Depth measures for multivariate functional data with data-driven weights

The notion of statistical depth have recently been extended to the case of multivariate functional data. Its definition involves the choice of proper weights, averaging the univariate functional depths of each component. The choice of weights is crucial and must be carefully done according to the problem at hand. We describe a procedure that, starting from data, allows to compute a set of weights which are suitable for classification based on depths. These weights incorporate information on distances between covariance operators of the sub-populations.We show the validity of our strategy through a case study in which we perform supervised classification on ECG traces referring to both physiological and pathological subjects.