Learning spatially localized, parts-based representation

In this paper, we propose a novel method, called local non-negative matrix factorization (LNMF), for learning spatially localized, parts-based subspace representation of visual patterns. An objective function is defined to impose a localization constraint, in addition to the non-negativity constraint in the standard 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 basic components. Experimental results are presented to compare LNMF with the NMF and PCA methods for face representation and recognition, which demonstrates advantages of LNMF.

[1]  Keinosuke Fukunaga,et al.  Introduction to Statistical Pattern Recognition , 1972 .

[2]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[3]  L Sirovich,et al.  Low-dimensional procedure for the characterization of human faces. , 1987, Journal of the Optical Society of America. A, Optics and image science.

[4]  Lawrence Sirovich,et al.  Application of the Karhunen-Loeve Procedure for the Characterization of Human Faces , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Alex Pentland,et al.  Face recognition using eigenfaces , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[6]  Christian Jutten,et al.  Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecture , 1991, Signal Process..

[7]  Tomaso Poggio,et al.  Example Based Image Analysis and Synthesis , 1993 .

[8]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[9]  Alex Pentland,et al.  View-based and modular eigenspaces for face recognition , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[10]  Penio S. Penev,et al.  Local feature analysis: A general statistical theory for object representation , 1996 .

[11]  Terrence J. Sejnowski,et al.  The “independent components” of natural scenes are edge filters , 1997, Vision Research.

[12]  H. Sebastian Seung,et al.  Learning the parts of objects by non-negative matrix factorization , 1999, Nature.

[13]  H. Sebastian Seung,et al.  Algorithms for Non-negative Matrix Factorization , 2000, NIPS.