Unsupervised curve clustering using wavelets

Umberto Amato (), Anestis Antoniadis (), Italia De Feis () and Irène Gijbels ()
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Umberto Amato: Consiglio Nazionale delle Ricerche, Istituto di Scienze Applicate e Sistemi Intelligenti
Anestis Antoniadis: Consiglio Nazionale delle Ricerche, Istituto di Scienze Applicate e Sistemi Intelligenti
Italia De Feis: Consiglio Nazionale delle Ricerche, Istituto per le Applicazioni del Calcolo ‘Mauro Picone’
Irène Gijbels: KU Leuven, Department of Mathematics

Advances in Data Analysis and Classification, 2025, vol. 19, issue 4, No 8, 1085 pages

Abstract: Abstract Clustering univariate functional data is mostly based on projecting the curves onto an adequate basis and applying some distance or similarity models on the coefficients. The basis functions should be chosen depending on features of the function being estimated. Commonly used are Fourier, polynomial and splines, but these may not be well suited for curves that exhibit inhomogeneous behavior. Wavelets on the contrary are well suited for identifying highly discriminant local time and scale features, and are able to adapt to the data smoothness. In recent years, few methods, relying on wavelet-based similarity measures, have been proposed for clustering curves, observed on equidistant points. In this work, we present a non-equidistant design wavelet based method for non-parametrically estimating and clustering a large number of curves. The method consists of several crucial stages: fitting functional data by non-equispaced design wavelet regression, screening out nearly flat curves, denoising the remaining curves with wavelet thresholding, and finally clustering the denoised curves. Simulation studies compare our proposed method with some other functional clustering methods. The method is applied for clustering some real functional data profiles.

Keywords: Clustering; False discovery rate; Functional data; High-dimensional testing; k-means; Thresholding; Primary 62Gxx; Secondary 62Hxx (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11634-024-00612-7

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