Non-negative Matrix Factorization (NMF) and spectral clustering have been proved to be efficient and effective for data clustering tasks and have been applied to various real-world scenes. However, there are still some drawbacks in traditional methods: (1) most existing algorithms only consider high-dimensional data directly while neglect the intrinsic data structure in the low-dimensional subspace; (2) the pseudo-information got in the optimization process is not relevant to most spectral clustering and manifold regularization methods. In this paper, a novel unsupervised matrix factorization method, Pseudo Supervised Matrix Factorization (PSMF), is proposed for data clustering. The main contributions are threefold: (1) to cluster in the discriminant subspace, Linear Discriminant Analysis (LDA) combines with NMF to become a unified framework; (2) we propose a pseudo supervised manifold regularization term which utilizes the pseudo-information to instruct the regularization term in order to find subspace that discriminates different classes; (3) an efficient optimization algorithm is designed to solve the proposed problem with proved convergence. Extensive experiments on multiple benchmark datasets illustrate that the proposed model outperforms other state-of-the-art clustering algorithms.
Single-cell data clustering based on sparse optimization and low-rank matrix factorization