人工神经网络的BP算法程序

以下是基于Python实现的BP算法程序，适用于多层前馈神经网络：

import numpy as np

class BPNN:
    
    def __init__(self, input_size, hidden_size, output_size, learning_rate):
        # 初始化权重和偏置
        self.weights1 = np.random.randn(input_size, hidden_size)
        self.bias1 = np.zeros((1, hidden_size))
        self.weights2 = np.random.randn(hidden_size, output_size)
        self.bias2 = np.zeros((1, output_size))
        # 设置学习率
        self.learning_rate = learning_rate
        
    def sigmoid(self, x):
        # Sigmoid函数
        return 1 / (1 + np.exp(-x))
    
    def sigmoid_derivative(self, x):
        # Sigmoid函数的导数
        return x * (1 - x)
    
    def feedforward(self, X):
        # 前向传播
        self.hidden_layer = self.sigmoid(np.dot(X, self.weights1) + self.bias1)
        self.output_layer = self.sigmoid(np.dot(self.hidden_layer, self.weights2) + self.bias2)
        return self.output_layer
    
    def backpropagation(self, X, y, output):
        # 反向传播
        self.output_error = y - output
        self.output_delta = self.output_error * self.sigmoid_derivative(output)
        self.hidden_error = np.dot(self.output_delta, self.weights2.T)
        self.hidden_delta = self.hidden_error * self.sigmoid_derivative(self.hidden_layer)
        # 更新权重和偏置
        self.weights2 += self.learning_rate * np.dot(self.hidden_layer.T, self.output_delta)
        self.bias2 += self.learning_rate * np.sum(self.output_delta, axis=0, keepdims=True)
        self.weights1 += self.learning_rate * np.dot(X.T, self.hidden_delta)
        self.bias1 += self.learning_rate * np.sum(self.hidden_delta, axis=0)
    
    def train(self, X, y, epochs):
        for i in range(epochs):
            output = self.feedforward(X)
            self.backpropagation(X, y, output)
    
    def predict(self, X):
        return self.feedforward(X)

其中，`input_size`、`hidden_size`、`output_size`分别代表输入层、隐藏层和输出层的神经元个数；`learning_rate`为学习率；`sigmoid`函数为Sigmoid激活函数；`sigmoid_derivative`为Sigmoid函数的导数；`feedforward`为前向传播函数；`backpropagation`为反向传播函数；`train`为训练函数；`predict`为预测函数。