神经网络算法

import numpy as np

# 定义激活函数
def sigmoid(x):
    return 1 / (1 + np.exp(-x))

# 定义神经网络类
class NeuralNetwork:
    def __init__(self, input_size, hidden_size, output_size):
        # 初始化权重
        self.W1 = np.random.randn(input_size, hidden_size)
        self.b1 = np.zeros((1, hidden_size))
        
        self.W2 = np.random.randn(hidden_size, output_size)
        self.b2 = np.zeros((1, output_size))
    
    def forward(self, X):
        # 前向传播计算输出
        self.z2 = np.dot(X, self.W1) + self.b1
        self.a2 = sigmoid(self.z2)
        
        self.z3 = np.dot(self.a2, self.W2) + self.b2
        self.a3 = sigmoid(self.z3)
        
        return self.a3
    
    def backward(self, X, y, learning_rate):
        # 反向传播更新参数
        m = len(X)
        
        delta3 = self.a3 - y
        dW2 = np.dot(self.a2.T, delta3) / m
        db2 = np.sum(delta3, axis=0) / m
        
        delta2 = np.dot(delta3, self.W2.T) * self.a2 * (1 - self.a2)
        dW1 = np.dot(X.T, delta2) / m
        db1 = np.sum(delta2, axis=0) / m
        
        self.W2 -= learning_rate * dW2
        self.b2 -= learning_rate * db2
        self.W1 -= learning_rate * dW1
        self.b1 -= learning_rate * db1
    
    def train(self, X, y, num_epochs, learning_rate):
        # 训练神经网络
        for epoch in range(num_epochs):
            # 前向传播计算输出
            output = self.forward(X)
            
            # 反向传播更新参数
            self.backward(X, y, learning_rate)
            
            # 打印损失函数值
            loss = np.mean((output - y) ** 2)
            print("Epoch:", epoch+1, "Loss:", loss)
    
    def predict(self, X):
        # 预测分类结果
        output = self.forward(X)
        predictions = np.round(output)
        return predictions

# 输入数据
X = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
y = np.array([[0], [1], [1], [0]])

# 初始化神经网络
input_size = X.shape[1]
hidden_size = 4
output_size = y.shape[1]
nn = NeuralNetwork(input_size, hidden_size, output_size)

# 训练神经网络
num_epochs = 10000
learning_rate = 0.1
nn.train(X, y, num_epochs, learning_rate)

# 预测新样本
test_X = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
predictions = nn.predict(test_X)

# 输出预测结果
print("预测结果:", predictions)