Compact matrix factorization with dependent subspaces
(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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- author
- Larsson, Viktor LU and Olsson, Carl LU
- organization
- publishing date
- 2017-11-06
- 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
- 2022-09-06 09:57:22
@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}}, }