Functional clustering of random curves

Nowadays, in many scientific fields, e.g. ecology, biology, geology, medicine, it is frequent to have large data sets usually collected as a sample of curves such as growth curves, temperature curves, rainfall curves, spectrometric curves, etc. This work aims at reviewing different curve-clustering methods. The study of a collection of functions is referred to as functional data analysis, a statistical framework increasingly used in the analysis of high dimensional data. Many real problems may have the need of detecting the clustering structure of a sample of curves. Traditional methods are not suitable when dealing with some form of infinite dimensional data. In the literature, substantial work has been done in order to perform functional cluster analysis for data that consists of a random trajectory for a sample of subjects. In this paper we review some techniques of clustering functional data. In particular we focus on the strategy of 1first approximating the discrete trajectories with polynomial spline in order to get smooth curves. Then, the coefficients of the smoothing fit can be used in place of the original data in order to perform functional cluster analysis. Results depend on the number of basis functions and on smoothing parameters. By means of a simulation study we evaluate the impact of different smoothing parameters. In particular, an application for clustering the continuous trajectories of the Galvanic Skin Response (GSR) recorded in an experiment examining the influence of different stimuli on the electro dermal activity of a sample of individuals is presented.