  The proliferation of data generation has spurred advancements in functional
data analysis. With the ability to analyze multiple variables simultaneously,
the demand for working with multivariate functional data has increased. This
study proposes a novel formulation of the epigraph and hypograph indexes, as
well as their generalized expressions, specifically tailored for the
multivariate functional context. These definitions take into account the
interrelations between components. Furthermore, the proposed indexes are
employed to cluster multivariate functional data. In the clustering process,
the indexes are applied to both the data and their first and second
derivatives. This generates a reduced-dimension dataset from the original
multivariate functional data, enabling the application of well-established
multivariate clustering techniques which have been extensively studied in the
literature. This methodology has been tested through simulated and real
datasets, performing comparative analyses against state-of-the-art to assess
its performance.
