Abstract
Nonnegative Matrix Factorization (NMF) is an efficient tool for a supervised classification of various objects such as text documents, gene expressions, spectrograms, facial images, and texture patterns. In this paper, we consider the projected Nesterov’s method for estimating nonnegative factors in NMF, especially for classification of texture patterns. This method belongs to a class of gradient (first-order) methods but its convergence rate is determined by O(1/k 2). The classification experiments for the selected images taken from the UIUC database demonstrate a high efficiency of the discussed approach.
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References
Lee, D.D., Seung, H.S.: Learning of the parts of objects by non-negative matrix factorization. Nature 401, 788–791 (1999)
Qin, L., Zheng, Q., Jiang, S., Huang, Q., Gao, W.: Unsupervised texture classification: Automatically discover and classify texture patterns. Image and Vision Computing 26(5), 647–656 (2008)
Sandler, R., Lindenbaum, M.: Nonnegative matrix factorization with earth mover’s distance metric. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 1873–1880. IEEE Computer Society, Los Alamitos (2009)
Nesterov, Y.: A method of solving a convex programming problem with convergence rate o(1/k 2). Soviet Mathematics Doklady 27(2), 372–376 (1983)
Cichocki, A., Zdunek, R., Phan, A.H., Amari, S.I.: Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation. Wiley and Sons (2009)
Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences 2(1), 183–202 (2009)
Zhou, T., Tao, D., Wu, X.: NESVM: A fast gradient method for support vector machines. In: ICDM, pp. 679–688 (2010)
Guan, N., Tao, D., Luo, Z., Yuan, B.: NeNMF: An optimal gradient method for solving non-negative matrix factorization and its variants. Technical report, Mendeley database (2010)
Zdunek, R.: Supervised classification of texture patterns with nonnegative matrix factorization. In: The 2011 International Conference on Image Processing, Computer Vision, and Pattern Recognition (IPCV 2011), vol. II, pp. 544–550. CSREA Press, Las Vegas (2011); WORLDCOMP 2011
Lindeberg, T., Garding, J.: Shape-adapted smoothing in estimation of 3-d depth cues from affine distortions of local 2-d brightness structure. Image and Vision Computing 15, 415–434 (1997)
Lowe, D.: Object recognition from local scale-invariant features. In: Proceedings of the International Conference on Computer Vision, pp. 1150–1157 (1999)
Zdunek, R., Phan, A., Cichocki, A.: Damped Newton iterations for nonnegative matrix factorization. Australian Journal of Intelligent Information Processing Systems 12(1), 16–22 (2010)
Lin, C.J.: Projected gradient methods for non-negative matrix factorization. Neural Computation 19(10), 2756–2779 (2007)
Benthem, M.H.V., Keenan, M.R.: Fast algorithm for the solution of large-scale non-negativity-constrained least squares problems. Journal of Chemometrics 18, 44–450 (2004)
Lawson, C.L., Hanson, R.J.: Solving Least Squares Problems. Prentice-Hall, Englewood Cliffs (1974)
Kim, H., Park, H.: Non-negative matrix factorization based on alternating non-negativity constrained least squares and active set method. SIAM Journal in Matrix Analysis and Applications 30(2), 713–730 (2008)
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Zdunek, R., He, Z. (2012). Nesterov’s Iterations for NMF-Based Supervised Classification of Texture Patterns. In: Theis, F., Cichocki, A., Yeredor, A., Zibulevsky, M. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2012. Lecture Notes in Computer Science, vol 7191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28551-6_59
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DOI: https://doi.org/10.1007/978-3-642-28551-6_59
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