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Dimension Reduction vs. Variable Selection

  • Wolfgang M. Hartmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3732)

Abstract

The paper clarifies the difference between dimension reduction and variable selection methods in statistics and data mining. Traditional and recent modeling methods are listed and a typical approach to variable selection is mentioned. In addition, the need for and types of cross validation in modeling is sketched.

Keywords

Support Vector Machine Cross Validation Variable Selection Dimension Reduction Pattern Search 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Anderberg, M.R.: Cluster Analysis for Applications. Academic Press, Inc, New York (1973)zbMATHGoogle Scholar
  2. 2.
    Benjamini, Y., Hochberg, Y.: Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. R. Statist. Soc., Ser. B, 289–300 (1995)Google Scholar
  3. 3.
    Bi, J., Bennett, K., Embrechts, M., Breneman, C., Song, M.: Dimensionality Reduction via Sparse Support Vector Machines. Journal of Machine Learning Research 1, 1–48 (2002)Google Scholar
  4. 4.
    Breiman, L., Friedman, J.H., Olshen, R.A., Stone, J.: Classification and Regression Trees. Wadsworth (1984)Google Scholar
  5. 5.
    Breiman, L.: Better subset selection using the non-negative garotte; TechnicalReport, Univ. of California, Berkeley (1993) Google Scholar
  6. 6.
    Carroll, J.D., Arabie, P.: Multidimensional scaling. In: Birnbaum, M.H. (ed.) Handbook of Perception and Cognition: Measurement, Judgment and Decision Making, pp. 179–250. Academic Press, San Diego (1998)Google Scholar
  7. 7.
    Chen, S.S., Donoho, D.L., Saunders, M.: Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing 20, 33–61 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Donoho, D., Johnstone, I., Tibshirani, R.: Wavelet shrinkage: asymptotia (with discussion). J. R. Statist. Soc., Ser. B 57, 301–337 (1995)zbMATHGoogle Scholar
  9. 9.
    Efron, B., Hastie, T., Johnstone, I., Tibshirani, R.: Least Angle Regression. The Annals of Statistics 32, 407–499 (2002)MathSciNetGoogle Scholar
  10. 10.
    Fung, G., Mangasarian, O.L.: A Feature Selection Newton Method for Support Vector Machine Classification. Computational Optimization and Aplications, 1–18 (2003)Google Scholar
  11. 11.
    Gifi, A.: Nonlinear Multivariate Analysis, Dep. of Data Theory, Univ. of Leiden (1981) Google Scholar
  12. 12.
    Greenacre, M.J.: Theory and Applications of Correspondence Analysis. Academic Press, London (1988)Google Scholar
  13. 13.
    Guyon, I., Weston, J., Barnhill, S., Vapnik, V.: Gene Selection for cancer classification using support vector machines. Machine Learning 46, 389–422 (2002)zbMATHCrossRefGoogle Scholar
  14. 14.
    Harman, H.H.: Modern Factor Analysis. University of Chicago Press, Chicago (1976)Google Scholar
  15. 15.
    Hartmann, W.: CMAT Users Manual (1995), see http://www.cmat.pair.com/cmat
  16. 16.
    Joachims, T.: Making large-scale SVM learning practical. In: Schölkopf, B., Burges, C.J.C., Smola, A.J. (eds.) Advances in Kernel Methods: Support Vector Learning, MIT Press, Cambridge (1999)Google Scholar
  17. 17.
    Kaufman, L., Rousseeuw, P.: Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York (1990)Google Scholar
  18. 18.
    Li, K.C.: Sliced inverse regression for dimension reduction. JASA 86, 316–342 (1991)zbMATHGoogle Scholar
  19. 19.
    Li, K.C.: On principal Hessian directions for data visualization and dimension reduction. JASA 87, 1025–1034 (1992)zbMATHGoogle Scholar
  20. 20.
    Mangasarian, O.L., Wild, E.W.: Feature Selection in k-Median Clustering, Technical Report 04-01, Data Mining Institute, Madison: University of Wisconsin (2004) Google Scholar
  21. 21.
    McCabe, G.P.: Principal variables. Technometrics 26, 139–144 (1984)CrossRefMathSciNetGoogle Scholar
  22. 22.
    Miller, A.: Subset Selection in Regression. CRC Press, Chapman & Hall (2002)Google Scholar
  23. 23.
    Mulaik, S.A.: The Foundations of Factor Analysis. Mc Graw Hill, New York (1972)Google Scholar
  24. 24.
    Osborne, M.R., Presnell, B., Turlach, B.A.: On the LASSO and its Dual. JCGS 9, 319–337 (2000)MathSciNetGoogle Scholar
  25. 25.
    Osborne, M.R., Presnell, B., Turlach, B.A.: A new approach to variable selection in least squares problems. IMA Journal of Numerical Analysis 20, 389–404 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    R Language and packages see: http://www.r-project.org/ and http://cran.r-project.org/
  27. 27.
    Ripley, B.D.: Pattern Recognition and Neural Networks. Cambridge University Press, Cambridge (1996)zbMATHGoogle Scholar
  28. 28.
    Rosipal, R., Trejo, L.J.: Kernel partial least squares regression in reproducing kernel Hilbert space. Journal of Machine Learning Research 2, 97–123 (2001)CrossRefGoogle Scholar
  29. 29.
    SAS/STAT User’s Guide, Version 6, Second Printing, SAS Institute Inc., Cary, NC (1990) Google Scholar
  30. 30.
    Schölkopf, B., Smola, A.J.: Learning with Kernels. MIT Press, Cambridge (2002)Google Scholar
  31. 31.
    Somerville, P.N.: Step-down FDR Procedures for large numbers of hypotheses. In: Dongarra, J., Madsen, K., Waśniewski, J. (eds.) PARA 2004. LNCS, vol. 3732, pp. 949–956. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  32. 32.
    Somerville, P.N.: FORTRAN90 and SAS-IML programs for computation of critical values for multiple testing and simultaneous confidence intervals. Journal of Statistical Software (2001)Google Scholar
  33. 33.
    Tibshirani, R.: Regression shrinkage and selection via the Lasso. J. R. Statist. Soc., Ser. B 58, 267–288 (1996)zbMATHMathSciNetGoogle Scholar
  34. 34.
    Tibshirani, R., Hastie, T., Narasimhan, B., Chu, G.: Diagnosis of multiple cancer types by shrunken centroids of gene expression. Proceeding of the National Academy of Sciences 99, 6567–6572 (2002)CrossRefGoogle Scholar
  35. 35.
    Weisberg, S.: Dimension reduction regression with R. JSS, 7 (2002) Google Scholar
  36. 36.
    Weston, J., Mukherje, S., Chapelle, O., Pontil, M., Poggio, T., Vapnik, V.: Feature Selection for SVMs. Neural Information Processing Systems 13, 668–674 (2000)Google Scholar
  37. 37.
    Vapnik, V.N.: The Nature of Statistical Learning. Springer, New York (1995)zbMATHGoogle Scholar
  38. 38.
    Wold, H.: Estimation of principal components and related models by iterative least squares. In: Multivariate Analysis, Academic Press, New York (1966)Google Scholar
  39. 39.
    Yang, J., Honavar, V.: Feature selection using a genetic algorithm, Technical Report, Iowa State University (1997) Google Scholar
  40. 40.
    Zou, H., Hastie, T.: Regression shrinkage and selection via the elastic net, with applications to micro arrays, Technical Report, Stanford University (2003) Google Scholar
  41. 41.
    Zou, H., Hastie, T., Tibshirani, R.: Sparse principal component analysis. Technical Report, Stanford University (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Wolfgang M. Hartmann
    • 1
  1. 1.SAS Institute, IncCaryUSA

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