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Geometric Optimization Methods for the Analysis of Gene Expression Data

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Principal Manifolds for Data Visualization and Dimension Reduction

DNA microarrays provide such a huge amount of data that unsupervised methods are required to reduce the dimension of the data set and to extract meaningful biological information. This work shows that Independent Component Analysis (ICA) is a promising approach for the analysis of genome-wide transcriptomic data. The paper first presents an overview of the most popular algorithms to perform ICA. These algorithms are then applied on a microarray breast-cancer data set. Some issues about the application of ICA and the evaluation of biological relevance of the results are discussed. This study indicates that ICA significantly outperforms Principal Component Analysis (PCA).

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References

  1. Riva, A., Carpentier, A. -S., Torrésani, B., and Hénaut A.: Comments on selec-ted fundamental aspects of microarray analysis. Computational Biology and Chemistry, 29 (5), 319-336 (2005)

    Article  MATH  Google Scholar 

  2. Alter, O., Brown, P. O., and Botstein, D.: Generalized singular value decom-position for comparative analysis of genome-scale expression data sets of two different organisms. Proc Natl Acad Sci USA, 100 (6), 3351-3356, March (2003)

    Article  Google Scholar 

  3. Wang, Y., Klijn, J. G., Zhang, Y., Sieuwerts, A. M., Look, M. P., Yang, F., Talantov, D., Timmermans, M., Meijer-van Gelder, M. E., Yu, J., Jatkoe, T., Berns, E. M., Atkins, D., and Foekens, J. A.: Gene-expression profiles to predict distant metastasis of lymph-node-negative primary breast cancer. Lancet, 365 (9460), 671-679, February (2005)

    Google Scholar 

  4. Liebermeister, W.: Linear modes of gene expression determined by independent component analysis. Bioinformatics, 18, 51-60 (2002)

    Article  Google Scholar 

  5. Martoglio, A. -M., Miskin, J. W., Smith, S. K., and MacKay, D. J. C.: A de-composition model to track gene expression signatures: preview on observer-independent classification of ovarian cancer. Bioinformatics, 18 (12), 1617-1624 (2002)

    Article  Google Scholar 

  6. Lee, S. -I. and Batzoglou, S.: Application of independent component analysis to microarrays. Genome Biology, 4, R76 (2003)

    Article  Google Scholar 

  7. Saidi, S. A., Holland, C. M., Kreil, D. P., MacKay, D. J. C., Charnock-Jones, D. S., Print, C. G., and Smith S. K.: Independent component analysis of mi-croarray data in the study of endometrial cancer. Oncogene, 23 (39), 6677-6683 (2003)

    Article  Google Scholar 

  8. Comon, P.: Independent Component Analysis, a new concept? Signal Process-ing, (Special issue on Higher-Order Statistics), 36 (3), 287-314, April (1994)

    MATH  Google Scholar 

  9. Absil, P. A., Mahony, R., and Sepulchre, R.: Optimization Algorithms on Matrix Manifolds. Princeton University Press, To appear.

    Google Scholar 

  10. Learned-Miller, E. G. and Fisher, J. W. III.: ICA using spacings estimates of entropy. Journal of Machine Learning Research, 4, 1271-1295 (2003)

    Article  MathSciNet  Google Scholar 

  11. Mackay, D. J. C.: Information Theory, Inference & Learning Algorithms. Cambridge University Press (2002)

    Google Scholar 

  12. Cover, T. M. and Thomas, J. A.: Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing). Wiley-Interscience (2006)

    Google Scholar 

  13. Vasicek, O.: A test for normality based on sample entropy. Journal of the Royal Statistical Society, Series B, 38, 54-59 (1976)

    MATH  MathSciNet  Google Scholar 

  14. Bach, F. R. and Jordan, M. I.: Kernel independent component analysis. Journal of Machine Learning Research, 3, 1-48 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  15. Saitoh, S.: Theory of Reproducing Kernels and its Applications. Longman Scientific & Technical, Harlow, England (1988)

    MATH  Google Scholar 

  16. Scholkopf, B. and Smola, A. J.:Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press, Cambridge, MA (2001)

    Google Scholar 

  17. Hyvärinen, A., Karhunen, J., and Oja, E.: Independent Component Analysis. John Wiley & Sons (2001)

    Book  Google Scholar 

  18. Mathis, H.: Nonlinear Functions for Blind Separation and Equalization. PhD thesis, Swiss Federal Institute of Technology, Zrich, Switzerland (2001)

    Google Scholar 

  19. Cardoso, J. -F.: High-order contrasts for independent component analysis. Neural Computation, 11 (1), 157-192 (1999)

    Article  MathSciNet  Google Scholar 

  20. De Lathauwer, L. and Vandewalle, J.: Dimensionality reduction in higher-order signal processing and rank-(R1, R2,…, Rn ) reduction in multilinear algebra. Lin. Alg. Appl., 391, 31-55 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  21. Belouchrani, A., Abed-Meraim, K., Cardoso, J. -F., and Moulines E.: A blind source separation technique using second-order statistics. IEEE Transactions on Signal Processing, 45, 434-444, February (1997)

    Article  Google Scholar 

  22. Absil, P. -A. and Gallivan, K. A.: Joint diagonalization on the oblique manifold for independent component analysis. In: Proceedings of ICASSP2006 (2006)

    Google Scholar 

  23. Journée, M., Teschendorff, A. E., Absil, P. -A., and R. Sepulchre: Geometric opti-mization methods for independent component analysis applied on gene expres-sion data. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2007), April (2007)

    Google Scholar 

  24. Golub, G. H. and Van Loan, C. F.: Matrix Computations. The Johns Hopkins University Press (1996)

    MATH  Google Scholar 

  25. Hansen, L., Larsen, J., and Kolenda, T.: Blind detection of independent dynamic components. In: Proceedings of ICASSP’2001, Salt Lake City, Utah, USA, SAM-P8. 10, vol. 5 (2001)

    Google Scholar 

  26. Minka, T. P.: Automatic choice of dimensionality for PCA. In: NIPS, pages 598-604 (2000)

    Google Scholar 

  27. Beißbarth, T., and Speed, T. P.: GOstat: find statistically overrepresented gene ontologies within a group of genes. Bioinformatics, 20 (9), 1464-1465 (2004)

    Article  Google Scholar 

  28. Subramanian, A., Tamayo, P., Mootha, V. K., Mukherjee, S., Ebert, B. L., Gillette, M. A., Paulovich, A., Pomeroy, S. L., Golub, T. R., Lander, E. S., and Mesirov J. P.: From the cover: Gene set enrichment analysis: A knowledge-based approach for interpreting genome-wide expression profiles. PNAS, 102 (43), 15545-15550, October (2005)

    Article  Google Scholar 

  29. Bild, A. H., Yao, G., Chang, J. T., Wang, Q., Potti, A., Chasse, D., Joshi, M. -B., Harpole, D., Lancaster, J. M., Berchuck, A., Olson, J. A., Marks, J. R., Dressman, H. K., West, M., and Nevins J. R.: Oncogenic pathway signatures in human cancers as a guide to targeted therapies. Nature, 439, 353-357 (2006)

    Article  Google Scholar 

  30. Teschendorff, A. E., Journée, M., Absil, P. -A., Sepulchre, R., and Caldas, C.: Elucidating the altered transcriptional programs in breast cancer using inde-pendent component analysis. Submitted to PLoS Biology (2007)

    Google Scholar 

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Journée, M., Teschendorff, A.E., Absil, PA., Tavaré, S., Sepulchre, R. (2008). Geometric Optimization Methods for the Analysis of Gene Expression Data. In: Gorban, A.N., Kégl, B., Wunsch, D.C., Zinovyev, A.Y. (eds) Principal Manifolds for Data Visualization and Dimension Reduction. Lecture Notes in Computational Science and Enginee, vol 58. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73750-6_12

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