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**Harvard**

Larsson, V., Olsson, C., Bylow, E. och Kahl, F. (2014) *Rank Minimization with Structured Data Patterns*.

** BibTeX **

@conference{

Larsson2014,

author={Larsson, Viktor and Olsson, Carl and Bylow, Erik and Kahl, Fredrik},

title={Rank Minimization with Structured Data Patterns},

booktitle={Lecture Notes in Computer Science: 13th European Conference on Computer Vision, ECCV 2014, Zurich, Switzerland, 6-12 September 2014},

isbn={978-331910577-2},

pages={250-265},

abstract={The problem of finding a low rank approximation of a given measurement matrix is of key interest in computer vision. If all the elements of the measurement matrix are available, the problem can be solved using factorization. However, in the case of missing data no satisfactory solution exists. Recent approaches replace the rank term with the weaker (but convex) nuclear norm. In this paper we show that this heuristic works poorly on problems where the locations of the missing entries are highly correlated and structured which is a common situation in many applications. Our main contribution is the derivation of a much stronger convex relaxation that takes into account not only the rank function but also the data. We propose an algorithm which uses this relaxation to solve the rank approximation problem on matrices where the given measurements can be organized into overlapping blocks without missing data. The algorithm is computationally efficient and we have applied it to several classical problems including structure from motion and linear shape basis estimation. We demonstrate on both real and synthetic data that it outperforms state-of-the-art alternatives.},

year={2014},

}

** RefWorks **

RT Conference Proceedings

SR Electronic

ID 210206

A1 Larsson, Viktor

A1 Olsson, Carl

A1 Bylow, Erik

A1 Kahl, Fredrik

T1 Rank Minimization with Structured Data Patterns

YR 2014

T2 Lecture Notes in Computer Science: 13th European Conference on Computer Vision, ECCV 2014, Zurich, Switzerland, 6-12 September 2014

SN 978-331910577-2

SP 250

OP 265

AB The problem of finding a low rank approximation of a given measurement matrix is of key interest in computer vision. If all the elements of the measurement matrix are available, the problem can be solved using factorization. However, in the case of missing data no satisfactory solution exists. Recent approaches replace the rank term with the weaker (but convex) nuclear norm. In this paper we show that this heuristic works poorly on problems where the locations of the missing entries are highly correlated and structured which is a common situation in many applications. Our main contribution is the derivation of a much stronger convex relaxation that takes into account not only the rank function but also the data. We propose an algorithm which uses this relaxation to solve the rank approximation problem on matrices where the given measurements can be organized into overlapping blocks without missing data. The algorithm is computationally efficient and we have applied it to several classical problems including structure from motion and linear shape basis estimation. We demonstrate on both real and synthetic data that it outperforms state-of-the-art alternatives.

LA eng

DO 10.1007/978-3-319-10578-9_17

LK http://dx.doi.org/10.1007/978-3-319-10578-9_17

OL 30