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PLS classification of functional data

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Abstract

Partial least squares (PLS) approach is proposed for linear discriminant analysis (LDA) when predictors are data of functional type (curves). Based on the equivalence between LDA and the multiple linear regression (binary response) and LDA and the canonical correlation analysis (more than two groups), the PLS regression on functional data is used to estimate the discriminant coefficient functions. A simulation study as well as an application to kneading data compare the PLS model results with those given by other methods.

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References

  • Aguilera AM, Ocaña F, Valderama MJ (1997) An approximated principal component prediction model for continuous-time stochastic process. Appl Stochast Models Data Anal 13:61–72

    Article  MATH  Google Scholar 

  • Barker M, Rayens W (2003) Partial least squares for discrimination. J Chemomet 17:166–173

    Article  Google Scholar 

  • Biau G, Bunea F, Wegkamp M (2005) Function classification in Hilbert spaces. IEEE Trans Inform Theory 51:2162–2172

    MathSciNet  Google Scholar 

  • Cardot H, Sarda P (2005) Estimation in generalized linear models for functional data via penalized likelihood. J Multivariate Anal 92:24–41

    Article  MATH  MathSciNet  Google Scholar 

  • Cardot H, Ferraty F, Sarda P (1999) Functional linear model. Statist Probab Lett 45:11–22

    Article  MATH  MathSciNet  Google Scholar 

  • Escabias M, Aguilera AM, Valderrama MJ (2004) Principal component estimation of functional logistic regression: discussion of two different approches. J Nonparamet Stat 3–4:365–385

    Google Scholar 

  • Escabias M, Aguilera AM, Valderrama MJ (2005) Modeling environmental data by functional principal component logistic regression. Environmetrics 16:95–107

    Article  MathSciNet  Google Scholar 

  • Escoufier Y (1970) Echantillonage dans une population de variables aléatoires réelles. Publications de l’Institut de Statistique de l’Université de Paris 19(4):1–47

    MathSciNet  Google Scholar 

  • Ferraty F, Vieu P (2003) Curves discrimination: a nonparametric approach. Comput Stat Data Anal 44:161–173

    Article  MathSciNet  MATH  Google Scholar 

  • Ferraty F, Vieu P (2004) Nonparametric models for functional data with application in regression, time series prediction and curve discrimination. J Nonparamet Stat 16(1–2):111–125

    Article  MATH  MathSciNet  Google Scholar 

  • Fisher RA (1936) The use of multiple measurement in taxonomic problems. Ann Eugen 7:179–188

    Google Scholar 

  • Frank I, Friedman J (1993) A statistical view of some chemometrics regression tools. Technometrics 35:109–148

    Article  MATH  Google Scholar 

  • James GM (2002) Generalized linear models with functional predictors. J R Stat Soc Ser B 64(3):411–432

    Article  MATH  MathSciNet  Google Scholar 

  • James GM, Hastie TJ (2001) Functional discrimnant analysis for irregularly sampled curves. J R Stat Soc Ser B 63(3):533–550

    Article  MATH  MathSciNet  Google Scholar 

  • de Jong S (1993) Pls fits closer than pcr. J Chemomet 7:551–557

    Article  Google Scholar 

  • Lévéder C, Abraham C, Cornillon PA, Matzner-Lober E, Molinari N (2004) Discrimination de courbes de pétrissage. Chimiométrie 2004, Paris, pp 37–43

  • Müler H-G, StadtMüler U (2005) Generalized functional linear models. Ann Stat 33(2):774–805

    Article  Google Scholar 

  • Preda C (2007) Regression models for functional data by reproducing kernel Hilbert spaces methods. J Stat Plan Infer 137:829–840

    Article  MATH  MathSciNet  Google Scholar 

  • Preda C, Saporta G (2002) Régression PLS sur un processus stochastique. Revue de Statistique Appliquée L(2):27–45

  • Ramsay JO, Silverman BW (1997) Functional data analysis. Springer, New York

    MATH  Google Scholar 

  • Ramsay JO, Silverman BW (2002) Applied functional data analysis:methods and case studies. Springer, Heidelberg

    MATH  Google Scholar 

  • Ratcliffe SJ, Leader LR, Heller GZ (2002) Functional data analysis with application to periodically stimulated foetal heart rate data. ii : functional logistic regression. Stat Med 21:1115–1127

    Article  Google Scholar 

  • Saporta G (1981) Méthodes exploratoires d’analyse de données temporelles. Cahiers du B.U.R.O, Université Pierre et Marie Curie, Paris

  • Tenenhaus M (2002) La régression PLS. Théorie et pratique. Editions Technip

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Correspondence to Cristian Preda.

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Preda, C., Saporta, G. & Lévéder, C. PLS classification of functional data. Computational Statistics 22, 223–235 (2007). https://doi.org/10.1007/s00180-007-0041-4

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