Abstract
Ordinal data analysis is an interesting direction in machinelearning. It mainly deals with data for which only the relationships ‘< ’, ‘= ’, ‘> ’between pairs of points are known. We do an attempt of formalizing structuresbehind ordinal data analysis by introducing the notion of ordinal spaces on thebase of a strict axiomatic approach. For these spaces we study general propertiesas isomorphism conditions, connections with metric spaces, embeddability inEuclidean spaces, topological properties etc.
| Original language | English |
|---|---|
| Journal | Acta Mathematica Hungarica |
| Volume | 160 |
| Issue number | 1 |
| Pages (from-to) | 119-152 |
| Number of pages | 34 |
| ISSN | 0236-5294 |
| DOIs | |
| Publication status | Published - 01.02.2020 |
Funding
The second author was supported by H2020-MSCA-RISE-2014, Project number 645672 (AMMODIT: “Approximation Methods for Molecular Modelling and Diagnosis Tools”). The research of the second author was also partially supported by Project 0117U006353 from the Department of Targeted Training of Taras Shevchenko National University of Kyiv at the NAS of Ukraine and by the National Academy of Sciences of Ukraine within scientific research works for young scientists, Project 0117U006050.