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