### 优化BP神经网络超参数的完整代码与详细步骤 以下是一个完整的Python代码示例，用于优化BP神经网络的超参数。代码可以在PyCharm环境中直接运行，并附有详细的说明。 --- #### 1. 导入必要的库 ```python import numpy as np from sklearn.model_selection import train_test_split from sklearn.metrics import accuracy_score ``` --- #### 2. 定义BP神经网络类 ```python class BPNeuralNetwork: def __init__(self, input_nodes, hidden_nodes, output_nodes, learning_rate, lambda_reg=0.01): self.wih = np.random.normal(0.0, pow(input_nodes, -0.5), (hidden_nodes, input_nodes)) self.who = np.random.normal(0.0, pow(hidden_nodes, -0.5), (output_nodes, hidden_nodes)) self.learning_rate = learning_rate self.lambda_reg = lambda_reg def relu(self, x): return np.maximum(0, x) def relu_derivative(self, x): return (x > 0).astype(float) def softmax(self, x): exps = np.exp(x - np.max(x)) return exps / np.sum(exps, axis=0) def train(self, inputs_list, targets_list): inputs = np.array(inputs_list, ndmin=2).T targets = np.array(targets_list, ndmin=2).T # 前向传播 hidden_inputs = np.dot(self.wih, inputs) hidden_outputs = self.relu(hidden_inputs) final_inputs = np.dot(self.who, hidden_outputs) final_outputs = self.softmax(final_inputs) # 反向传播 output_errors = targets - final_outputs hidden_errors = np.dot(self.who.T, output_errors) # 更新权重并加入正则化项 self.who += self.learning_rate * ( np.dot(output_errors * final_outputs * (1.0 - final_outputs), hidden_outputs.T) - self.lambda_reg * self.who ) self.wih += self.learning_rate * ( np.dot(hidden_errors * self.relu_derivative(hidden_inputs), inputs.T) - self.lambda_reg * self.wih ) def query(self, inputs_list): inputs = np.array(inputs_list, ndmin=2).T # 前向传播 hidden_inputs = np.dot(self.wih, inputs) hidden_outputs = self.relu(hidden_inputs) final_inputs = np.dot(self.who, hidden_outputs) final_outputs = self.softmax(final_inputs) return final_outputs ``` --- #### 3. 数据准备 假设使用的是MNIST手写数字数据集，以下是数据加载和预处理的代码。 ```python from sklearn.datasets import fetch_openml from sklearn.preprocessing import LabelBinarizer # 加载MNIST数据集 X, y = fetch_openml('mnist_784', version=1, return_X_y=True) X = X / 255.0 # 归一化到[0, 1] # 将标签转换为独热编码 label_binarizer = LabelBinarizer() y = label_binarizer.fit_transform(y) # 划分训练集和测试集 X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2, random_state=42) ``` --- #### 4. 超参数优化 通过调整学习率、隐藏层节点数、批量大小等超参数来优化模型性能。 ```python def optimize_hyperparameters(): input_nodes = X_train.shape[1] output_nodes = y_train.shape[1] best_accuracy = 0 best_params = {} # 学习率候选值 learning_rates = [0.01, 0.1, 0.5] # 隐藏层节点数候选值 hidden_nodes_list = [50, 100, 200] # 批量大小候选值 batch_sizes = [32, 64, 128] for lr in learning_rates: for hn in hidden_nodes_list: for bs in batch_sizes: nn = BPNeuralNetwork(input_nodes, hn, output_nodes, lr) epochs = 10 for e in range(epochs): for i in range(0, len(X_train), bs): inputs = X_train[i:i+bs] targets = y_train[i:i+bs] nn.train(inputs, targets) # 在验证集上评估模型 predictions = [] for record in X_val: prediction = nn.query(record) predictions.append(np.argmax(prediction)) true_labels = [np.argmax(label) for label in y_val] accuracy = accuracy_score(true_labels, predictions) if accuracy > best_accuracy: best_accuracy = accuracy best_params = {'learning_rate': lr, 'hidden_nodes': hn, 'batch_size': bs} print(f"最佳超参数组合: {best_params}, 准确率: {best_accuracy}") return best_params ``` --- #### 5. 模型训练与评估 使用优化后的超参数训练最终模型。 ```python def train_final_model(best_params): input_nodes = X_train.shape[1] output_nodes = y_train.shape[1] nn = BPNeuralNetwork(input_nodes, best_params['hidden_nodes'], output_nodes, best_params['learning_rate']) batch_size = best_params['batch_size'] epochs = 20 for e in range(epochs): for i in range(0, len(X_train), batch_size): inputs = X_train[i:i+batch_size] targets = y_train[i:i+batch_size] nn.train(inputs, targets) # 在测试集上评估模型 predictions = [] for record in X_val: prediction = nn.query(record) predictions.append(np.argmax(prediction)) true_labels = [np.argmax(label) for label in y_val] accuracy = accuracy_score(true_labels, predictions) print(f"最终模型准确率: {accuracy}") ``` --- #### 6. 运行主程序 将上述代码整合到主程序中。 ```python if __name__ == "__main__": best_params = optimize_hyperparameters() train_final_model(best_params) ``` --- ###