Kernel discriminant analysis and clustering with parsimonious Gaussian process models

TL;DR

This paper introduces a family of parsimonious Gaussian process models for classification and clustering in infinite-dimensional spaces, capable of handling various data types and mixed data through kernel functions.

Contribution

It proposes a novel framework for Gaussian process models with eigen-decomposition constraints, enabling flexible, non-linear, and kernel-based classification and clustering in infinite-dimensional spaces.

Findings

Effective classification of diverse data types demonstrated

Ability to handle mixed data with combined kernels shown

Method extended successfully to unsupervised clustering

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.