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arXiv · 2412.17391

Ordinal spaces

Karsten Keller·Evgeniy Petrov
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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.

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Karsten Keller, Evgeniy Petrov. 2024-12-23. Ordinal spaces. https://doi.org/10.1007/s10474-019-00972-z

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