Abstract
Techniques of matrix factorization or decomposition always play a central role in numerical analysis and statistics with many applications in real-world problems. Recently, the NMF dimension-reduction technique, popularized by Lee and Seung with their multiplicative update algorithm (an adapted gradient approach) has drawn much attention of researchers and practitioners. Since many of existing algorithms lack a firm theoretical foundation, and designing efficient scalable algorithms for NMF still is a challenging problem, we investigate DC programming and DCA for NMF.
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References
Berry, M., Browne, M., Langville, A., Pauca, P., Plemmons, R.: Algorithms and applications for approximate nonnegative matrix factorization. Computational Statistics and Data Analysis, 155–173 (2006)
Devarajan, K.: Nonnegative Matrix Factorization: An Analytical and Interpretive Tool in Computational Biology. PLoS Computational Biology 4(7) (2008)
Gonzalez, E.F., Zhang, Y.: Accelerating the Lee-Seung algorithm for non-negative matrix factorization. Tech Report, Department of Computational and Applied Mathematics, Rice University (2005)
Guillamet, D., Vitria, J.: a, Non-negative matrix factorization for face recognition. Topics in Artificial Intelligence, 336–344 (2002)
Ho, N.-D.: Nonnegative Matrix Factorization: Algorithms and Applications. PhD Thesis, University catholique de Louvain (2008)
Lee, D.D., Seung, H.S.: Learning the Parts of Objects by Nonnegative Matrix Factorization. Nature 401, 788–791 (1999)
Lee, D.D., Seung, H.S.: Algorithms for Non-negetive matrix factorization. In: Advances in Neural Information Processing Systems, vol. 13, pp. 556–562 (2001)
Le Thi, H.A., Pham Dinh, T.: The DC (difference of convex functions) Programming and DCA revisited with DC models of real world nonconvex optimization problems. Annals of Operations Research 133, 23–46 (2005)
Lin, C.-J.: On the convergence of multiplicative update algorithm for non-negative matrix factorization. IEEE Transactions on Neural Networks (2007)
Lin, C.-J.: Projected gradient methods for nonnegative matrix factorization. Neural Computation 19, 2756–2779 (2007)
Kim, H., Park, H.: Sparse non-negative matrix factorizations via alternating non-negativity constrained least squares for microarray data analysis. Bioinformatics 23, 1495–1502 (2007)
Kim, J., Park, H.: Toward faster nonnegative matrix factorization: A new algorithm and comparisons. In: Proceedings of the 8th IEEE ICDM, pp. 353–362 (2008)
Paatero, P., Tapper, U.: Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values. Environmetrics 5, 111–126 (1994)
Pauca, V.P., Piper, J., Plemmons, R.J.: Nonnegative Matrix Factorization for Spectral Data Analysis. Linear Algebra and its Applications 416, 29–47 (2006)
Pham Dinh, T., Le Thi, H.A.: Convex analysis approach to DC programming: Theory, algorithms and applications. Acta Math. Vietnamica 22(1), 289–357 (1997)
Pham Dinh, T., Le Thi, H.A.: Dc optimization algorithms for solving the trust region subproblem. SIAM J. Optimization 8, 476–505 (1998)
Shahnaz, F., Berry, M.W., Langville, A.N., Pauca, V.P., Plemmons, R.J.: Document clustering using nonnegative matrix factorization. Information Processing and Management 42, 373–386 (2006)
Schmidt, M.N., Larsen, J., Hsiao, F.T.: Wind noise reduction using non-negative sparse coding. In: IEEE Workshop on Machine Learning for Signal Processing, pp. 431–436 (2007)
Vavasis, S.A.: On the complexity of nonnegative matrix factorization. SIAM Journal on Optimization 20, 1364–1377 (2009)
Xu, W., Liu, X., Gong, Y.: Document clustering based on non-negative matrix factorization. In: Proceedings of the 26th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, pp. 267–273 (2003)
Zhang, S., Wang, W., Ford, J., Makedon, F.: Learning from Incomplete Ratings Using Non-negative Matrix Factorization. In: Proc. of the 6th SIAM Conference on Data mining, pp. 549–553 (2006)
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Thi, H.A.L., Dinh, T.P., Vo, X.T. (2014). DC Programming and DCA for Nonnegative Matrix Factorization. In: Hwang, D., Jung, J.J., Nguyen, NT. (eds) Computational Collective Intelligence. Technologies and Applications. ICCCI 2014. Lecture Notes in Computer Science(), vol 8733. Springer, Cham. https://doi.org/10.1007/978-3-319-11289-3_58
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DOI: https://doi.org/10.1007/978-3-319-11289-3_58
Publisher Name: Springer, Cham
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