Dual local learning regularized nonnegative matrix factorization and its semi-supervised extension for clustering

Abstract

Nonnegative matrix factorization (NMF) has received considerable attention in data representation due to its strong interpretability. However, traditional NMF methods neglect the discriminative information and geometric structure of both the data space and the feature space, simultaneously. In this paper, we propose a dual local learning regularized nonnegative matrix factorization (DLLNMF) method, which not only considers the geometric structure of both the data manifold and the feature manifold, simultaneously, but also takes advantage of the discriminative information of both the data space and the feature space. To make full use of the partial label information among samples, we further propose its semi-supervised extension, called dual local learning regularized nonnegative matrix factorization with label constraint (DLLNMF-LC), which imposes the label information as a hard constraint without additional parameters. Experimental results on some benchmark datasets have demonstrated the effectiveness of our proposed methods.