Clustering with Mixture Models and Conditional Density
joint work with S. Cohen, L. Montuelle and E. Derman
Unsupervised classification is often perform using Gaussian Mixture Model, whose components are associated to classes. With S. Cohen, we have proposed an extension of this model in which the mixture proportions depend of a covariate, the position. We have proposed an efficient numerical scheme that leads to an unsupervised hyperspectral image segmentation used with real datasets at IPANEMA, an ancient material study platform located at Synchrotron Soleil.
The unsupervised algorithm relies on a model selection principle to select a suitable number of classes. In this work, with S. Cohen, we prove that, more generally, conditional density estimation can be performed by a penalized maximum likelihood principle under weak assumptions on the model selection. This analysis is exemplified by two piecewise constant with respect to the covariate partition-based conditional density strategy, one combined with piecewise polynomial density and the other with Gaussian Mixture densities. During her PhD, L. Montuelle developed extension to mixture of Gaussian regressions.
With E. Derman, we have shown how to extend those results to mixture of histograms.