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Cancer Class Discovery Using Non-negative Matrix Factorization Based on Alternating Non-negativity-Constrained Least Squares

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Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 4463))

Abstract

Many bioinformatics problems deal with chemical concentrations that should be non-negative. Non-negative matrix factorization (NMF) is an approach to take advantage of non-negativity in data. We have recently developed sparse NMF algorithms via alternating non-negativity-constrained least squares in order to obtain sparser basis vectors or sparser mixing coefficients for each sample, which lead to easier interpretation. However, the additional sparsity constraints are not always required. In this paper, we conduct cancer class discovery using NMF based on alternating non-negativity-constrained least squares (NMF/ANLS) without any additional sparsity constraints after introducing a rigorous convergence criterion for biological data analysis.

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References

  1. Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401, 788–791 (1999)

    Article  Google Scholar 

  2. Pauca, V.P., et al.: Text mining using non-negative matrix factorizations. In: Proc. SIAM Int’l Conf. Data Mining (SDM’04) (April 2004)

    Google Scholar 

  3. Kim, P.M., Tidor, B.: Subsystem identification through dimensionality reduction of large-scale gene expression data. Genome Research 13, 1706–1718 (2003)

    Article  Google Scholar 

  4. Brunet, J.P., et al.: Metagenes and molecular pattern discovery using matrix factorization. Proc. Natl Acad. Sci. USA 101(12), 4164–4169 (2004)

    Article  Google Scholar 

  5. Gao, Y., Church, G.: Improving molecular cancer class discovery through sparse non-negative matrix factorization. Bioinformatics 21(21), 3970–3975 (2005)

    Article  Google Scholar 

  6. Kim, H., Park, H.: Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares. In: Du, D.Z. (ed.) Proceedings of the IASTED International Conference on Computational and Systems Biology (CASB2006), November 2006, pp. 95–100 (2006)

    Google Scholar 

  7. Lee, D.D., Seung, H.S.: Algorithms for non-negative matrix factorization. In: Proceedings of Neural Information Processing Systems, pp. 556–562 (2000)

    Google Scholar 

  8. 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 

  9. Lin, C.J.: Projected gradient methods for non-negative matrix factorization. Technical Report Information and Support Service ISSTECH-95-013, Department of Computer Science, National Taiwan University (2005)

    Google Scholar 

  10. Berry, M.W., et al.: Algorithms and applications for approximate nonnegative matrix factorization. Computational Statistics and Data Analysis, to appear (2006)

    Google Scholar 

  11. Bro, R., de Jong, S.: A fast non-negativity-constrained least squares algorithm. J. Chemometrics 11, 393–401 (1997)

    Article  Google Scholar 

  12. Lawson, C.L., Hanson, R.J.: Solving Least Squares Problems. Prentice-Hall, Englewood Cliffs (1974)

    MATH  Google Scholar 

  13. van Benthem, M.H., Keenan, M.R.: Fast algorithm for the solution of large-scale non-negativity-constrained least squares problems. J. Chemometrics 18, 441–450 (2004)

    Article  Google Scholar 

  14. Gonzales, E.F., Zhang, Y.: Accelerating the Lee-Seung algorithm for non-negative matrix factorization. Technical report, Department of Computational and Applied Mathematics, Rice University (2005)

    Google Scholar 

  15. MATLAB: User’s Guide. The MathWorks, Inc., Natick (1992)

    Google Scholar 

  16. Golub, T.R., et al.: Molecular classification of cancer: Class discovery and class prediction by gene expression monitoring. Science 286, 531–537 (1999)

    Article  Google Scholar 

  17. Ding, C., He, X., Simon, H.D.: On the equivalence of nonnegative matrix factorization and spectral clustering. In: Proc. SIAM Int’l Conf. Data Mining (SDM’05), April 2005, pp. 606–610 (2005)

    Google Scholar 

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Ion Măndoiu Alexander Zelikovsky

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© 2007 Springer-Verlag Berlin Heidelberg

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Kim, H., Park, H. (2007). Cancer Class Discovery Using Non-negative Matrix Factorization Based on Alternating Non-negativity-Constrained Least Squares. In: Măndoiu, I., Zelikovsky, A. (eds) Bioinformatics Research and Applications. ISBRA 2007. Lecture Notes in Computer Science(), vol 4463. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72031-7_43

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  • DOI: https://doi.org/10.1007/978-3-540-72031-7_43

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72030-0

  • Online ISBN: 978-3-540-72031-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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