Escaping Spurious Local Minima of Low-Rank Matrix Factorization Through
Convex Lifting
- URL: http://arxiv.org/abs/2204.14067v1
- Date: Fri, 29 Apr 2022 13:04:36 GMT
- Title: Escaping Spurious Local Minima of Low-Rank Matrix Factorization Through
Convex Lifting
- Authors: Ching-pei Lee, Ling Liang, Tianyun Tang, Kim-Chuan Toh
- Abstract summary: This work proposes a global rapid solver for non low-rank matrix factorization (MF) problems that we name MF-Global.
Through convex steps, our method efficiently escapes saddle and spurious local minima ubiquitous in noisy real-world data.
We show that MF-Global can indeed effectively escapes local solutions at which existing MF approaches stuck, and is magnitudes faster than state-of-the-art algorithms for the lifted convex form.
- Score: 10.76492224896965
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: This work proposes a rapid global solver for nonconvex low-rank matrix
factorization (MF) problems that we name MF-Global. Through convex lifting
steps, our method efficiently escapes saddle points and spurious local minima
ubiquitous in noisy real-world data, and is guaranteed to always converge to
the global optima. Moreover, the proposed approach adaptively adjusts the rank
for the factorization and provably identifies the optimal rank for MF
automatically in the course of optimization through tools of manifold
identification, and thus it also spends significantly less time on parameter
tuning than existing MF methods, which require an exhaustive search for this
optimal rank. On the other hand, when compared to methods for solving the
lifted convex form only, MF-Global leads to significantly faster convergence
and much shorter running time. Experiments on real-world large-scale
recommendation system problems confirm that MF-Global can indeed effectively
escapes spurious local solutions at which existing MF approaches stuck, and is
magnitudes faster than state-of-the-art algorithms for the lifted convex form.
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