Clustering multivariate functional data with the epigraph and hypograph indices: a case study on Madrid air quality

Abstract

With the rapid growth of data generation, advancements in functional data analysis have become essential, especially for approaches that handle multiple variables at the same time. This paper introduces a novel formulation of the epigraph and hypograph indices, along with their generalized expressions, specifically designed for multivariate functional data (MFD). These new definitions account for interrelationships between variables, enabling effective clustering of MFD based on the original data curves and their first two derivatives. The methodology developed here has been tested on simulated datasets, demonstrating strong performance compared to state-of-the-art methods. Its practical utility is further illustrated with two environmental datasets: the Canadian weather dataset and a 2023 air quality study in Madrid. These applications highlight the potential of the method as a great tool for analyzing complex environmental data, offering valuable insights for researchers and policymakers in climate and environmental research.