B1911
Title: Clustering functional data with the aid of epigraph and hypograph indexes: the journey
Authors: Rosa Lillo - Universidad Carlos III de Madrid (Spain) [presenting]
Belen Pulido Bravo - Universidad Carlos III de Madrid (Spain)
Alba Franco-Pereira - Universidad Complutense de Madrid (Spain)
Abstract: The growing interest in the use of functional data to model real-world scenarios implies the need for the development of statistical methodologies tailored to this data type, characterized by inherent complexity stemming from the necessity to tackle problems in infinite dimensions. The purpose is to bridge two fundamental concepts associated with datasets of any nature: ordering and clustering. The proposed ordering method (applicable to both univariate and multivariate functional data) is based on the epigraph and hypograph indexes, thoughtfully adapted to suit the multivariate context. The clustering process hinges on dimensionality reduction for functional data, complemented by the inclusion of derivatives, in conjunction with clustering techniques found in the multivariate data literature. The approach is illustrated through the use of simulated and real-world data, showcasing superior performance (in almost all scenarios) and computational efficiency.
