Professor Jochen Einbeck jochen.einbeck@durham.ac.uk
Professor
Practical Considerations on Nonparametric Methods for Estimating Intrinsic Dimensions of Nonlinear Data Structures
Einbeck, Jochen; Kalantan, Zakiah; Kruger, Uwe
Authors
Zakiah Kalantan
Uwe Kruger
Abstract
This paper develops readily applicable methods for estimating the intrinsic dimension of multivariate datasets. The proposed methods, which make use of theoretical properties of the empirical distribution functions of (pairwise or pointwise) distances, build on the existing concepts of (i) correlation dimensions and (ii) charting manifolds that are contrasted with (iii) a maximum likelihood technique and (iv) other recently proposed geometric methods including MiND and IDEA. This comparison relies on application studies involving simulated examples, a recorded dataset from a glucose processing facility, as well as several benchmark datasets available from the literature. The performance of the proposed techniques is generally in line with other dimension estimators, speci¯cally noting that the correlation dimension variants perform favorably to the maximum likelihood method in terms of accuracy and computational e±ciency.
Citation
Einbeck, J., Kalantan, Z., & Kruger, U. (2020). Practical Considerations on Nonparametric Methods for Estimating Intrinsic Dimensions of Nonlinear Data Structures. International Journal of Pattern Recognition and Artificial Intelligence, 34(9), Article 2058010. https://doi.org/10.1142/s0218001420580100
Journal Article Type | Article |
---|---|
Acceptance Date | Sep 9, 2019 |
Online Publication Date | Nov 20, 2019 |
Publication Date | 2020-08 |
Deposit Date | Dec 4, 2019 |
Publicly Available Date | Dec 4, 2019 |
Journal | International Journal of Pattern Recognition and Artificial Intelligence |
Print ISSN | 0218-0014 |
Electronic ISSN | 1793-6381 |
Publisher | World Scientific Publishing |
Peer Reviewed | Peer Reviewed |
Volume | 34 |
Issue | 9 |
Article Number | 2058010 |
DOI | https://doi.org/10.1142/s0218001420580100 |
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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/
Copyright Statement
Advance online version This is an Open Access article published by World Scientific Publishing Company. It is distributed under
the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and
reproduction in any medium, provided the original work is properly cited.
Published Journal Article
(1.6 Mb)
PDF
Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/
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