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  <doc>
    <id>8864</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Qualitative Euclidean embedding of Disjoint Sets of Points</title>
    <abstract language="eng">We consider two disjoint sets of points with a distance metric, or a&#13;
proximity function, associated with each set. If each set can be separately&#13;
embedded into separate Euclidean spaces, then we provide sufficient conditions&#13;
for the two sets to be jointly embedded in one Euclidean space. In this joint&#13;
Euclidean embedding, the distances between the points are generated by a&#13;
specific relation-preserving function. Consequently, the mutual distances&#13;
between two points of the same set are specific qualitative transformations of&#13;
their mutual distances in their original space; the pairwise distances between&#13;
the points of different sets can be constructed from an arbitrary proximity&#13;
function (might require scaling).</abstract>
    <identifier type="url">https://arxiv.org/abs/2212.00058</identifier>
    <enrichment key="PeerReviewed">no</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">false</enrichment>
    <licence>Creative Commons - CC BY-NC-SA - Namensnennung - Nicht kommerziell -  Weitergabe unter gleichen Bedingungen 4.0 International</licence>
    <author>N. Alexia Raharinirina</author>
    <submitter>N. Alexia Raharinirina</submitter>
    <author>Konstantin Fackeldey</author>
    <author>Marcus Weber</author>
    <collection role="persons" number="fackeldey">Fackeldey, Konstantin</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="MathPlus EF5-4_Ancient-Egyptian">MathPlus EF5-4_Ancient-Egyptian</collection>
  </doc>
</export-example>
