On Distance Mapping from Non-Euclidean Spaces to Euclidean Spaces
Abstract
Most Machine Learning Techniques Traditionally Rely on Some Forms of Euclidean Distances, Computed in a Euclidean Space (Typically (Formula Presented)). 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 (Formula Presented). 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.
Recommended Citation
W. Ren et al., "On Distance Mapping from Non-Euclidean Spaces to Euclidean Spaces," Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10410 LNCS, pp. 3 - 13, Springer, Jan 2017.
The definitive version is available at https://doi.org/10.1007/978-3-319-66808-6_1
Department(s)
Engineering Management and Systems Engineering
International Standard Book Number (ISBN)
978-331966807-9
International Standard Serial Number (ISSN)
1611-3349; 0302-9743
Document Type
Article - Conference proceedings
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Springer, All rights reserved.
Publication Date
01 Jan 2017
