Local non-negative matrix factorization as a visual representation

In this paper, we propose a novel method, called local non-negative matrix factorization (LNMF), for learning spa-tially localized, parts-based subspace representation of vi-sual patterns. An objective function is defined to impose lo-calization constraint, in addition to the non-negativity con-straint in the standard NMF [1]. This gives a set of bases which not only allows a non-subtractive (part-based) repre-sentation of images but also manifests localized features. An algorithm is presented for the learning of such basis components. Experimental results are presented to compare LNMF with the NMF and PCA methods for face represen-tation and recognition, which demonstrates advantages of LNMF. Based on our LNMF approach, a set of orthogonal, bi-nary, localized basis components are learned from a well aligned face image database. It leads to a Walsh function based representation of the face images. These properties can be used to resolve occlusion problem, improve the com-puting efficiency, and compress the storage requirement of face detection and recognition system.