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Effective Principal Component Analysis

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Similarity Search and Applications (SISAP 2012)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 7404))

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Abstract

Principal Component Analysis (PCA) is one of the most widely used algorithmic techniques. When is PCA provably effective? What are its main limitations and how can we get around them? In this note, we discuss three specific challenges.

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References

  1. Achlioptas, D., McSherry, F.: On Spectral Learning of Mixtures of Distributions. In: Auer, P., Meir, R. (eds.) COLT 2005. LNCS (LNAI), vol. 3559, pp. 458–469. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  2. Arora, S., Kannan, R.: Learning mixtures of arbitrary gaussians. Annals of Applied Probability 15(1A), 69–92 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  3. Belkin, M., Sinha, K.: Polynomial learning of distribution families. In: FOCS, pp. 103–112 (2010)

    Google Scholar 

  4. Belkin, M., Sinha, K.: Toward learning gaussian mixtures with arbitrary separation. In: COLT, pp. 407–419 (2010)

    Google Scholar 

  5. Brubaker, S.C.: Robust pca and clustering on noisy mixtures. In: Proc. of SODA (2009)

    Google Scholar 

  6. Brubaker, S.C., Vempala, S.: Isotropic pca and affine-invariant clustering. In: Grötschel, M., Katona, G. (eds.) Building Bridges Between Mathematics and Computer Science. Bolyai Society Mathematical Studies, vol. 19 (2008)

    Google Scholar 

  7. Chaudhuri, K., Rao, S.: Learning mixtures of product distributions using correlations and independence. In: Proc. of COLT (2008)

    Google Scholar 

  8. Comon, P.: Independent Component Analysis. In: Proc. Int. Sig. Proc. Workshop on Higher-Order Statistics, Chamrousse, France, July 10-12, pp. 111–120 (1991); Keynote address. Republished in Lacoume, J.L. (ed.): Higher-Order Statistics, pp 29–38. Elsevier (1992)

    Google Scholar 

  9. DasGupta, S.: Learning mixtures of gaussians. In: Proc. of FOCS (1999)

    Google Scholar 

  10. DasGupta, S., Schulman, L.: A two-round variant of em for gaussian mixtures. In: Proc. of UAI (2000)

    Google Scholar 

  11. Eckart, C., Young, G.: The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936)

    Article  MATH  Google Scholar 

  12. Frieze, A., Jerrum, M., Kannan, R.: Learning linear transformations. In: FOCS, pp. 359–368 (1996)

    Google Scholar 

  13. Jutten, C., Herault, J.: Blind separation of sources, part i: An adaptive algorithm based on neuromimetic architecture. Signal Processing 24(1), 1–10 (1991)

    Article  MATH  Google Scholar 

  14. Kalai, A.T., Moitra, A., Valiant, G.: Efficiently learning mixtures of two gaussians. In: STOC, pp. 553–562 (2010)

    Google Scholar 

  15. Kannan, R., Salmasian, H., Vempala, S.: The spectral method for general mixture models. SIAM Journal on Computing 38(3), 1141–1156 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Kannan, R., Vempala, S.: Spectral algorithms. Foundations and Trends in Theoretical Computer Science 4(3-4), 157–288 (2009)

    MathSciNet  Google Scholar 

  17. Lacoume, J.-L., Ruiz, P.: Separation of independent sources from correlated inputs. IEEE Transactions on Signal Processing 40(12), 3074–3078 (1992)

    Article  Google Scholar 

  18. Moitra, A., Valiant, G.: Settling the polynomial learnability of mixtures of gaussians. In: FOCS, pp. 93–102 (2010)

    Google Scholar 

  19. Vempala, S., Wang, G.: A spectral algorithm for learning mixtures of distributions. Journal of Computer and System Sciences 68(4), 841–860 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  20. Vempala, S., Xiao, Y.: Structure from local optima: Learning subspace juntas via higher order pca. CoRR, abs/1108.3329 (2011)

    Google Scholar 

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Vempala, S.S. (2012). Effective Principal Component Analysis. In: Navarro, G., Pestov, V. (eds) Similarity Search and Applications. SISAP 2012. Lecture Notes in Computer Science, vol 7404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32153-5_1

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  • DOI: https://doi.org/10.1007/978-3-642-32153-5_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32152-8

  • Online ISBN: 978-3-642-32153-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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