Abstract
Orthogonal Non-negative Matrix Factorization (ONMF) approximates a data matrix X by the product of two lower-dimensional factor matrices: X ≈ UVT, with one of them orthogonal. ONMF has been widely applied for clustering, but it often suffers from high computational cost due to the orthogonality constraint. In this paper, we propose a method, called Nonlinear Riemannian Conjugate Gradient ONMF (NRCG-ONMF), which updates U and V alternatively and preserves the orthogonality of U while achieving fast convergence speed. Specifically, in order to update U, we develop a Nonlinear Riemannian Conjugate Gradient (NRCG) method on the Stiefel manifold using Barzilai-Borwein (BB) step size. For updating V, we use a closed-form solution under non-negativity constraint. Extensive experiments on both synthetic and real-world data sets show consistent superiority of our method over other approaches in terms of orthogonality preservation, convergence speed and clustering performance.
Original language | English |
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Title of host publication | CIKM 16 |
Subtitle of host publication | Proceedings of the 25th ACM International on Conference on Information and Knowledge Management |
Place of Publication | New York, NY |
Publisher | Association for Computing Machinery |
Pages | 1743-1752 |
Number of pages | 10 |
ISBN (Electronic) | 9781450340731 |
DOIs | |
Publication status | Published - 2016 |
Externally published | Yes |
Event | 25th ACM International Conference on Information and Knowledge Management, CIKM 2016 - Indianapolis, United States Duration: 24 Oct 2016 → 28 Oct 2016 |
Other
Other | 25th ACM International Conference on Information and Knowledge Management, CIKM 2016 |
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Country/Territory | United States |
City | Indianapolis |
Period | 24/10/16 → 28/10/16 |
Keywords
- Orthogonal NMF
- Stiefel Manifold
- clustering
- Clustering