On Distance Mapping from non-Euclidean Spaces to Euclidean Spaces

Wei Ren, Yoan Miche, Ian Oliver, Silke Holtmanns, Kaj-Mikael Björk, Amaury Lendasse

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

Abstract

Most Machine Learning techniques traditionally rely on some forms of Euclidean Distances, computed in a Euclidean space (typically 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 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.
Original languageEnglish
Title of host publicationCD-MAKE 2017: Machine Learning and Knowledge Extraction
Number of pages11
Place of PublicationCham
PublisherSpringer
Publication date24.08.2017
Pages3-13
ISBN (Print)978-3-319-66807-9
ISBN (Electronic)978-3-319-66808-6
DOIs
Publication statusPublished - 24.08.2017
MoE publication typeA4 Article in conference proceedings
Event2017 International Cross-Domain Conference for Machine Learning and Knowledge Extraction - Reggio, Italy
Duration: 29.08.201701.09.2017

Publication series

NameLecture Notes in Computer Science (LNCS)
Volume10410

Keywords

  • 512 Business and Management

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    Ren, W., Miche, Y., Oliver, I., Holtmanns, S., Björk, K-M., & Lendasse, A. (2017). On Distance Mapping from non-Euclidean Spaces to Euclidean Spaces. In CD-MAKE 2017: Machine Learning and Knowledge Extraction (pp. 3-13). (Lecture Notes in Computer Science (LNCS); Vol. 10410). Springer. https://doi.org/10.1007/978-3-319-66808-6_1