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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
and
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
IEEE - 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
2025-10-14 12:39:17
@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}},
  booktitle    = {{Proceedings - 30th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017}},
  isbn         = {{9781538604571}},
  language     = {{eng}},
  month        = {{11}},
  pages        = {{4361--4370}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  title        = {{Compact matrix factorization with dependent subspaces}},
  url          = {{http://dx.doi.org/10.1109/CVPR.2017.464}},
  doi          = {{10.1109/CVPR.2017.464}},
  volume       = {{2017-January}},
  year         = {{2017}},
}