bp神经网络python

Python是一个非常流行的编程语言，也可以用于实现BP神经网络。以下是一个简单的BP神经网络的Python实现示例：

import numpy as np

class NeuralNetwork:
    def __init__(self, input_size, hidden_size, output_size):
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.output_size = output_size
        
        # 初始化权重
        self.weights1 = np.random.rand(self.input_size, self.hidden_size)
        self.weights2 = np.random.rand(self.hidden_size, self.output_size)
        
        # 初始化偏置
        self.bias1 = np.zeros((1, self.hidden_size))
        self.bias2 = np.zeros((1, self.output_size))
        
    def sigmoid(self, x):
        return 1 / (1 + np.exp(-x))
    
    def sigmoid_derivative(self, x):
        return x * (1 - x)
    
    def forward(self, X):
        # 前向传播
        self.z1 = np.dot(X, self.weights1) + self.bias1
        self.a1 = self.sigmoid(self.z1)
        self.z2 = np.dot(self.a1, self.weights2) + self.bias2
        y_hat = self.sigmoid(self.z2)
        return y_hat
    
    def backward(self, X, y, y_hat, learning_rate):
        # 反向传播
        delta2 = (y - y_hat) * self.sigmoid_derivative(y_hat)
        d_weights2 = np.dot(self.a1.T, delta2)
        d_bias2 = np.sum(delta2, axis=0, keepdims=True)
        delta1 = np.dot(delta2, self.weights2.T) * self.sigmoid_derivative(self.a1)
        d_weights1 = np.dot(X.T, delta1)
        d_bias1 = np.sum(delta1, axis=0)
        
        # 更新权重和偏置
        self.weights1 += learning_rate * d_weights1
        self.bias1 += learning_rate * d_bias1
        self.weights2 += learning_rate * d_weights2
        self.bias2 += learning_rate * d_bias2
    
    def train(self, X, y, num_epochs, learning_rate):
        for epoch in range(num_epochs):
            # 前向传播
            y_hat = self.forward(X)
            
            # 反向传播
            self.backward(X, y, y_hat, learning_rate)
            
            # 计算损失
            loss = np.mean(np.square(y - y_hat))
            
            # 输出每个epoch的损失
            if epoch % 1000 == 0:
                print(f"Epoch {epoch}: Loss = {loss}")
                
if __name__ == '__main__':
    X = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
    y = np.array([[0], [1], [1], [0]])
    
    nn = NeuralNetwork(2, 3, 1)
    nn.train(X, y, 10000, 0.1)
    
    print("Predictions:")
    for i in range(X.shape[0]):
        print(f"{X[i]} -> {nn.forward(X[i])}")    

这个示例实现了一个具有2个输入，3个隐藏神经元和1个输出的BP神经网络。使用XOR问题作为训练数据，通过指定10000个epochs和0.1的学习速率进行训练。最后，使用训练好的模型进行预测，并打印结果。