Title :
Nonlinear Nonnegative Component Analysis
Author :
Zafeiriou, Stefanos ; Petrou, M.
Author_Institution :
Dept. of Electr. & Electron. Eng., Imperial Coll. London, London, UK
Abstract :
In this paper general solutions for nonlinear nonnegative component analysis for data representation and recognition are proposed. That is, motivated by a combination of the Nonnegative Matrix Factorization (NMF) algorithm and kernel theory, which has lead to an NMF algorithm in a polynomial feature space, we propose a general framework where one can build a nonlinear nonnegative component analysis using kernels, the so-called projected gradient Kernel Nonnegative Matrix Factorization (PGKNMF). In the proposed approach, arbitrary positive kernels can be adopted while at the same time it is ensured that the limit point of the procedure is a stationary point of the optimization problem. Moreover, we propose fixed point algorithms for the special case of Radial Basis Function (RBF) kernels. We demonstrate the power of the proposed methods in face and facial expression recognition applications.
Keywords :
face recognition; gradient methods; matrix decomposition; principal component analysis; radial basis function networks; NMF algorithm; RBF kernel; data recognition; data representation; face recognition; facial expression recognition; fixed point algorithm; kernel theory; nonlinear nonnegative component analysis; optimization problem; polynomial feature space; projected gradient kernel nonnegative matrix factorization; radial basis function; Data engineering; Educational institutions; Face recognition; Independent component analysis; Kernel; Matrix decomposition; Pixel; Polynomials; Principal component analysis; Vectors;
Conference_Titel :
Computer Vision and Pattern Recognition, 2009. CVPR 2009. IEEE Conference on
Conference_Location :
Miami, FL
Print_ISBN :
978-1-4244-3992-8
DOI :
10.1109/CVPR.2009.5206584