Geodesic Analysis on the Gaussian RKHS Hypersphere
Abstract
Using kernels to embed non linear data into high dimensional spaces where linear analysis is possible has become utterly classical. In the case of the Gaussian kernel however, data are distributed on a hypersphere in the corresponding Reproducing Kernel Hilbert Space (RKHS). Inspired by previous works in non-linear statistics, this article investigates the use of dedicated tools to take into account this particular geometry. Within this geometrical interpretation of the kernel theory, Riemannian distances are preferred over Euclidean distances. It is shown that this amounts to consider a new kernel and its corresponding RKHS. Experiments on real publicly available datasets show the possible benefits of the method on clustering tasks, notably through the definition of a new variant of kernel k -means on the hypersphere. Classification problems are also considered in a classwise setting. In both cases, the results show improvements over standard techniques.
Cite
Text
Courty et al. "Geodesic Analysis on the Gaussian RKHS Hypersphere." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2012. doi:10.1007/978-3-642-33460-3_25Markdown
[Courty et al. "Geodesic Analysis on the Gaussian RKHS Hypersphere." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2012.](https://mlanthology.org/ecmlpkdd/2012/courty2012ecmlpkdd-geodesic/) doi:10.1007/978-3-642-33460-3_25BibTeX
@inproceedings{courty2012ecmlpkdd-geodesic,
title = {{Geodesic Analysis on the Gaussian RKHS Hypersphere}},
author = {Courty, Nicolas and Burger, Thomas and Marteau, Pierre-François},
booktitle = {European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases},
year = {2012},
pages = {299-313},
doi = {10.1007/978-3-642-33460-3_25},
url = {https://mlanthology.org/ecmlpkdd/2012/courty2012ecmlpkdd-geodesic/}
}