Ordinal spaces
General Topology
2024-12-24 v1
Abstract
Ordinal data analysis is an interesting direction in machine learning. It mainly deals with data for which only the relationships `', `', `' between pairs of points are known. We do an attempt of formalizing structures behind ordinal data analysis by introducing the notion of ordinal spaces on the base of a strict axiomatic approach. For these spaces we study general properties as isomorphism conditions, connections with metric spaces, embeddability in Euclidean spaces, topological properties etc.
Cite
@article{arxiv.2412.17391,
title = {Ordinal spaces},
author = {Karsten Keller and Evgeniy Petrov},
journal= {arXiv preprint arXiv:2412.17391},
year = {2024}
}
Comments
28 pages, 3 figures