%0 Conference Proceedings
%T On Distance Mapping from non-Euclidean Spaces to Euclidean Spaces
%+ Nokia Bell Labs [Espoo]
%+ Arcada University of Applied Sciences
%+ University of Iowa [Iowa City]
%A Ren, Wei
%A Miche, Yoan
%A Oliver, Ian
%A Holtmanns, Silke
%A Björk, Kaj-Mikael
%A Lendasse, Amaury
%Z Part 1: MAKE Topology
%< avec comité de lecture
%( Lecture Notes in Computer Science
%B 1st International Cross-Domain Conference for Machine Learning and Knowledge Extraction (CD-MAKE)
%C Reggio, Italy
%Y Andreas Holzinger
%Y Peter Kieseberg
%Y A Min Tjoa
%Y Edgar Weippl
%I Springer International Publishing
%3 Machine Learning and Knowledge Extraction
%V LNCS-10410
%P 3-13
%8 2017-08-29
%D 2017
%R 10.1007/978-3-319-66808-6_1
%Z Computer Science [cs]
%Z Humanities and Social Sciences/Library and information sciencesConference papers
%X 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.
%G English
%Z TC 5
%Z TC 8
%Z TC 12
%Z WG 8.4
%Z WG 8.9
%Z WG 12.9
%2 https://inria.hal.science/hal-01677143/document
%2 https://inria.hal.science/hal-01677143/file/456304_1_En_1_Chapter.pdf
%L hal-01677143
%U https://inria.hal.science/hal-01677143
%~ SHS
%~ IFIP-LNCS
%~ IFIP
%~ IFIP-TC
%~ IFIP-TC5
%~ IFIP-WG
%~ IFIP-TC12
%~ IFIP-TC8
%~ IFIP-WG8-4
%~ IFIP-WG8-9
%~ IFIP-LNCS-10410
%~ IFIP-CD-MAKE
%~ IFIP-WG12-9