Abstract
Eigenvector computation, e.g., k-SVD for finding top-k singular subspaces, is often of central importance to many scientific and engineering tasks. There has been resurgent interest recently in analyzing relevant methods in terms of singular value gap dependence. Particularly, when the gap vanishes, the convergence of k-SVD is considered to be capped by a gap-free sub-linear rate. We argue in this work both theoretically and empirically that this is not necessarily the case, refreshing our understanding on this significant problem. Specifically, we leverage the recently proposed structured gap in a careful analysis to establish a unified linear convergence of k-SVD to one of the ground-truth solutions, regardless of what target matrix and how large target rank k are given. Theoretical results are evaluated and verified by experiments on synthetic or real data.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.