Section: New Results

Mixture models

Taking into account the curse of dimensionality

Participants : Stéphane Girard, Alessandro Chiancone, Seydou-Nourou Sylla.

Joint work with: C. Bouveyron (Univ. Paris 5), M. Fauvel (ENSAT Toulouse) and J. Chanussot (Gipsa-lab and Grenoble-INP)

In the PhD work of Charles Bouveyron (co-advised by Cordelia Schmid from the Inria LEAR team)  [61] , we proposed new Gaussian models of high dimensional data for classification purposes. We assume that the data live in several groups located in subspaces of lower dimensions. Two different strategies arise:

• the introduction in the model of a dimension reduction constraint for each group

• the use of parsimonious models obtained by imposing to different groups to share the same values of some parameters

This modelling yields a supervised classification method called High Dimensional Discriminant Analysis (HDDA) [4] . Some versions of this method have been tested on the supervised classification of objects in images. This approach has been adapted to the unsupervised classification framework, and the related method is named High Dimensional Data Clustering (HDDC) [3] . Our recent work consists in adding a kernel in the previous methods to deal with nonlinear data classification and heterogeneous data [13] . We first investigate the use of kernels derived from similary measures on binary data [30] . The targeted application is the analysis of verbal autopsy data (PhD thesis of N. Sylla): Indeed, health monitoring and evaluation make more and more use of data on causes of death from verbal autopsies in countries which do not keep records of civil status or with incomplete records. The application of verbal autopsy method allows to discover probable cause of death. Verbal autopsy has become the main source of information on causes of death in these populations. Second, the kernel classification method is applied to three real hyperspectral data sets,and compared with three others classifiers. The proposed models show good results in terms of classification accuracy and processing time [21] .