Approximation Algorithms for Orthogonal Non-negative Matrix Factorization
In the non-negative matrix factorization (NMF) problem, the input is an m×n matrix M with non-negative entries and the goal is to factorize it as M ≈ AW. The m × k matrix A and the k × n matrix W are both constrained to have non-negative entries. This is in contrast to singular value decomposition, where the matrices A and W can have negative entries but must satisfy the orthogonality constraint: the columns of A are orthogonal and the rows of W are also orthogonal. The orthogonal non-negative matrix factorization (ONMF) problem imposes both the non-negativity and the orthogonality constraints, and previous work showed that it leads to better performances than NMF on many clustering tasks. We give the first constant-factor approximation algorithm for ONMF when one or both of A and W are subject to the orthogonality constraint. We also show an interesting connection to the correlation clustering problem on bipartite graphs. Our experiments on synthetic and real-world data show that our algorithm achieves similar or smaller errors compared to previous ONMF algorithms while ensuring perfect orthogonality (many previous algorithms do not satisfy the hard orthogonality constraint).
Authors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10299301
Journal Name:
Proeedings of the International Workshop on Artificial Intelligence and Statistics
Volume:
130
Page Range or eLocation-ID:
2728-2736
ISSN:
1525-531X
National Science Foundation
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2. Abstract

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4. Abstract

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