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.

This work has been accepted as a full paper by CIKM 2016. Codes are available here:[zip].


  • Efficient Orthogonal Non-negative Matrix Factorization over Stiefel Manifold. Wei Emma Zhang, Mingkui Tan, Quan Z. Sheng, Lina Yao and Qinfeng Shi. The 25th ACM International Conference on Information and Knowledge Management (CIKM 2017), Indianapolis, USA, October 2016.