bp神经网络python

在 Python 中实现 BP（反向传播）神经网络，可以使用一些第三方库，例如 NumPy、Keras、TensorFlow 等。

这里以 NumPy 为例，给出一个简单的 BP 神经网络实现的代码：

import numpy as np

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

# BP 神经网络类
class BPNeuralNetwork:
    def __init__(self, input_size, hidden_size, output_size):
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.output_size = output_size

        # 初始化权重和偏置
        self.W1 = np.random.randn(hidden_size, input_size)
        self.b1 = np.zeros((hidden_size, 1))
        self.W2 = np.random.randn(output_size, hidden_size)
        self.b2 = np.zeros((output_size, 1))

    # 前向传播
    def forward(self, X):
        self.Z1 = np.dot(self.W1, X) + self.b1
        self.A1 = sigmoid(self.Z1)
        self.Z2 = np.dot(self.W2, self.A1) + self.b2
        self.A2 = sigmoid(self.Z2)
        return self.A2

    # 反向传播
    def backward(self, X, y, learning_rate):
        m = X.shape[1]
        dZ2 = self.A2 - y
        dW2 = (1 / m) * np.dot(dZ2, self.A1.T)
        db2 = (1 / m) * np.sum(dZ2, axis=1, keepdims=True)
        dZ1 = np.dot(self.W2.T, dZ2) * sigmoid(self.Z1) * (1 - sigmoid(self.Z1))
        dW1 = (1 / m) * np.dot(dZ1, X.T)
        db1 = (1 / m) * np.sum(dZ1, axis=1, keepdims=True)

        # 更新权重和偏置
        self.W2 = self.W2 - learning_rate * dW2
        self.b2 = self.b2 - learning_rate * db2
        self.W1 = self.W1 - learning_rate * dW1
        self.b1 = self.b1 - learning_rate * db1

    # 训练
    def train(self, X, y, num_epochs, learning_rate):
        for i in range(num_epochs):
            # 前向传播
            y_hat = self.forward(X)
            # 计算损失
            loss = -(1 / y.shape[1]) * np.sum(y * np.log(y_hat) + (1 - y) * np.log(1 - y_hat))
            # 反向传播
            self.backward(X, y, learning_rate)
            # 输出损失
            print(f"Epoch {i+1}/{num_epochs}: loss = {loss:.4f}")

    # 预测
    def predict(self, X):
        y_hat = self.forward(X)
        return np.round(y_hat)

使用示例：

# 构造数据
X = np.array([[0, 0, 1], [0, 1, 1], [1, 0, 1], [1, 1, 1]]).T
y = np.array([[0, 1, 1, 0]])

# 创建 BP 神经网络
nn = BPNeuralNetwork(input_size=X.shape[0], hidden_size=4, output_size=1)

# 训练
nn.train(X, y, num_epochs=10000, learning_rate=0.1)

# 预测
X_test = np.array([[1, 0, 0], [1, 1, 0], [0, 0, 0], [0, 1, 0]]).T
y_pred = nn.predict(X_test)
print(y_pred)

参考资料：

- [Build Your Own Neural Network in Python](https://towardsdatascience.com/build-your-own-neural-network-in-python-8d13e5916345)
- [Neural Networks and Deep Learning](http://neuralnetworksanddeeplearning.com/)