Classifying and clustering functional data using projections

We show that, in the functional data context, by appropriately exploiting the functional nature of the data, it is possible to classify and cluster the observations asymptotically perfectly. We demonstrate that this level of performance can often be achieved as the data are projected on a carefully chosen finite dimensional space. 

In the clustering case, we propose an iterative algorithm to choose the projection functions in a way that optimises clustering performance, where, to avoid peculiar solutions, we use a weighted least-squares criterion. We apply our iterative clustering procedure on simulated and real data.