Bi-level optimization-based projective non-negative matrix factorization

Abstract

Non-negative matrix factorization (NMF) is a powerful tool for image data analysis and has been utilized in a range of applications involving data classification, clustering, and image processing. Nevertheless, NMF and most of its variants are unsupervised learning algorithms and do not take account of the projection property of the basis image matrix. These flaws will have a negative impact on their classification performance. To resolve the mentioned drawbacks of NMF-based methods, this paper establishes a novel projective non-negative matrix factorization (PNMF) framework using the class-label information and deals with the model via a bi-level quadratic optimization (BLO) strategy. The convergence of the proposed BLO-PNMF algorithm is theoretically analyzed and proved in detail, and also verified by experiments. Our approach and the related state-of-the-art methods are evaluated and compared on three face databases. The experimental results indicate that the BLO-PNMF method can extract more localized features for image data representation and achieve superior performance in face recognition.