Multi-Component Nonnegative Matrix Factorization

Real data are usually complex and contain various components. For example, face images have ex- pressions and genders. Each component mainly re- flects one aspect of data and provides information others do not have. Therefore, exploring the seman- tic information of multiple components as well as the diversity among them is of great benefit to un- derstand data comprehensively and in-depth. How- ever, this cannot be achieved by current nonneg- ative matrix factorization (NMF)-based methods, despite that NMF has shown remarkable compet- itiveness in learning parts-based representation of data. To overcome this limitation, we propose a novel multi-component nonnegative matrix factor- ization (MCNMF). Instead of seeking for only one representation of data, MCNMF learns multiple representations simultaneously, with the help of the Hilbert Schmidt Independence Criterion (HSIC) as a diversity term. HSIC explores the diverse infor- mation among the representations, where each rep- resentation corresponds to a component. By inte- grating the multiple representations, a more com- prehensive representation is then established. Ex- tensive experimental results on real-world datasets have shown that MCNMF not only achieves more accurate performance over the state-of-the-arts us- ing the aggregated representation, but also inter- prets data from different aspects with the multi- ple representations, which is beyond what current NMFs can offer