B1082
Title: Sparse and smooth clustering of functional data
Authors: Fabio Centofanti - Universita di Napoli Federico II (Italy) [presenting]
Antonio Lepore - Universita di Napoli Federico II (Italy)
Biagio Palumbo - University of Naples Federico II (Italy)
Abstract: A novel approach is devised to perform sparse clustering of functional data with the objective of categorizing a set of curves into homogeneous clusters while simultaneously identifying the most informative portions of the domain. The proposed technique, named sparse and smooth functional clustering (SaS-Funclust), is based on a functional Gaussian mixture model. The model parameters are estimated by maximizing a log-likelihood function that is penalized with a functional adaptive pairwise fusion penalty and a roughness penalty. The former enables the identification of uninformative portions of the domain by shrinking the means of distinct clusters towards common values, while the latter enhances interpretability by enforcing some level of smoothness in the estimated cluster means. Estimation of the model is accomplished using an expectation-conditional maximization algorithm in conjunction with a cross-validation procedure. In a Monte Carlo simulation study, the SaS-Funclust method demonstrates superior performance in terms of clustering accuracy and interpretability when compared to existing methods in the literature. Additionally, real-world examples are presented to showcase the favourable performance of the proposed method. The SaS-Funclust method is implemented in the \textsf{R} package \textsf{sasfunclust}, which can be downloaded from CRAN.
