试编程实现标准bp算法试编程实现标准BP算法和累计BP算法,在⻄瓜数据集3.0上分别⽤这两 个算法训练⼀个单隐层⽹络，并进⾏比较。（⻄瓜数据集3.0在表4.3， P84）

标准的Back Propagation (BP) 算法是一种用于训练神经网络的监督学习方法，它通过计算梯度并反向传播误差来更新网络权重。下面是简化的Python伪代码，展示了如何使用BP算法训练一个简单的单隐藏层神经网络：

import numpy as np

class SingleLayerNN:
    def __init__(self, input_size, hidden_size, output_size):
        self.weights1 = np.random.randn(input_size, hidden_size)
        self.bias1 = np.zeros((1, hidden_size))
        self.weights2 = np.random.randn(hidden_size, output_size)
        self.bias2 = np.zeros((1, output_size))

    # BP算法核心部分
    def backprop(self, inputs, targets, learning_rate):
        # Forward pass
        hidden_layer = sigmoid(np.dot(inputs, self.weights1) + self.bias1)
        predictions = sigmoid(np.dot(hidden_layer, self.weights2) + self.bias2)

        # Error calculation
        error = targets - predictions
        d_weights2 = np.dot(hidden_layer.T, error * predictions * (1 - predictions))
        d_bias2 = np.sum(error * predictions * (1 - predictions), axis=0, keepdims=True)
        d_weights1 = np.dot(inputs.T, error * hidden_layer * (1 - hidden_layer) * np.dot(error, self.weights2.T))
        d_bias1 = np.sum(error * hidden_layer * (1 - hidden_layer), axis=0, keepdims=True)

        # Weight updates
        self.weights2 += learning_rate * d_weights2
        self.bias2 += learning_rate * d_bias2
        self.weights1 += learning_rate * d_weights1
        self.bias1 += learning_rate * d_bias1

# 使用西瓜数据集3.0
# ... (假设已经读取和预处理了数据)

# 初始化网络和设置学习率等参数
nn = SingleLayerNN(X_train.shape[1], hidden_size, y_train.shape[1])
learning_rate = 0.1

# 训练过程（循环迭代）
for _ in range(num_epochs):
    nn.backprop(X_train, y_train, learning_rate)

# 累计BP算法（如果存在，可能会有额外的累积误差或记忆项）

cumulative_bp_network = CumulativeBPNetwork()  # 类似于SingleLayerNN，但包含累积误差处理

# 使用相同的训练数据，但用CumulativeBPNetwork进行训练
cumulative_bp_network.train(X_train, y_train, learning_rate)

# 比较
print("Standard BP accuracy:", calculate_accuracy(nn, X_test, y_test))
print("Cumulative BP accuracy:", calculate_accuracy(cumulative_bp_network, X_test, y_test))