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Title: A unified linear convergence analysis of k-SVD
Authors: Xu, Zhiqiang
Ke, Yiping
Cao, Xin
Zhou, Chunlai
Wei, Pengfei
Gao, Xin
Keywords: Science
Issue Date: 2020
Source: Xu, Z., Ke, Y., Cao, X., Zhou, C., Wei, P. & Gao, X. (2020). A unified linear convergence analysis of k-SVD. Memetic Computing, 12(4), 343-353.
Journal: Memetic Computing
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.
ISSN: 1865-9284
DOI: 10.1007/s12293-020-00315-4
Schools: School of Computer Science and Engineering 
Rights: © 2020 Springer-Verlag GmbH Germany, part of Springer Nature. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
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