Discrimination-Aware Projected Matrix Factorization

Non-negative Matrix Factorization (NMF) has been one of the most popular clustering techniques in machine leaning, and involves various real-world applications. Most existing works perform matrix factorization on high-dimensional data directly. However, the intrinsic data structure is always hidden within the low-dimensional subspace. And, the redundant features within the input space may affect the final result adversely. In this paper, a new unsupervised matrix factorization method, Discrimination-aware Projected Matrix Factorization (DPMF), is proposed for data clustering. The main contributions are threefold: (1) The linear discriminant analysis is jointly incorporated into the unsupervised matrix factorization framework, so the clustering can be accomplished in the discriminant subspace. (2) The manifold regularization is introduced to perceive the geometric information, and the ${\ell _{2,1}}ell;2,1-norm is utilized to improve the robustness. (3) An efficient optimization algorithm is designed to solve the proposed problem with proved convergence. Experimental results on one toy dataset and eight real-world benchmarks show the effectiveness of the proposed method.