Efficient orthogonal non-negative matrix factorization over stiefel manifold

Wei Emma Zhang*, Mingkui Tan, Quan Z. Sheng, Lina Yao, Qingfeng Shi

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contribution

4 Citations (Scopus)

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 languageEnglish
Title of host publicationCIKM 16
Subtitle of host publicationProceedings of the 25th ACM International on Conference on Information and Knowledge Management
Place of PublicationNew York, NY
PublisherAssociation for Computing Machinery
Pages1743-1752
Number of pages10
ISBN (Electronic)9781450340731
DOIs
Publication statusPublished - 2016
Externally publishedYes
Event25th ACM International Conference on Information and Knowledge Management, CIKM 2016 - Indianapolis, United States
Duration: 24 Oct 201628 Oct 2016

Other

Other25th ACM International Conference on Information and Knowledge Management, CIKM 2016
CountryUnited States
CityIndianapolis
Period24/10/1628/10/16

Keywords

  • Orthogonal NMF
  • Stiefel Manifold
  • clustering

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