Modélisation et classification des données de grande dimension : application à l’analyse d’images
PhD thesis, Université Grenoble 1.
The main topic of this thesis is modeling and classification of high-dimensional data. Based on the
assumption that high-dimensional data live in subspaces with intrinsic dimensions smaller than the dimension of the original space and that the data of different classes live in different subspaces with different
intrinsic dimensions, we propose a re-parametrization of the Gaussian mixture model. By forcing some
parameters to be common within or between classes, we show a family of 28 Gaussian models appropriated for
high-dimensional data, from the most general model to the most parsimonious one. These models are then used
for discrimination and clustering of high-dimensional data. The classifiers associated with these models are
called respectively High Dimensional Discriminant Analysis (HDDA) and High Dimensional Data Clustering
(HDDC) and their construction is based on the maximum likelihood estimation of model parameters. The nature
of our re-parametrization allows HDDA and HDDC not to be disturbed by the ill-conditioning or the singularity of empirical covariance matrices and to be efficient in terms of computing time. The methods HDDA and HDDC are then used in a probabilistic framework to object recognition in images. This approach, which can be supervised or weakly-supervised, allows to locate in a probabilistic way an object in a new image. Our approach is validated on two recent image databases and compared to the most efficient object recognition methods.