Attributed Non-negative Matrix Multi-factorization for Data Representation

Abstract

Non-negative matrix factorization (NMF) is an important method of latent data representation learning. Most of the existing NMF methods focus only on one single factorization and obtain one clustering solution. However, real data are usually complex and can be described from multiple attributes or sub-features. For example, face image consists of genders attribute and expressions attribute. And, the various attributes provide complementary information of data. Failing to explore multi-attribute representation and exploit the complementary information, it may be difficult to learn discriminative representation. In order to solve the above issue and obtain richer low-dimensional representations, we propose the Attributed Non-negative Matrix Multi-Factorization for Data Representation (ANMMF) model which simultaneously learns multiple low-dimensional representations from original data. By utilizing Hilbert Schmidt Independence Criterion (HSIC) to constrain the pairwise attributes, ANMMF enforces that each low-dimensional attribute representation is independent, which effectively mines complementary multi-attribute information embed in the original data. Further, graph Laplacian regularization is constrained to maintain the local geometrical structure. The low dimensional multi-attribute representation information embedded in the original data is fused to improve the clustering results. Finally, we develop the iterative updating schemes for the ANMMF model optimization, and extensive experiments on real-world databases demonstrate that our method has the most advanced performance compared with other related algorithms.