Qualitative Euclidean embedding of Disjoint Sets of Points
- We consider two disjoint sets of points with a distance metric, or a proximity function, associated with each set. If each set can be separately embedded into separate Euclidean spaces, then we provide sufficient conditions for the two sets to be jointly embedded in one Euclidean space. In this joint Euclidean embedding, the distances between the points are generated by a specific relation-preserving function. Consequently, the mutual distances between two points of the same set are specific qualitative transformations of their mutual distances in their original space; the pairwise distances between the points of different sets can be constructed from an arbitrary proximity function (might require scaling).
| Author: | N. Alexia RaharinirinaORCiD, Konstantin FackeldeyORCiD, Marcus Weber |
|---|---|
| Document Type: | Article |
| Year of first publication: | 2022 |
| URL: | https://arxiv.org/abs/2212.00058 |
| Licence (German): |  Creative Commons - CC BY-NC-SA - Namensnennung - Nicht kommerziell - Weitergabe unter gleichen Bedingungen 4.0 International |
