构建BP神经网络代码

以下是构建BP神经网络的Python代码，其中包括了数据预处理、模型构建、训练和预测等步骤：

import numpy as np

# 数据预处理
def preprocess_data(X, y):
    X = np.array(X)
    y = np.array(y)
    X = X / np.max(X)  # 归一化
    y = y.reshape(-1, 1)
    return X, y

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

# 损失函数
def loss(y_pred, y_true):
    return np.mean((y_pred - y_true) ** 2)

# BP神经网络模型
class BPNeuralNetwork:
    def __init__(self, input_dim, hidden_dim, output_dim):
        self.input_dim = input_dim
        self.hidden_dim = hidden_dim
        self.output_dim = output_dim
        self.W1 = np.random.randn(input_dim, hidden_dim)  # 输入层到隐藏层的权重
        self.b1 = np.zeros((1, hidden_dim))  # 隐藏层的偏置
        self.W2 = np.random.randn(hidden_dim, output_dim)  # 隐藏层到输出层的权重
        self.b2 = np.zeros((1, output_dim))  # 输出层的偏置

    # 前向传播
    def forward(self, X):
        self.z1 = np.dot(X, self.W1) + self.b1
        self.a1 = sigmoid(self.z1)
        self.z2 = np.dot(self.a1, self.W2) + self.b2
        self.a2 = sigmoid(self.z2)
        return self.a2

    # 反向传播
    def backward(self, X, y_true, y_pred, learning_rate):
        delta2 = (y_pred - y_true) * self.a2 * (1 - self.a2)
        dW2 = np.dot(self.a1.T, delta2)
        db2 = np.sum(delta2, axis=0, keepdims=True)
        delta1 = np.dot(delta2, self.W2.T) * self.a1 * (1 - self.a1)
        dW1 = np.dot(X.T, delta1)
        db1 = np.sum(delta1, axis=0)
        self.W2 -= learning_rate * dW2
        self.b2 -= learning_rate * db2
        self.W1 -= learning_rate * dW1
        self.b1 -= learning_rate * db1

    # 训练模型
    def train(self, X, y, epochs, learning_rate):
        X, y = preprocess_data(X, y)
        for i in range(epochs):
            y_pred = self.forward(X)
            l = loss(y_pred, y)
            self.backward(X, y, y_pred, learning_rate)
            if i % 100 == 0:
                print("Epoch %d: loss = %f" % (i, l))

    # 预测
    def predict(self, X):
        X = np.array(X)
        X = X / np.max(X)  # 归一化
        y_pred = self.forward(X)
        return y_pred