Section: New Results

Statistical learning methodology and theory

Participants : Gilles Celeux, Christine Keribin, Erwan Le Pennec, Pascal Massart, Lucie Montuelle, Jean-Michel Poggi.

Unsupervised segmentation is an issue similar to unsupervised classification with an added spatial aspect. Functional data is acquired on points in a spatial domain and the goal is to segment the domain in homogeneous domain. The range of applications includes hyperspectral images in conservation sciences, fMRi data and all spatialized functional data. Erwan Le Pennec and Lucie Montuelle are focusing on the questions of the way to handle the spatial component from both the theoretical and the practical point of views as well as the choice of the number of clusters. Furthermore, as functional data require heavy computation, they are required to propose numerically efficient algorithms.

Gilles Celeux, Christine Keribin and the Ph D. student Vincent Brault continue their work on the Latent Block Model. They have proposed an efficient algorithm coupling a Stochastic version of the EM algorithm including a Gibbs sampling step and the Variational EM algorithm. This SEM-VEM algorithm is insensible to its initial position. On the other hand they got a closed formed expression of the Integrated Completed Likelihood for binary tables which allows for a reliable model selection criterion avoiding asymptotic approximation. Moreover, Christine Keribin derived sufficient conditions ensuring the identifiability of the Latent Block Model.