A Manifold ADMM for Orthogonal Nonnegative Matrix Factorization with Application to Clustering

Abstract

Clustering has attracted more and more attention for big data. Studies have shown that orthogonal nonnegative matrix factorization (ONMF) is a promising clustering model, it can produce better clustering results in clustering tasks, such as image classification. However, the ONMF optimization problem is challenging to solve due to the coupling problems of orthogonality and non-negative constraints. In this paper, we transform the original ONMF model into a new equivalent optimization model. We solve the model based on the Alternating Direction Method of Multipliers (ADMM) framework and use Riemann Manifold optimization method to solve the subproblem on Stiefel manifold. Numerical experiments show that our algorithm performs well in clustering, normalized residual and function values.