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Discriminant analysis on functional data

Gilbert Saporta 1
1 CEDRIC - MSDMA - CEDRIC. Méthodes statistiques de data-mining et apprentissage
CEDRIC - Centre d'études et de recherche en informatique et communications
Abstract : Discriminant analysis or “supervised” classification for functional data occurs when for each curve or path of a stochastic process we have a single categorical response Y. Linear methods looks for predictors which may be expressed as an integral sum .Fisher’s linear discriminant function being equivalent to a multiple regression with a coded response, one can use techniques for the regression problem when Y is continuous. When t takes continuously its values in an interval [0;T], multicollinearity leads to inconsistent estimation of the parameters. Components derived from the Karhunen-Loeve decomposition are, for functional data, the equivalent of principal components regression (PCR). Partial least squares performs better than PCR, since principal components are obtained irrespective of the response (Preda & al., 2007). Functional logistic regression is another approach advocated by Aguilera & al , 2006. We determine an optimal time t*
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Gilbert Saporta. Discriminant analysis on functional data. XV Congresso Annual da Sociedade Portuguesa de Estadistica, Aug 2007, Lisbonne, Portugal. ⟨hal-01125374⟩

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