Effective Solutions to Robust Orthogonal Nonnegative Matrix Factorization via Oblique Manifold Transformation

Abstract. In this paper, we address the problem of robust orthogonal nonnegative matrix factorization (RONMF), a crucial challenge in data analysis. We first propose a RONMF model that explicitly handles both dense and sparse noise, making it suitable for a wide range of real-world applications. To circumvent the computational complexity associated with the Stiefel manifold and effectively solve the proposed model, we introduce an exact penalty method that transforms the optimization problem from the Stiefel manifold to the Oblique manifold. To achieve this, we develop the EP-RONMF algorithm, which seeks a point satisfying the weak second-order optimality conditions through an alternating proximal method and iterative updates of the penalty parameter. This approach successfully addresses the nonconvex nature of the ONMF problem and ensures convergence to a stable solution. To validate the efficacy of our method, we conducted extensive experiments on diverse datasets, including image, text, and hyperspectral data. The results clearly demonstrate the superiority of our approach compared to existing techniques.