Classification methods for Hilbert data based on surrogate density

• Published in: Computational statistics & data analysis Vol. 99; pp. 204 - 222
• Main Authors: Bongiorno, Enea G., Goia, Aldo
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2016
• Subjects: Asymptotic properties; Classification; Computation; Data processing; Density; Density based clustering; Discriminant Bayes rule; Factorization; Functional principal component; Hilbert data; Kernel density estimate; Small-ball probability mixture; Statistics; Tuning; Hilbert data; Density based clustering; Discriminant Bayes rule; Kernel density estimate; Small-ball probability mixture; Functional principal component
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2016.01.019

An unsupervised and a supervised classification approach for Hilbert random curves are studied. Both rest on the use of a surrogate of the probability density which is defined, in a distribution-free mixture context, from an asymptotic factorization of the small-ball probability. That surrogate density is estimated by a kernel approach from the principal components of the data. The focus is on the illustration of the classification algorithms and the computational implications, with particular attention to the tuning of the parameters involved. Some asymptotic results are sketched. Applications on simulated and real datasets show how the proposed methods work.