Thursday, June 30, 2016

Literature survey on low rank approximation of matrices



Low rank approximation of matrices has been well studied in literature. Singular value decomposition, QR decomposition with column pivoting, rank revealing QR factorization (RRQR), Interpolative decomposition etc are classical deterministic algorithms for low rank approximation. But these techniques are very expensive )operations (O(n^3) are required for n x n matrices). There are several randomized algorithms available in the literature which are not so expensive as the classical techniques (but the complexity is not linear in n). So, it is very expensive to construct the low rank approximation of a matrix if the dimension of the matrix is very large. There are alternative techniques like Cross/Skeleton approximation which gives the low-rank approximation with linear complexity in n . In this article we review low rank approximation techniques briefly and give extensive references of many techniques.


This image was taken by Navcam: Right B (NAV_RIGHT_B) onboard NASA's Mars rover Curiosity on Sol 1385 (2016-06-29 06:31:23 UTC). 

Image Credit: NASA/JPL-Caltech 

Full Resolution

Join the CompressiveSensing subreddit or the Google+ Community or the Facebook page and post there !
Liked this entry ? subscribe to Nuit Blanche's feed, there's more where that came from. You can also subscribe to Nuit Blanche by Email, explore the Big Picture in Compressive Sensing or the Matrix Factorization Jungle and join the conversations on compressive sensing, advanced matrix factorization and calibration issues on Linkedin.

No comments:

Printfriendly