  This work presents a family of parsimonious Gaussian process models which
allow to build, from a finite sample, a model-based classifier in an infinite
dimensional space. The proposed parsimonious models are obtained by
constraining the eigen-decomposition of the Gaussian processes modeling each
class. This allows in particular to use non-linear mapping functions which
project the observations into infinite dimensional spaces. It is also
demonstrated that the building of the classifier can be directly done from the
observation space through a kernel function. The proposed classification method
is thus able to classify data of various types such as categorical data,
functional data or networks. Furthermore, it is possible to classify mixed data
by combining different kernels. The methodology is as well extended to the
unsupervised classification case. Experimental results on various data sets
demonstrate the effectiveness of the proposed method.
