BP 神经网络代码实现及应用实验

BP（Back Propagation，反向传播）神经网络是一种常用的深度学习模型，用于训练多层感知机（Multi-Layer Perceptron, MLP）。它通过梯度下降算法来调整网络权重，以便最小化预测值与实际值之间的误差。以下是简化的BP神经网络代码实现步骤和一个应用实验示例：

1. **代码实现**：
- **导入库**：首先，你需要Python的机器学习库如`numpy`、`tensorflow`或`pytorch`。

   import numpy as np
   import tensorflow as tf

- **初始化网络**：定义输入层、隐藏层和输出层的节点数，以及随机初始化权重。

   def initialize_weights(input_nodes, hidden_nodes, output_nodes):
       weights = {
           'hidden': np.random.normal(0, 1, (hidden_nodes, input_nodes)),
           'output': np.random.normal(0, 1, (output_nodes, hidden_nodes))
       }
       return weights

- **前向传播**：计算神经元的激活值。

   def forward_propagation(weights, inputs):
       hidden_layer = np.dot(inputs, weights['hidden'])
       hidden_layer_activation = sigmoid(hidden_layer)
       output_layer = np.dot(hidden_layer_activation, weights['output'])
       output_layer_activation = sigmoid(output_layer)
       return output_layer_activation

- **反向传播**：计算梯度并更新权重。

   def backpropagation(loss, learning_rate, weights, inputs, targets):
       d_output_error = loss * sigmoid_derivative(output)
       d_hidden_error = np.dot(d_output_error, weights['output'].T) * sigmoid_derivative(hidden)
       # 更新权重
       weights['hidden'] -= learning_rate * np.dot(inputs.T, d_hidden_error)
       weights['output'] -= learning_rate * np.dot(hidden_layer_activation.T, d_output_error)

2. **应用实验**：你可以用BP神经网络解决分类或回归问题，例如手写数字识别或房价预测。将数据集分为训练集和测试集，训练网络并评估性能。

# 训练过程
inputs, targets = load_data()  # 加载数据
learning_rate = 0.01
epochs = 1000

weights = initialize_weights(input_nodes, hidden_nodes, output_nodes)
for epoch in range(epochs):
    output = forward_propagation(weights, inputs)
    loss = compute_loss(output, targets)
    backpropagation(loss, learning_rate, weights, inputs, targets)

# 测试阶段
test_output = forward_propagation(weights, test_inputs)
accuracy = compute_accuracy(test_output, test_targets)