基于Matlab实现降维与特征选择源码demo

%% I. 清空环境变量 clear all clc %% II. 导入数据 load spectra; %% III. 随机划分训练集与测试集 temp = randperm(size(NIR, 1)); % temp = 1:60; %% % 1. 训练集——50个样本 P_train = NIR(temp(1:50),:); T_train = octane(temp(1:50),:); %% % 2. 测试集——10个样本 P_test = NIR(temp(51:end),:); T_test = octane(temp(51:end),:); %% IV. 主成分分析 %% % 1. 主成分贡献率分析 [PCALoadings,PCAScores,PCAVar] = princomp(NIR); figure percent_explained = 100 * PCAVar / sum(PCAVar); pareto(percent_explained) xlabel('主成分') ylabel('贡献率(%)') title('主成分贡献率') %% % 2. 第一主成分vs.第二主成分 [PCALoadings,PCAScores,PCAVar] = princomp(P_train); figure plot(PCAScores(:,1),PCAScores(:,2),'r+') hold on [PCALoadings_test,PCAScores_test,PCAVar_test] = princomp(P_test); plot(PCAScores_test(:,1),PCAScores_test(:,2),'o') xlabel('1st Principal Component') ylabel('2nd Principal Component') legend('Training Set','Testing Set','location','best') %% V. 主成分回归模型 %% % 1. 创建模型 k = 4; betaPCR = regress(T_train-mean(T_train),PCAScores(:,1:k)); betaPCR = PCALoadings(:,1:k) * betaPCR; betaPCR = [mean(T_train)-mean(P_train) * betaPCR;betaPCR]; %% % 2. 预测拟合 N = size(P_test,1); T_sim = [ones(N,1) P_test] * betaPCR; %% VI. 结果分析与绘图 %% % 1. 相对误差error error = abs(T_sim - T_test) ./ T_test; %% % 2. 决定系数R^2 R2 = (N * sum(T_sim .* T_test) - sum(T_sim) * sum(T_test))^2 / ((N * sum((T_sim).^2) - (sum(T_sim))^2) * (N * sum((T_test).^2) - (sum(T_test))^2)); %% % 3. 结果对比 result = [T_test T_sim error] %% % 4. 绘图 figure plot(1:N,T_test,'b:*',1:N,T_sim,'r-o') legend('真实值','预测值','location','best') xlabel('预测样本') ylabel('辛烷值') string = {'测试集辛烷值含量预测结果对比';['R^2=' num2str(R2)]}; title(string)