Two-Dimensional Non-negative Matrix Factorization for Face Representation and Recognition

Non-negative matrix factorization (NMF) is a recently developed method for finding parts-based representation of non-negative data such as face images. Although it has successfully been applied in several applications, directly using NMF for face recognition often leads to low performance. Moreover, when performing on large databases, NMF needs considerable computational costs. In this paper, we propose a novel NMF method, namely 2DNMF, which stands for 2-D non-negative matrix factorization. The main difference between NMF and 2DNMF is that the former first align images into 1D vectors and then represents them with a set of 1D bases, while the latter regards images as 2D matrices and represents them with a set of 2D bases. Experimental results on several face databases show that 2DNMF has better image reconstruction quality than NMF under the same compression ratio. Also the running time of 2DNMF is less, and the recognition accuracy higher than that of NMF.

[1]  Daoqiang Zhang,et al.  Representing Image Matrices: Eigenimages Versus Eigenvectors , 2005, ISNN.

[2]  Jordi Vitrià,et al.  A weighted non-negative matrix factorization for local representations , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[3]  Daoqiang Zhang,et al.  Representing Image Matrices : Eigenimages vs . Eigenvectors , 2005 .

[4]  A. Martínez,et al.  The AR face databasae , 1998 .

[5]  Erkki Oja,et al.  A "nonnegative PCA" algorithm for independent component analysis , 2004, IEEE Transactions on Neural Networks.

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

[7]  Aleix M. Martinez,et al.  The AR face database , 1998 .

[8]  Victoria Stodden,et al.  When Does Non-Negative Matrix Factorization Give a Correct Decomposition into Parts? , 2003, NIPS.

[9]  Nanning Zheng,et al.  Non-negative matrix factorization based methods for object recognition , 2004, Pattern Recognit. Lett..

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

[11]  Stefan M. Wild,et al.  Improving non-negative matrix factorizations through structured initialization , 2004, Pattern Recognit..

[12]  Patrik O. Hoyer,et al.  Non-negative Matrix Factorization with Sparseness Constraints , 2004, J. Mach. Learn. Res..

[13]  Stan Z. Li,et al.  Learning representative local features for face detection , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[14]  Bernt Schiele,et al.  Introducing a weighted non-negative matrix factorization for image classification , 2003, Pattern Recognit. Lett..

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

[16]  M. Turk,et al.  Eigenfaces for Recognition , 1991, Journal of Cognitive Neuroscience.

[17]  Ioannis Pitas,et al.  Application of non-negative and local non negative matrix factorization to facial expression recognition , 2004, Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004..

[18]  Bernhard Schölkopf,et al.  Nonlinear Component Analysis as a Kernel Eigenvalue Problem , 1998, Neural Computation.

[19]  Xijin Ge,et al.  Learning the parts of objects by auto-association , 2002, Neural Networks.

[20]  G. Buchsbaum,et al.  Color categories revealed by non-negative matrix factorization of Munsell color spectra , 2002, Vision Research.

[21]  Stan Z. Li,et al.  Learning spatially localized, parts-based representation , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[22]  Nanning Zheng,et al.  Learning sparse features for classification by mixture models , 2004, Pattern Recognit. Lett..