A project I'm currently working on requires me to compute the eigenvectors / eigenvalues of sparse symmetric integer matrices. This is needed in the context of Principal Component Analysis. I tried to look around for efficient algorithms but am not 100% sure where to start.
Ideally, I'd like to find the first 10 eigenvectors (e.g. corresponding to the 10 biggest eigen values) of a 10k x 10k matrix in less than 10 seconds.
Is that a crazy objective? What property of the matrices would you leverage? Integer + symmetric screams Smith Normal Form but I'm wondering if there exists better than that...
Any help appreciated! Thanks in advance,