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DC Programming and DCA for Nonnegative Matrix Factorization

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Computational Collective Intelligence. Technologies and Applications (ICCCI 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8733))

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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

  1. 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)

    Google Scholar 

  2. Devarajan, K.: Nonnegative Matrix Factorization: An Analytical and Interpretive Tool in Computational Biology. PLoS Computational Biology 4(7) (2008)

    Google Scholar 

  3. 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)

    Google Scholar 

  4. Guillamet, D., Vitria, J.: a, Non-negative matrix factorization for face recognition. Topics in Artificial Intelligence, 336–344 (2002)

    Google Scholar 

  5. Ho, N.-D.: Nonnegative Matrix Factorization: Algorithms and Applications. PhD Thesis, University catholique de Louvain (2008)

    Google Scholar 

  6. Lee, D.D., Seung, H.S.: Learning the Parts of Objects by Nonnegative Matrix Factorization. Nature 401, 788–791 (1999)

    Article  Google Scholar 

  7. 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)

    Google Scholar 

  8. 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)

    Article  MATH  MathSciNet  Google Scholar 

  9. Lin, C.-J.: On the convergence of multiplicative update algorithm for non-negative matrix factorization. IEEE Transactions on Neural Networks (2007)

    Google Scholar 

  10. Lin, C.-J.: Projected gradient methods for nonnegative matrix factorization. Neural Computation 19, 2756–2779 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  11. 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)

    Google Scholar 

  12. 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)

    Google Scholar 

  13. 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)

    Article  Google Scholar 

  14. Pauca, V.P., Piper, J., Plemmons, R.J.: Nonnegative Matrix Factorization for Spectral Data Analysis. Linear Algebra and its Applications 416, 29–47 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  15. 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)

    MATH  Google Scholar 

  16. Pham Dinh, T., Le Thi, H.A.: Dc optimization algorithms for solving the trust region subproblem. SIAM J. Optimization 8, 476–505 (1998)

    Article  MATH  Google Scholar 

  17. 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)

    Article  MATH  Google Scholar 

  18. 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)

    Google Scholar 

  19. Vavasis, S.A.: On the complexity of nonnegative matrix factorization. SIAM Journal on Optimization 20, 1364–1377 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  20. 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)

    Google Scholar 

  21. 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)

    Google Scholar 

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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

  • Print ISBN: 978-3-319-11288-6

  • Online ISBN: 978-3-319-11289-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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