Funclust: A curves clustering method using functional random variables density approximation

A new method for clustering functional data is proposed under the name Funclust. This method relies on the approximation of the notion of probability density for functional random variables, which generally does not exist. Using the Karhunen–Loeve expansion of a stochastic process, this approximation leads to define an approximation for the density of functional variables. Based on this density approximation, a parametric mixture model is proposed. The parameter estimation is carried out by an EM-like algorithm, and the maximum a posteriori rule provides the clusters. The efficiency of Funclust is illustrated on several real datasets, as well as for the characterization of the Mars surface.