On Distance Mapping from non-Euclidean Spaces to Euclidean Spaces

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10410)


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.


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Copyright information

© IFIP International Federation for Information Processing 2017

Authors and Affiliations

  1. 1.Nokia Bell LabsEspooFinland
  2. 2.Arcada University of Applied SciencesHelsinkiFinland
  3. 3.The University of IowaIowa CityUSA

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