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Quantification of the Impact of Feature Selection on the Variance of Cross-Validation Error Estimation

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Given the relatively small number of microarrays typically used in gene-expression-based classification, all of the data must be used to train a classifier and therefore the same training data is used for error estimation. The key issue regarding the quality of an error estimator in the context of small samples is its accuracy, and this is most directly analyzed via the deviation distribution of the estimator, this being the distribution of the difference between the estimated and true errors. Past studies indicate that given a prior set of features, cross-validation does not perform as well in this regard as some other training-data-based error estimators. The purpose of this study is to quantify the degree to which feature selection increases the variation of the deviation distribution in addition to the variation in the absence of feature selection. To this end, we propose the coefficient of relative increase in deviation dispersion (CRIDD), which gives the relative increase in the deviation-distribution variance using feature selection as opposed to using an optimal feature set without feature selection. The contribution of feature selection to the variance of the deviation distribution can be significant, contributing to over half of the variance in many of the cases studied. We consider linear-discriminant analysis, 3-nearest-neighbor, and linear support vector machines for classification; sequential forward selection, sequential forward floating selection, and the -test for feature selection; and -fold and leave-one-out cross-validation for error estimation. We apply these to three feature-label models and patient data from a breast cancer study. In sum, the cross-validation deviation distribution is significantly flatter when there is feature selection, compared with the case when cross-validation is performed on a given feature set. This is reflected by the observed positive values of the CRIDD, which is defined to quantify the contribution of feature selection towards the deviation variance.



  1. 1.

    Devroye L, Gyorfi L, Lugosi G: A Probabilistic Theory of Pattern Recognition. Springer, New York, NY, USA; 1996.

  2. 2.

    Braga-Neto U, Dougherty ER: Is cross-validation valid for small-sample microarray classification? Bioinformatics 2004, 20(3):374-380. 10.1093/bioinformatics/btg419

  3. 3.

    Braga-Neto U, Dougherty ER: Bolstered error estimation. Pattern Recognition 2004, 37(6):1267-1281. 10.1016/j.patcog.2003.08.017

  4. 4.

    Sima C, Braga-Neto U, Dougherty ER: Superior feature-set ranking for small samples using bolstered error estimation. Bioinformatics 2005, 21(7):1046-1054. 10.1093/bioinformatics/bti081

  5. 5.

    Sima C, Attoor S, Brag-Neto U, Lowey J, Suh E, Dougherty ER: Impact of error estimation on feature selection. Pattern Recognition 2005, 38(12):2472-2482. 10.1016/j.patcog.2005.03.026

  6. 6.

    Molinaro AM, Simon R, Pfeiffer RM: Prediction error estimation: a comparison of resampling methods. Bioinformatics 2005, 21(15):3301-3307. 10.1093/bioinformatics/bti499

  7. 7.

    Pudil P, Novovicova J, Kittler J: Floating search methods in feature selection. Pattern Recognition Letters 1994, 15(11):1119-1125. 10.1016/0167-8655(94)90127-9

  8. 8.

    Xiao Y, Hua J, Dougherty ER: Feature selection increases cross-validation imprecision. Proceedings of the 4th IEEE International Workshop on Genomic Signal Processing and Statistics (GENSIPS '06), College Station, Tex, USA, May 2006

  9. 9.

    van't Veer LJ, Dai H, van de Vijver MJ, et al.: Gene expression profiling predicts clinical outcome of breast cancer. Nature 2002, 415(6871):530-536. 10.1038/415530a

  10. 10.

    van de Vijver MJ, He YD, van't Veer LJ, et al.: A gene-expression signature as a predictor of survival in breast cancer. New England Journal of Medicine 2002, 347(25):1999-2009. 10.1056/NEJMoa021967

  11. 11.

    Choudhary A, Brun M, Hua J, Lowey J, Suh E, Dougherty ER: Genetic test bed for feature selection. Bioinformatics 2006, 22(7):837-842. 10.1093/bioinformatics/btl008

  12. 12.

    Jain A, Zongker D: Feature selection: evaluation, application, and small sample performance. IEEE Transactions on Pattern Analysis and Machine Intelligence 1997, 19(2):153-158. 10.1109/34.574797

  13. 13.

    Kudo M, Sklansky J: Comparison of algorithms that select features for pattern classifiers. Pattern Recognition 2000, 33(1):25-41. 10.1016/S0031-3203(99)00041-2

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Correspondence to Yufei Xiao.

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Xiao, Y., Hua, J. & Dougherty, E.R. Quantification of the Impact of Feature Selection on the Variance of Cross-Validation Error Estimation. J Bioinform Sys Biology 2007, 16354 (2007) doi:10.1155/2007/16354

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  • Error Estimation
  • Feature Selection
  • System Biology