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Kernel discriminant analysis and clustering with parsimonious Gaussian process models

Charles Bouveyron 1, * Mathieu Fauvel 2 Stéphane Girard 3
* Corresponding author
3 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : 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.
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Charles Bouveyron, Mathieu Fauvel, Stéphane Girard. Kernel discriminant analysis and clustering with parsimonious Gaussian process models. Statistics and Computing, Springer Verlag (Germany), 2015, 25 (6), pp.1143-1162. ⟨10.1007/s11222-014-9505-x⟩. ⟨hal-00687304v4⟩

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