TY - JOUR
T1 - Ordinal spaces
AU - Keller, K.
AU - Petrov, E.
N1 - Publisher Copyright:
© 2019, Akadémiai Kiadó, Budapest, Hungary.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/2/1
Y1 - 2020/2/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85073951894&partnerID=8YFLogxK
U2 - 10.1007/s10474-019-00972-z
DO - 10.1007/s10474-019-00972-z
M3 - Journal articles
AN - SCOPUS:85073951894
SN - 0236-5294
VL - 160
SP - 119
EP - 152
JO - Acta Mathematica Hungarica
JF - Acta Mathematica Hungarica
IS - 1
ER -