用Python实现机器学习算法之神经网络算法并做注释说明

当实现神经网络算法时，可以使用Python编程语言以及相关的库和框架来简化开发过程。下面是一个用Python实现神经网络算法的示例代码，并包含了详细的注释说明：

# 导入所需的库
import numpy as np

# 定义神经网络类
class NeuralNetwork:
    def __init__(self, input_size, hidden_size, output_size):
        # 初始化网络参数
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.output_size = output_size

        # 初始化权重
        self.W1 = np.random.randn(self.input_size, self.hidden_size)
        self.W2 = np.random.randn(self.hidden_size, self.output_size)

    def forward(self, X):
        # 前向传播计算
        self.z = np.dot(X, self.W1)
        self.z2 = self.sigmoid(self.z)
        self.z3 = np.dot(self.z2, self.W2)
        y_hat = self.sigmoid(self.z3)
        return y_hat

    def backward(self, X, y, y_hat, learning_rate):
        # 反向传播更新权重
        delta3 = (y_hat - y) * self.sigmoid_derivative(self.z3)
        dW2 = np.dot(self.z2.T, delta3)
        delta2 = np.dot(delta3, self.W2.T) * self.sigmoid_derivative(self.z)
        dW1 = np.dot(X.T, delta2)

        # 根据学习率更新权重
        self.W1 -= learning_rate * dW1
        self.W2 -= learning_rate * dW2

    def train(self, X, y, learning_rate, epochs):
        for epoch in range(epochs):
            # 前向传播计算预测值
            y_hat = self.forward(X)

            # 反向传播更新权重
            self.backward(X, y, y_hat, learning_rate)

    def sigmoid(self, x):
        return 1 / (1 + np.exp(-x))

    def sigmoid_derivative(self, x):
        return self.sigmoid(x) * (1 - self.sigmoid(x))

# 创建训练数据集
X = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
y = np.array([[0], [1], [1], [0]])

# 创建神经网络对象并训练
nn = NeuralNetwork(input_size=2, hidden_size=4, output_size=1)
nn.train(X, y, learning_rate=0.1, epochs=1000)

# 使用训练好的神经网络进行预测
predictions = nn.forward(X)
print(predictions)