Section: New Results

Wavelet based clustering using mixed effects functional models

Participant : Guillemette Marot.

Curve clustering in the presence of inter-individual variability has longly been studied, especially using splines to account for functional random effects. However splines are not appropriate when dealing with high-dimensional data and can not be used to model irregular curves such as peak-like data. We propose a wavelet based clustering procedure [23] and apply it to high dimensional data. We suggest a dimension reduction step based on wavelet thresholding adapted to multiple curves and using an appropriate structure for the random effect variance, we ensure that both fixed and random effects lie in the same functional space even when dealing with irregular functions that belong to Besov spaces. In the wavelet domain our model resumes to a linear mixed-effects model that can be used for a model-based clustering algorithm and for which we develop an EM algorithm for maximum likelihood estimation. An R package curvclust implementing this procedure is under building and should be posted to the CRAN, the official website of the R software, before Dec. 2011. An article has been submitted once to Biometrics and received good reports. This paper should also be submitted again to Biometrics once curvclust is on the CRAN.