Python使用numpy实现BP神经网络

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