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Compact matrix factorization with dependent subspaces

Larsson, Viktor LU and Olsson, Carl LU (2017) IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017 2017-January. p.4361-4370
Abstract

Traditional matrix factorization methods approximate high dimensional data with a low dimensional subspace. This imposes constraints on the matrix elements which allow for estimation of missing entries. A lower rank provides stronger constraints and makes estimation of the missing entries less ambiguous at the cost of measurement fit. In this paper we propose a new factorization model that further constrains the matrix entries. Our approach can be seen as a unification of traditional low-rank matrix factorization and the more recent union-of-subspace approach. It adaptively finds clusters that can be modeled with low dimensional local subspaces and simultaneously uses a global rank constraint to capture the overall scene interactions.... (More)

Traditional matrix factorization methods approximate high dimensional data with a low dimensional subspace. This imposes constraints on the matrix elements which allow for estimation of missing entries. A lower rank provides stronger constraints and makes estimation of the missing entries less ambiguous at the cost of measurement fit. In this paper we propose a new factorization model that further constrains the matrix entries. Our approach can be seen as a unification of traditional low-rank matrix factorization and the more recent union-of-subspace approach. It adaptively finds clusters that can be modeled with low dimensional local subspaces and simultaneously uses a global rank constraint to capture the overall scene interactions. For inference we use an energy that penalizes a trade-off between data fit and degrees-of-freedom of the resulting factorization. We show qualitatively and quantitatively that regularizing both local and global dynamics yields significantly improved missing data estimation.

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Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
Proceedings - 30th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017
volume
2017-January
pages
10 pages
publisher
Institute of Electrical and Electronics Engineers Inc.
conference name
IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017
conference location
Honolulu, United States
conference dates
2017-07-21 - 2017-07-26
external identifiers
  • scopus:85044265428
ISBN
9781538604571
DOI
10.1109/CVPR.2017.464
language
English
LU publication?
yes
id
81bb086b-75cf-4e0d-a1ab-b07e5c2ac874
date added to LUP
2018-04-10 13:57:27
date last changed
2019-02-20 11:13:39
@inproceedings{81bb086b-75cf-4e0d-a1ab-b07e5c2ac874,
  abstract     = {<p>Traditional matrix factorization methods approximate high dimensional data with a low dimensional subspace. This imposes constraints on the matrix elements which allow for estimation of missing entries. A lower rank provides stronger constraints and makes estimation of the missing entries less ambiguous at the cost of measurement fit. In this paper we propose a new factorization model that further constrains the matrix entries. Our approach can be seen as a unification of traditional low-rank matrix factorization and the more recent union-of-subspace approach. It adaptively finds clusters that can be modeled with low dimensional local subspaces and simultaneously uses a global rank constraint to capture the overall scene interactions. For inference we use an energy that penalizes a trade-off between data fit and degrees-of-freedom of the resulting factorization. We show qualitatively and quantitatively that regularizing both local and global dynamics yields significantly improved missing data estimation.</p>},
  author       = {Larsson, Viktor and Olsson, Carl},
  isbn         = {9781538604571},
  language     = {eng},
  location     = {Honolulu, United States},
  month        = {11},
  pages        = {4361--4370},
  publisher    = {Institute of Electrical and Electronics Engineers Inc.},
  title        = {Compact matrix factorization with dependent subspaces},
  url          = {http://dx.doi.org/10.1109/CVPR.2017.464},
  volume       = {2017-January},
  year         = {2017},
}