Abstract
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.
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References
Buchsbaum, G., Bloch, O.: Color categories revealed by non-negative matrix factorization of Munsell color spectra. Vision Research 42, 559–563 (2002)
Buciu, I., Pitas, I.: Application of non-negative and local non-negative matrix factorization to facial expression recognition. In: ICPR, Cambridge (2004)
Chen, X., Gu, L., Li, S.Z., Zhang, H.J.: Learning representative local features for face detection. In: CVPR, Hawaii (2001)
Comon, P.: Independent component analysis- a new comcept? Signal Processing 36, 287–314 (1994)
Donoho, D., Stodden, V.: When does non-negative matrix factorization give a correct decomposition into parts? In: NIPS (2004)
Ge, X., Iwata, S.: Learning the parts of objects by auto-association. Neural Networks 15, 285–295 (2002)
Guillamet, D., Bressan, M., Vitria, J.: A weighted non-negative matrix factorization for local representation. In: CVPR, Hawaii (2001)
Guillamet, D., Vitria, J., Schiele, B.: Introducing a weighted non-negative matrix factorization for image classification. Pattern Recognition Letters 24, 2447–2454 (2003)
Hoyer, P.O.: Non-negative matrix factorization with sparseness constraints. Journal of machine Learning Research 5, 1457–1469 (2004)
Jolliffe, I.T.: Principal Component Analysis. Springer, New York (1986)
Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401, 788–791 (1999)
Lee, D.D., Seung, H.S.: Algorithms for non-negative matrix factorization. In: NIPS, vol. 13, pp. 556–562 (2001)
Li, S.Z., Hou, X.W., Zhang, H.J., Cheng, Q.S.: Learning spatially localized, parts-based representation. In: CVPR, Hawaii (2001)
Liu, W., Zheng, N.: Learning sparse features for classification by mixture models. Pattern Recognition Letters 25, 155–161 (2004)
Liu, W., Zheng, N.: Non-negative matrix factorization based methods for object recognition. Pattern Recognition Letters 25, 893–897 (2004)
Martinez, A., Benavente, R.: The ar face database (Technical Report CVC Tech. Report No. 24)
Plumbley, M.D., Oja, E.: A ‘nonnegative PCA’ algorithm for independent component analysis. IEEE Trans. on Neural Networks 15(1), 66–76 (2004)
Scholkopf, B., Smola, A.J., Muller, K.R.: Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation 10, 1299–1319 (1998)
Turk, M., Pentland, A.: Eigenfaces for recognition. J. Cognitive Neuroscience 3(1), 71–86 (1991)
Wild, S., Curry, J., Dougherty, A.: Improving non-negative matrix factorizations through structured initialization. Pattern Recognition 37(11), 2217–2232 (2004)
Zhang, D.Q., Chen, S.C., Liu, J.: Representing image matrices: Eigenimages vs. Eigenvectors. In: ISNN, Chongqing, China (2005)
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Zhang, D., Chen, S., Zhou, ZH. (2005). Two-Dimensional Non-negative Matrix Factorization for Face Representation and Recognition. In: Zhao, W., Gong, S., Tang, X. (eds) Analysis and Modelling of Faces and Gestures. AMFG 2005. Lecture Notes in Computer Science, vol 3723. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11564386_27
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DOI: https://doi.org/10.1007/11564386_27
Publisher Name: Springer, Berlin, Heidelberg
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