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            <title xml:lang="en">On Distance Mapping from non-Euclidean Spaces to Euclidean Spaces</title>
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                  <title>1st International Cross-Domain Conference for Machine Learning and Knowledge Extraction (CD-MAKE)</title>
                  <date type="start">2017-08-29</date>
                  <date type="end">2017-09-01</date>
                  <settlement>Reggio</settlement>
                  <country key="IT">Italy</country>
                </meeting>
                <editor>Andreas Holzinger</editor>
                <editor>Peter Kieseberg</editor>
                <editor>A Min Tjoa</editor>
                <editor>Edgar Weippl</editor>
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                  <publisher>Springer International Publishing</publisher>
                  <biblScope unit="serie">Machine Learning and Knowledge Extraction</biblScope>
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              <p>Most Machine Learning techniques traditionally rely on some forms of Euclidean Distances, computed in a Euclidean space (typically $$\mathbb {R}^{d}$$). In more general cases, data might not live in a classical Euclidean space, and it can be difficult (or impossible) to find a direct representation for it in $$\mathbb {R}^{d}$$. Therefore, distance mapping from a non-Euclidean space to a canonical Euclidean space is essentially needed. We present in this paper a possible distance-mapping algorithm, such that the behavior of the pairwise distances in the mapped Euclidean space is preserved, compared to those in the original non-Euclidean space. Experimental results of the mapping algorithm are discussed on a specific type of datasets made of timestamped GPS coordinates. The comparison of the original and mapped distances, as well as the standard errors of the mapped distributions, are discussed.</p>
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