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 

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