Name
Abstract | ||
|---|---|---|
We address the problem of efficient sparse fixed-rank (S-FR) matrix decomposition, i.e., splitting a corrupted matrix $M$ into an uncorrupted matrix $L$ of rank $r$ and a sparse matrix of outliers $S$. Fixed-rank constraints are usually imposed by the physical restrictions of the system under study. Here we propose a method to perform accurate and very efficient S-FR decomposition that is more suitable for large-scale problems than existing approaches. Our method is a grateful combination of geometrical and algebraical techniques, which avoids the bottleneck caused by the Truncated SVD (TSVD). Instead, a polar factorization is used to exploit the manifold structure of fixed-rank problems as the product of two Stiefel and an SPD manifold, leading to a better convergence and stability. Then, closed-form projectors help to speed up each iteration of the method. We introduce a novel and fast projector for the $\text{SPD}$ manifold and a proof of its validity. Further acceleration is achieved using a Nystrom scheme. Extensive experiments with synthetic and real data in the context of robust photometric stereo and spectral clustering show that our proposals outperform the state of the art. |
Year | Venue | Field |
|---|---|---|
2015 | CoRR | Rank (linear algebra),Convergence (routing),Singular value decomposition,Spectral clustering,Computer science,Matrix (mathematics),Matrix decomposition,Artificial intelligence,Factorization,Sparse matrix,Machine learning |
DocType | Volume | Citations |
Journal | abs/1503.03004 | 0 |
PageRank | References | Authors |
0.34 | 15 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Germán Ros | 1 | 223 | 11.13 |
| Julio Guerrero | 2 | 0 | 0.34 |