Classification methods for Hilbert data based on surrogate density

We study an unsupervised and a supervised classification approaches for Hilbert random curves. Both rest on the use of a surrogate of the probability density which is defined, in a distribution-free mixture context, from an asymptotic factorization of the small-ball probability. That surrogate density is estimated by a kernel approach from the principal components of the data. The paper focuses on the illustration of the classification algorithms and the computational implications, with particular attention to the tuning of parameters involved. Some asymptotic results are sketched. Applications on simulated and real datasets show how the proposed methods work.