How to speed up c++ eigen decomposition

Question

I use the MATLAB to do eigenvalue decomposition, and the dimension of data is about 10000, so the covariance matrix is 10000*10000. When I use the eig() function in MATLAB, it is very slow. Is there any way to speed up the eigenvalue decomposition. I use the eigenvalue decomposition to do principal component analysis(PCA), so I just use the top K eigenvalues and eigenvectors. There is no need to get all the eigenvalues and eigenvectors. I have tried to use the Intel-MKL to do eigen decomposition, but when I use the mex interface, there are some errors. I posted it in the link https://stackoverflow.com/questions/19220271/how-to-use-intel-mkl-for-speed-my-own-matlab-mex-cpp-applications

Please give me some advice, Thanks.

Answer 1

use eigs if your data is sparse, or if you are interested in the first k values. For example, eigs(A,k) returns the k largest magnitude eigenvalues. Note that eigs will be faster only for the first few eigen-values, and will be slower for k > some value (probably 5...)