scatter_PCA_label2d.m

function [PC_ind] = scatter_PCA_label2d(X,pc1,pc2,pct,title_text,dd)
%Plot 2d scatter plot of principle components of X
%Input:
%X: The columns are different coordinates of data; and rows are samples of data
%pc1: The index of the first component to be plotted
%pc2: The index of the second component to be plotted
%pct: the percentage of threhold eigen-values
%title_text: The title text used in plot
%dd: the factor of shifted translation for labels
%Output: A figure of scatter plot of PCA score

%Singular Value Decomposition
[V,D,U] = svd(X,'econ');
display(diag(D));
sum_eig = sum(diag(D)); %Sum of all eigen-values
th_ind = 1; %The threshold index of principle components
tem_sum_eig = D(th_ind,th_ind);

while th_ind <= size(D,1) && tem_sum_eig/sum_eig < pct
    th_ind = th_ind + 1;
    tem_sum_eig = tem_sum_eig + D(th_ind,th_ind);
end
PC_ind = (1:th_ind);

%Plot principle components with index pc1 and pc2, according to the printed
%eigenvalues
%(1) If there are some nonlinear curves in the plot in any pair of index, 
%then there will be some nonlinear manifold inside the data
%(2) If data are randomly scattering in all pairs of principle components,
%then data are pretty linearly in those principle components.
PCA_score = X*U;
axis equal;
scatter_label2d(PCA_score(:,[pc1,pc2]),title_text,dd);
end