This work has been accepted as a full paper by CIKM 2016. Non-negative Matrix Factorization is an important mathematical tool for various data mining applications. In this paper, CDIT researchers develop an efficient orthogonal non-negative matrix factorization over Stiefel manifold, which significantly outperforms other state-of-the-art algorithms in terms of convergence speed and clustering performance.
Efficient Orthogonal Non-negative Matrix Factorization over Stiefel Manifold. Wei Emma Zhang, Mingkui Tan, Quan Z. Sheng, Qinfeng Shi, and Lina Yao. The 25th ACM Conference on Information and Knowledge Management (CIKM 2016). Indianapolis, USA, October 24-28, 2016.
Abstract: Orthogonal Non-negative Matrix Factorization (ONMF) approximates the data matrix X by the product of two lower-dimensional factor matrices: X ≈ UVT, enforcing one of them orthogonal. ONMF works well for clustering, but does not preserve orthogonality well, and does not have fast convergence. In this paper, we propose to preserve the orthogonality of U in the setting of Stiefel manifold and develop a nonlinear Riemannian Conjugate Gradient (NRCG) method to search on Stiefel manifold with Barzilai-Borwein (BB) step size. We update V using a closed-form solution with a non-negativity constraint. Our approach allows the mixed sign on the orthogonal factor matrix U, which is a variant of Semi-NMF being preferable for clustering. Extensive experiments on both synthetic and real-world datasets show consistent superiority of our method over other approaches in terms of orthogonality preservation, convergence speed and clustering performance.