Projecting data points onto eigenvector space
40 visualizaciones (últimos 30 días)
Mostrar comentarios más antiguos
Konstantinos Bampilis
el 28 de En. de 2021
Comentada: Konstantinos Bampilis
el 28 de En. de 2021
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.
0 comentarios
Respuestas (1)
Christine Tobler
el 28 de En. de 2021
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);
3 comentarios
Christine Tobler
el 28 de En. de 2021
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.
Ver también
Categorías
Más información sobre Dimensionality Reduction and Feature Extraction en Help Center y File Exchange.
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!