We present 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 and an EM algorithm
is derived for the inference. Experimental results on various data sets demonstrate the effectiveness
of the proposed method. A Matlab toolbox implementing the proposed classification methods is provided
as supplementary material.
+ C. Bouveyron, M. Fauvel and S. Girard, Kernel discriminant analysis and clustering with parsimonious Gaussian process models, Statistics and Computing, vol. 25(6), pp. 1143-1162, 2015.
+ C. Bouveyron, M. Fauvel and S. Girard, Parsimonious Gaussian process models for the classification of hyperspectral remote sensing images, IEEE Geoscience and Remote Sensing Letters, vol. 12, pp. 2423-2427, 2015.