Orthogonal nonnegative matrix tri-factorization for co-clustering: Multiplicative updates on Stiefel manifolds
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- Title
- Orthogonal nonnegative matrix tri-factorization for co-clustering: Multiplicative updates on Stiefel manifolds
- Authors
- Yoo, J; Choi, Seungjin
- Date Issued
- 2010-09
- Publisher
- Elsevier
- Abstract
- Matrix factorization-based methods become popular in dyadic data analysis, where a fundamental problem, for example, is to perform document clustering or co-clustering words and documents given a term-document matrix. Nonnegative matrix tri-factorization (NMTF) emerges as a promising tool for co-clustering, seeking a 3-factor decomposition X approximate to USVT with all factor matrices restricted to be nonnegative, i.e.. U >= 0.S >= 0, V >= 0. In this paper we develop multiplicative updates for orthogonal NMTF where X approximate to USVT is pursued with orthogonality constraints, (UU)-U-T = I. and (VV)-V-T = I, exploiting true gradients on Stiefel manifolds. Experiments on various document data sets demonstrate that our method works well for document clustering and is useful in revealing polysemous words via co-clustering words and documents. (C) 2010 Elsevier Ltd. All rights reserved.
- Keywords
- Co-clustering; Document clustering; Multiplicative updates; Nonnegative matrix factorization; Stiefel manifolds
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/17050
- DOI
- 10.1016/j.ipm.2009.12.007
- ISSN
- 0306-4573
- Article Type
- Article
- Citation
- INFORMATION PROCESSING & MANAGEMENT, vol. 46, no. 5, page. 559 - 570, 2010-09
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