Discriminative concept factorization for data representation

Non-negative matrix factorization (NMF) has become a popular technique for finding low-dimensional representations of data. While the standard NMF can only be performed in the original feature space, one variant of NMF, named concept factorization, can be naturally kernelized and inherits all the strengths of NMF. To make use of label information, we propose a semi-supervised concept factorization technique called discriminative concept factorization (DCF) for data representation in this paper. DCF adopts a unified objective to combine the task of data reconstruction with the task of classification. These two tasks have mutual impacts on each other, which results in a concept factorization adapted to the classification task and a classifier built on the low-dimensional representations. Furthermore, we develop an iterative algorithm to solve the optimization problem through alternative convex programming. Experimental results on three real-word classification tasks demonstrate the effectiveness of DCF.