MAT之PCA：利用PCA(四個主成分的貢獻率就才達100%)降維提高測試集辛烷值含量預測準确度并《測試集辛烷值含量預測結果對比》

輸出結果

後期更新……

實作代碼

load spectra;   <br>

temp = randperm(size(NIR, 1));

P_train = NIR(temp(1:50),:);

T_train = octane(temp(1:50),:);

P_test = NIR(temp(51:end),:);

T_test = octane(temp(51:end),:);

[PCALoadings,PCAScores,PCAVar] = princomp(NIR);

figure

percent_explained = 100 * PCAVar / sum(PCAVar);

pareto(percent_explained)

xlabel('主成分')

ylabel('貢獻率(%)')

title('PCA：調用princomp函數實作各個主成分的貢獻率—Jason niu')

[PCALoadings,PCAScores,PCAVar] = princomp(P_train);

plot(PCAScores(:,1),PCAScores(:,2),'r+')

title('PCA：通過PCA判斷樣本的測試集是否都在訓練範圍内—Jason niu')

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')

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];

N = size(P_test,1);

T_sim = [ones(N,1) P_test] * betaPCR;

error = abs(T_sim - T_test) ./ T_test;

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));

result = [T_test T_sim error]

plot(1:N,T_test,'b:*',1:N,T_sim,'r-o')

legend('真實值','預測值','location','best')

xlabel('預測樣本')

ylabel('辛烷值')

string = {'PCA：利用PCA降維提高《測試集辛烷值含量預測結果對比》的準确度—Jason niu';['R^2=' num2str(R2)]};

title(string)