Secrets of Matrix Factorization: Approximations, Numerics, Manifold Optimization and Random Restarts

ICCV 2015  ·  Je Hyeong Hong, Andrew Fitzgibbon ·

Matrix factorization (or low-rank matrix completion) with missing data is a key computation in many computer vision and machine learning tasks, and is also related to a broader class of nonlinear optimization problems such as bundle adjustment. The problem has received much attention recently, with renewed interest in variable-projection approaches, yielding dramatic improvements in reliability and speed... However, on a wide class of problems, no one approach dominates, and because the various approaches have been derived in a multitude of different ways, it has been difficult to unify them. This paper provides a unified derivation of a number of recent approaches, so that similarities and differences are easily observed. We also present a simple meta-algorithm which wraps any existing algorithm, yielding 100% success rate on many standard datasets. Given 100% success, the focus of evaluation must turn to speed, as 100% success is trivially achieved if we do not care about speed. Again our unification allows a number of generic improvements applicable to all members of the family to be isolated, yielding a unified algorithm that outperforms our re-implementation of existing algorithms, which in some cases already outperform the original authors' publicly available codes. read more

PDF Abstract

Datasets


Results from the Paper


  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.

Methods


No methods listed for this paper. Add relevant methods here