竞争性自适应重加权算法CARS的MATLAB实现

一、算法实现

function [bestVars, bestRMSE] = CARS(X, y, numSamples, numCV, maxVars)% 输入参数：% X: 输入数据矩阵 (样本数×变量数)% y: 响应变量向量 (样本数×1)% numSamples: 蒙特卡洛采样次数% numCV: 交叉验证折数% maxVars: 最大主成分数[nSamples, nVars] = size(X);A = min([nSamples, maxVars]);% 最大主成分数% 初始化参数W = zeros(nVars, numSamples);RMSECV = zeros(numSamples, 1);% 主循环for iter = 1:numSamples% 蒙特卡洛采样（80%训练集）idx = randperm(nSamples);trainIdx = idx(1:round(0.8*nSamples));testIdx = idx(round(0.8*nSamples) 1:end);% PLS建模[Xcal, Xval, ycal, yval] = splitData(X, y, trainIdx, testIdx);[B, ~, ~, ~] = plsregress(Xcal, ycal, A);% 计算回归系数权重w = abs(B(1:end-1, end));W(:, iter) = w / sum(w);% 归一化% 自适应重加权采样keepRatio = 0.3;% 保留比例numKeep = round(keepRatio * nVars);[~, sortedIdx] = sort(w, 'descend');selectedVars = sortedIdx(1:numKeep);% 交叉验证评估cvModel = fitrpls(X(:,selectedVars), y, 'CVPartition', cvpartition(nSamples,'KFold',numCV));RMSECV(iter) = kfoldLoss(cvModel);end% 选择最优子集[~, bestIter] = min(RMSECV);bestVars = find(W(:, bestIter) > 0);bestRMSE = RMSECV(bestIter);end%% 辅助函数：数据分割function [Xtrain, Xtest, ytrain, ytest] = splitData(X, y, trainIdx, testIdx)Xtrain = X(trainIdx, :);Xtest = X(testIdx, :);ytrain = y(trainIdx);ytest = y(testIdx);end

二、测试案例（XRF光谱分析）

% 加载示例数据（土壤重金属检测）load('soil_spectrum.mat');% 包含X（光谱）和y（重金属含量）% 参数设置numSamples = 200;numCV = 5;maxVars = 50;% 运行CARS算法[bestVars, bestRMSE] = CARS(X, y, numSamples, numCV, maxVars);% 结果可视化figure;subplot(2,1,1);stem(bestVars, 'r', 'LineWidth', 1.5);xlabel('变量索引'); ylabel('选择次数');title('变量选择频率分布');subplot(2,1,2);plot(1:numSamples, bestRMSE*ones(numSamples,1), 'b-o');xlabel('迭代次数'); ylabel('RMSECV');title('最优模型性能');

三、算法优化

动态权重调整

引入指数衰减函数优化变量保留比例：

mu = (nVars/2)^(1/(numSamples-1));k = log(nVars/(2)) / (numSamples-1);keepRatio = mu * exp(-k*iter);

并行计算加速

使用parfor加速蒙特卡洛采样：

parfor iter = 1:numSamples% 并行执行采样和建模end

GPU加速

对大规模数据使用GPU计算：

X_gpu = gpuArray(X);% 后续计算使用gpuArray操作

参考代码 竞争性自适应重加权算法 www.youwenfan.com/contentalj/79180.html

四、应用场景

光谱特征提取

% 高光谱图像分析（示例）hyperspectralData = load('hypercube.mat');[selectedBands, ~] = CARS(hyperspectralData, labels, 300, 10, 20);

工业过程监控

% 过程变量优化（示例）processVars = load('process_data.mat');[keyVars, rmse] = CARS(processVars.X, processVars.y, 200, 5, 15);