nodes,learning_rate): 
    # Set number of nodes in input,hidden and output layers.设定输入层、隐藏层和输出层的node数目 
    self.input_nodes = input_nodes 
    self.hidden_nodes = hidden_nodes 
    self.output_nodes = output_nodes 
 
    # Initialize weights，初始化权重和学习速率 
    self.weights_input_to_hidden = np.random.normal(0.0,self.hidden_nodes**-0.5,( self.hidden_nodes,self.input_nodes)) 
 
    self.weights_hidden_to_output = np.random.normal(0.0,self.output_nodes**-0.5,(self.output_nodes,self.hidden_nodes)) 
    self.lr = learning_rate 
     
    # 隐藏层的激励函数为sigmoid函数，Activation function is the sigmoid function 
    self.activation_function = (lambda x: 1/(1 + np.exp(-x))) 
   
  def train(self,inputs_list,targets_list): 
    # Convert inputs list to 2d array 
    inputs = np.array(inputs_list,ndmin=2).T  # 输入向量的shape为 [feature_diemension,1] 
    targets = np.array(targets_list,ndmin=2).T  
 
    # 向前传播，Forward pass 
    # TODO: Hidden layer 
    hidden_inputs = np.dot(self.weights_input_to_hidden,inputs) # signals into hidden layer 
    hidden_outputs = self.activation_function(hidden_inputs) # signals from hidden layer 
 
     
    # 输出层，输出层的激励函数就是 y = x 
    final_inputs = np.dot(self.weights_hidden_to_output,hidden_outputs) # signals into final output layer 
    final_outputs = final_inputs # signals from final output layer 
     
    ### 反向传播 Backward pass，使用梯度下降对权重进行更新 ### 
     
    # 输出误差 
    # Output layer error is the difference between desired target and actual output. 
    output_errors = (targets_list-final_outputs) 
 
    # 反向传播误差 Backpropagated error 
    # errors propagated to the hidden layer 
    hidden_errors = np.dot(output_errors,self.weights_hidden_to_output)*(hidden_outputs*(1-hidden_outputs)).T 
 
    # 更新权重 Update the weights 
    # 更新隐藏层与输出层之间的权重 update hidden-to-output weights with gradient descent step 
    self.weights_hidden_to_output += output_errors * hidden_outputs.T * self.lr 
    # 更新输入层与隐藏层之间的权重 update input-to-hidden weights with gradient descent step 
    self.weights_input_to_hidden += (inputs * hidden_errors * self.lr).T 
  
  # 进行预测   
  def run(self,inputs_list): 
    # Run a forward pass through the network 
    inputs = np.array(inputs_list,ndmin=2).T 
     
    #### 实现向前传播 Implement the forward pass here #### 
    # 隐藏层 Hidden layer 
    hidden_inputs = np.dot(self.weights_input_to_hidden,inputs) # signals into hidden layer 
    hidden_outputs = self.activation_function(hidden_inputs) # signals from hidden layer 
     
    # 输出层 Output layer 
    final_inputs = np.dot(self.weights_hidden_to_output,hidden_outputs) # signals into final output layer 
    final_outputs = final_inputs # signals from final output layer  
     
    return final_outputs 

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