On Distance Mapping from non-Euclidean Spaces to Euclidean Spaces

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

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Sammanfattning

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.
OriginalspråkEngelska
Titel på gästpublikationCD-MAKE 2017: Machine Learning and Knowledge Extraction
Antal sidor11
UtgivningsortCham
FörlagSpringer
Utgivningsdatum24.08.2017
Sidor3-13
ISBN (tryckt)978-3-319-66807-9
ISBN (elektroniskt)978-3-319-66808-6
DOI
StatusPublicerad - 24.08.2017
MoE-publikationstypA4 Artikel i en konferenspublikation
Evenemang2017 International Cross-Domain Conference for Machine Learning and Knowledge Extraction - Reggio, Italien
Varaktighet: 29.08.201701.09.2017

Publikationsserier

NamnLecture Notes in Computer Science (LNCS)
Volym10410

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  • 512 Företagsekonomi

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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. I CD-MAKE 2017: Machine Learning and Knowledge Extraction (s. 3-13). (Lecture Notes in Computer Science (LNCS); Vol. 10410). Springer. https://doi.org/10.1007/978-3-319-66808-6_1