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