Local non-negative matrix factorization as a visual representation

Abstract

Proposes a novel method, called local non-negative matrix factorization (LNMF), for learning a spatially localized, parts-based subspace representation of visual patterns. An objective function is defined to impose the localization constraint, in addition to the non-negativity constraint in the standard non-negative matrix factorization (NMF). This gives a set of bases which not only allows a non-subtractive (part-based) representation 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 principal component analysis (PCA) methods for face representation and recognition, which demonstrates the advantages of LNMF. Based on our LNMF approach, a set of orthogonal, binary, 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 the occlusion problem, improve the computing efficiency and compress the storage requirements of a face detection and recognition system.