Resumen: This talk will be focused on supervised binary classification problems in which the data space is infinite-dimensional. Such a situation arises in many typical cases of functional data, such as temperature registrations, spectral curves, electrocardiograms etc., but also in pattern recognition problems involving images or shapes. The choice of an appropriate distance between data is particularly important in such settings.
Three particular examples will be briefly discussed: a functional version of the Mahalanobis distance (suitable for trajectories of L2-processes), a “visual metric” (suitable for spectrometric curves) and a “probabilistic distance” (adapted to problems of shape discrimination).
The contents of this talk are a summary of several recent joint works with different co-authors: J. R. Berrendero, A. Cholaquidis, B. Bueno, R. Fraiman, and B. Pateiro.