Constrained Projective Non-negative Matrix Factorization for Semi-supervised Multi-label Learning

This paper formulates multi-label learning as a constrained projective non-negative matrix factorization (CPNMF) problem which concentrates on a variant of the original projective NMF (PNMF) and explicitly introduces an auxiliary basis to learn the semantic subspace and boosts its discriminating ability by exploiting labeled and unlabeled examples together. Particularly, it propagates labels of the labeled examples to the unlabeled ones by enforcing coefficients of examples sharing identical semantic contents to be identical based on a hard constraint, i.e., embedding the class indicator of labeled examples into their coefficients. CPNMF preserves the geometrical structure of dataset via manifold regularization meanwhile captures the inherent structure of labels by using label correlations. We developed a multiplicative update rule (MUR) based algorithm to optimize CPNMF and proved its convergence. Experiments of image annotation on Corel dataset, text categorization on Rcv1v2 dataset, and text clustering on two popular text corpuses suggest the effectiveness of CPNMF.