Python使用numpy实现BP神经网络

Python使用numpy实现BP神经网络

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