The Mahalanobis Distance for Functional Data With Applications to Classification

This article presents a new semidistance for functional observations that generalizes the Mahalanobis distance for multivariate datasets. The main characteristics of the functional Mahalanobis semidistance are shown. To illustrate the applicability of this measure of proximity between functional obs...

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Bibliographic Details
Published in:Technometrics 2015-04, Vol.57 (2), p.281-291
Main Authors: Galeano, Pedro, Joseph, Esdras, Lillo, Rosa E.
Format: Article
Language:English
Subjects:
Classification
Classification methods
Functional data analysis
Functional Mahalanobis semidistance
Functional principal components
Monte Carlo simulation
Multivariate analysis
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Description
Summary:This article presents a new semidistance for functional observations that generalizes the Mahalanobis distance for multivariate datasets. The main characteristics of the functional Mahalanobis semidistance are shown. To illustrate the applicability of this measure of proximity between functional observations, new versions of several well-known functional classification procedures are developed using the functional Mahalanobis semidistance. A Monte Carlo study and the analysis of two real examples indicate that the classification methods used in conjunction with the functional Mahalanobis semidistance give better results than other well-known functional classification procedures. This article has supplementary material online.
ISSN:0040-1706
1537-2723
DOI:10.1080/00401706.2014.902774