A Combinatorial Approach to $L_1$-Matrix Factorization
Författare
Summary, in English
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.
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.
Avdelning/ar
Publiceringsår
2015
Språk
Engelska
Sidor
430-441
Publikation/Tidskrift/Serie
Journal of Mathematical Imaging and Vision
Volym
51
Issue
3
Fulltext
Dokumenttyp
Artikel i tidskrift
Förlag
Springer
Ämne
- Computer Vision and Robotics (Autonomous Systems)
- Mathematics
Nyckelord
- $L_1$-Matrix Factorization
- Robust Estimation
- Structure-from-Motion
- Photometric Stereo
Status
Published
Forskningsgrupp
- Mathematical Imaging Group
ISBN/ISSN/Övrigt
- ISSN: 0924-9907