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Practical Considerations on Nonparametric Methods for Estimating Intrinsic Dimensions of Nonlinear Data Structures

Einbeck, Jochen; Kalantan, Zakiah; Kruger, Uwe

Practical Considerations on Nonparametric Methods for Estimating Intrinsic Dimensions of Nonlinear Data Structures Thumbnail


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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Published Journal Article (Advance online version) (2.3 Mb)
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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.






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