A Proposal for Robust Curve Clustering

Autores: Luis Angel García Escudero , Alfonso Gordaliza Ramos
Localización: Journal of classification, ISSN 0176-4268, Vol. 22, Nº 2, 2005, págs. 185-201
Idioma: inglés
DOI: 10.1007/s00357-005-0013-8
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Resumen
- Functional data sets appear in many areas of science. Although each data point may be seen as a large finite-dimensional vector it is preferable to think of them as functions, and many classical multivariate techniques have been generalized for this kind of data. A widely used technique for dealing with functional data is to choose a finite-dimensional basis and find the best projection of each curve onto this basis. Therefore, given a functional basis, an approach for doing curve clustering relies on applying the k-means methodology to the fitted basis coefficients corresponding to all the curves in the data set. Unfortunately, a serious drawback follows from the lack of robustness of k-means. Trimmed k-means clustering (Cuesta-Albertos, Gordaliza, and Matran 1997) provides a robust alternative to the use of k-means and, consequently, it may be successfully used in this functional framework. The proposed approach will be exemplified by considering cubic B-splines bases, but other bases can be applied analogously depending on the application at hand.