K-means algorithms for functional data

López García, María Luz and García-Rodenas, Ricardo and González Gómez, Antonia (2015). K-means algorithms for functional data. "NEUROCOMPUTING", v. 151 ; pp. 231-245. ISSN 0925-2312. https://doi.org/10.1016/j.neucom.2014.09.048.


Title: K-means algorithms for functional data
  • López García, María Luz
  • García-Rodenas, Ricardo
  • González Gómez, Antonia
Item Type: Article
Título de Revista/Publicación: NEUROCOMPUTING
Date: 2015
ISSN: 0925-2312
Volume: 151
Freetext Keywords: Functional data, K-means, Reproducing Kernel Hilbert Space.
Faculty: E.T.S.I. Montes (UPM)
Department: Matemática Aplicada
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Cluster analysis of functional data considers that the objects on which you want to perform a taxonomy are functions f : X e Rp ↦R and the available information about each object is a sample in a finite set of points f ¼ fðx ; y ÞA X x Rgn . The aim is to infer the meaningful groups by working explicitly with its infinite-dimensional nature. In this paper the use of K-means algorithms to solve this problem is analysed. A comparative study of three K-means algorithms has been conducted. The K-means algorithm for raw data, a kernel K-means algorithm for raw data and a K-means algorithm using two distances for functional data are tested. These distances, called dVn and dϕ, are based on projections onto Reproducing Kernel Hilbert Spaces (RKHS) and Tikhonov regularization theory. Although it is shown that both distances are equivalent, they lead to two different strategies to reduce the dimensionality of the data. In the case of dVn distance the most suitable strategy is Johnson–Lindenstrauss random projections. The dimensionality reduction for dϕ is based on spectral methods.

Funding Projects

Government of SpainTRA2011-27791-C03-03UnspecifiedUnspecifiedUnspecified

More information

Item ID: 44822
DC Identifier: https://oa.upm.es/44822/
OAI Identifier: oai:oa.upm.es:44822
DOI: 10.1016/j.neucom.2014.09.048
Official URL: https://www.sciencedirect.com/science/article/pii/S0925231214012521
Deposited by: Memoria Investigacion
Deposited on: 14 Mar 2017 12:17
Last Modified: 10 Jun 2019 14:35
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