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Fast DD-classification of functional data

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  • Karl Mosler

    (University of Cologne)

  • Pavlo Mozharovskyi

    (University of Cologne)

Abstract

A fast nonparametric procedure for classifying functional data is introduced. It consists of a two-step transformation of the original data plus a classifier operating on a low-dimensional space. The functional data are first mapped into a finite-dimensional location-slope space and then transformed by a multivariate depth function into the DD-plot, which is a subset of the unit square. This transformation yields a new notion of depth for functional data. Three alternative depth functions are employed for this, as well as two rules for the final classification in $$[0,1]^2$$ [ 0 , 1 ] 2 . The resulting classifier has to be cross-validated over a small range of parameters only, which is restricted by a Vapnik–Chervonenkis bound. The entire methodology does not involve smoothing techniques, is completely nonparametric and allows to achieve Bayes optimality under standard distributional settings. It is robust, efficiently computable, and has been implemented in an R environment. Applicability of the new approach is demonstrated by simulations as well as by a benchmark study.

Suggested Citation

  • Karl Mosler & Pavlo Mozharovskyi, 2017. "Fast DD-classification of functional data," Statistical Papers, Springer, vol. 58(4), pages 1055-1089, December.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:4:d:10.1007_s00362-015-0738-3
    DOI: 10.1007/s00362-015-0738-3
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    3. Agostinelli, Claudio, 2018. "Local half-region depth for functional data," Journal of Multivariate Analysis, Elsevier, vol. 163(C), pages 67-79.

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