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**Harvard**

Jiang, F., Enqvist, O. och Kahl, F. (2015) *A Combinatorial Approach to L1-Matrix Factorization*.

** BibTeX **

@article{

Jiang2015,

author={Jiang, Fangyuan and Enqvist, Olof and Kahl, Fredrik},

title={A Combinatorial Approach to L1-Matrix Factorization},

journal={Journal of Mathematical Imaging and Vision},

issn={0924-9907},

volume={51},

issue={3},

pages={430-441},

abstract={Recent work on low-rank matrix factorization has focused on the missing data problem and robustness to outliers and therefore the problem has often been studied under the $L_1$-norm. However, due to the non-convexity of the problem, most algorithms are sensitive to initialization and tend to get stuck in a local optimum. In this paper, we present a new theoretical framework aimed at achieving optimal solutions to the factorization problem. We define a set of stationary points to the problem that will normally contain the optimal solution. It may be too time-consuming to check all these points, but we demonstrate on several practical applications that even by just computing a random subset of these stationary points, one can achieve significantly better results than current state of the art. In fact, in our experimental results we empirically observe that our competitors rarely find the optimal solution and that our approach is less sensitive to the existence of multiple local minima.},

year={2015},

keywords={Matrix factorization, Robust estimation, Structure-from-motion, Photometric stereo},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 210199

A1 Jiang, Fangyuan

A1 Enqvist, Olof

A1 Kahl, Fredrik

T1 A Combinatorial Approach to L1-Matrix Factorization

YR 2015

JF Journal of Mathematical Imaging and Vision

SN 0924-9907

VO 51

IS 3

SP 430

OP 441

AB Recent work on low-rank matrix factorization has focused on the missing data problem and robustness to outliers and therefore the problem has often been studied under the $L_1$-norm. However, due to the non-convexity of the problem, most algorithms are sensitive to initialization and tend to get stuck in a local optimum. In this paper, we present a new theoretical framework aimed at achieving optimal solutions to the factorization problem. We define a set of stationary points to the problem that will normally contain the optimal solution. It may be too time-consuming to check all these points, but we demonstrate on several practical applications that even by just computing a random subset of these stationary points, one can achieve significantly better results than current state of the art. In fact, in our experimental results we empirically observe that our competitors rarely find the optimal solution and that our approach is less sensitive to the existence of multiple local minima.

LA eng

DO 10.1007/s10851-014-0533-0

LK http://dx.doi.org/10.1007/s10851-014-0533-0

OL 30