Depth-based methods for clustering of functional data.

The problem of detecting clusters is a common issue in the analysis of functionaldata and some interesting intuitions from approaches relied on depth measures canbe considered for construction of basic tools for clustering of curves. Motivated byrecent contributions on the problem clustering and alignment of functional data, wealso consider the problem of aligning a set of curves when classification proceduresare implemented. The variability among curves can be interpreted in terms oftwo components, phase and amplitude; phase variability, or misalignment, can beeliminated by aligning the curves, according to a similarity index and a warpingfunction. Some approaches address the misalignment as a confounding factor, ifit is not suitably taken into account; as opposed to treating phase variability as anuisance effect, other approaches recognize that both amplitude and phase of curvescontain cluster information. The search for suitable transformation of the originaldata involves the optimization of specific similarities between the warped curvesand a natural consequence seems to incorporate the warping step in a clusteringapproach. Among the similarity indexes considered in the literature on functionaldata analysis, those defined via statistical depth provide a way to robustly clusterfunctional data. We implement a procedure exploiting the idea of functional depth,searching both for the set of optimal groups to obtain efficient aligning and clusteringcurves. We also try to deal with the implications of preprocessing the curves via awarping procedure or alternatively ignoring the misalignment in the further analysis,or explicitly recognizing it as a source of information for clustering. This approachprovides an useful tool for analyzing many phenomena and in particular we apply itto seismic curves clustering. Paper supported by the national grant MIUR, PRIN-2015 program, Prot.20157PRZC4.