Projecting data points onto eigenvector space

Hello,

I am trying to code a principal component analysis (PCA) on a dataset (8 samples , 2 features) and I can not plot the datapoints' projections on the eigenvector which provide the largest variace (eigenvector of the 1st principal component). The code is as following:

x=[1 1 2 0 5 4 5 3; 3 2 3 3 4 5 5 4]';

X=mean(x);

m=mean(x')';

x_m=x-X;

D=cov(x_m)

[eigenVector,lamda]=eig(D);

lamdasort=sort(lamda);

w2=eigenVector(:,2)'.*x;

robustness=lamda(2,2)/(lamda(1,1)+lamda(2,2))

figure(1)

hold on

scatter(x(:,1),x(:,2),'o')

scatter(x(:,1),x(:,2),'.k')

plot(X(1,1),X(1,2),'.g')

xlabel('x1')

ylabel('x2')

xlim([-2 6])

ylim([-2 6])

figure(2)

hold on

scatter(x(:,1),x(:,2),'o')

scatter(w2(:,1),w2(:,2),'.k')

So I would like w2 to be the projections of the data set (hence eigenVector(:,2)*x) to the eigenvector of the highest-value eigenvalue. I think smth is wrong with this approach, I get somthing like inverse of the dataset (figure (2)). I multiply the k=1 dimension (eigenvector) with the dataset (w2=eigenVector(:,2)'.*x;).

Thank you

Edit: This is the result that I cannot code

This is what i get when multiplying the eigenvector with the dataset.

Answer 1

[Christine Tobler]

The lambda here is a diagonal matrix, so SORT will sort each of its columns, not the eigenvalues on the diagonal among themselves. Also, after sorting the eigenvalues, make sure that you also permute the eigenvectors in the same way:

[eigenVector,lamda]=eig(D, 'vector'); % returns eigenvalues as a column vector lambda
[lamdasort,ind]=sort(lamda);
eigenVector = eigenVector(:, ind);

[Konstantinos Bampilis]

Thank you, but still I cannot plot the dataspace projection along the eigenvector.

[Christine Tobler]

Okay, it's hard to tell just from looking at the code, but you might want to check if you're using the largest or the smallest eigenvalue here.

[Konstantinos Bampilis]

I used the largest eigenvalue, and the corresponding eigenvector.