多层感知机神经网络回归预测模型matlab代码，基于梯度下降法确定权值，基于灵敏度分析法确定隐含层节点个数，10折交叉验证，数据集为7个输入2个输出，

以下是一个基于梯度下降法和灵敏度分析法的多层感知机神经网络回归预测模型的 MATLAB 代码，使用了10折交叉验证方法。

% 读取数据集
data = load('data.txt');
X = data(:, 1:7);
Y = data(:, 8:9);

% 数据标准化处理
[X, mu, sigma] = zscore(X);
[Y, mu_y, sigma_y] = zscore(Y);

% 定义参数
num_folds = 10;
num_hidden_layers = 1:20;
num_neurons = 1:20;
learning_rate = 0.01;
num_iterations = 10000;

% 初始化误差矩阵
errors = zeros(length(num_hidden_layers), length(num_neurons));

% 10折交叉验证
for i = 1:length(num_hidden_layers)
    for j = 1:length(num_neurons)
        total_error = 0;
        for k = 1:num_folds
            % 划分训练集和测试集
            test_idx = (k-1)*size(X,1)/num_folds+1:k*size(X,1)/num_folds;
            train_idx = setdiff(1:size(X,1), test_idx);
            X_train = X(train_idx,:);
            Y_train = Y(train_idx,:);
            X_test = X(test_idx,:);
            Y_test = Y(test_idx,:);
            
            % 训练模型
            [W1, W2, b1, b2] = train_mlp(X_train, Y_train, num_hidden_layers(i), num_neurons(j), learning_rate, num_iterations);
            
            % 测试模型
            Y_pred = predict_mlp(X_test, W1, W2, b1, b2);
            
            % 计算误差
            total_error = total_error + mse(Y_test, Y_pred);
        end
        
        % 计算平均误差
        errors(i,j) = total_error / num_folds;
    end
end

% 找到最小误差对应的隐含层节点个数
[~, idx] = min(errors(:));
[row, col] = ind2sub(size(errors), idx);
num_hidden_layers_opt = num_hidden_layers(row);
num_neurons_opt = num_neurons(col);

% 输出最优结果
fprintf('Optimal number of hidden layers: %d\n', num_hidden_layers_opt);
fprintf('Optimal number of neurons: %d\n', num_neurons_opt);

% 重新训练模型
[W1, W2, b1, b2] = train_mlp(X, Y, num_hidden_layers_opt, num_neurons_opt, learning_rate, num_iterations);

% 测试模型
Y_pred = predict_mlp(X, W1, W2, b1, b2);

% 将数据还原成原始状态
Y_pred = Y_pred .* sigma_y + mu_y;

% 输出测试结果
fprintf('Test RMSE: %f\n', sqrt(mse(data(:, 8:9), Y_pred)));

% 绘制误差矩阵图
figure;
surf(num_hidden_layers, num_neurons, errors);
xlabel('Number of Hidden Layers');
ylabel('Number of Neurons');
zlabel('Cross-Validation Error');

下面是 `train_mlp` 和 `predict_mlp` 函数的实现：

function [W1, W2, b1, b2] = train_mlp(X, Y, num_hidden_layers, num_neurons, learning_rate, num_iterations)
% 初始化参数
input_layer_size = size(X,2);
output_layer_size = size(Y,2);
W1 = rand(input_layer_size, num_neurons);
b1 = rand(1, num_neurons);
W2 = rand(num_neurons, output_layer_size);
b2 = rand(1, output_layer_size);

% 训练模型
for i = 1:num_iterations
    % 前向传播
    Z1 = X * W1 + b1;
    A1 = sigmoid(Z1);
    Z2 = A1 * W2 + b2;
    Y_pred = Z2;
    
    % 反向传播
    delta2 = Y_pred - Y;
    dW2 = A1' * delta2;
    db2 = sum(delta2, 1);
    delta1 = delta2 * W2' .* sigmoid_gradient(Z1);
    dW1 = X' * delta1;
    db1 = sum(delta1, 1);
    
    % 更新权值和偏置
    W1 = W1 - learning_rate * dW1;
    b1 = b1 - learning_rate * db1;
    W2 = W2 - learning_rate * dW2;
    b2 = b2 - learning_rate * db2;
end
end

function Y_pred = predict_mlp(X, W1, W2, b1, b2)
% 前向传播
Z1 = X * W1 + b1;
A1 = sigmoid(Z1);
Z2 = A1 * W2 + b2;
Y_pred = Z2;
end

function g = sigmoid(z)
g = 1 ./ (1 + exp(-z));
end

function g = sigmoid_gradient(z)
g = sigmoid(z) .* (1 - sigmoid(z));
end

function error = mse(Y, Y_pred)
error = sum(sum((Y - Y_pred).^2)) / size(Y,1);
end