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Practical considerations on nonparametric methods for estimating intrinsic dimensions of nonlinear data structures.

Einbeck, Jochen and Kalantan, Zakiah and Kruger, Uwe (2020) 'Practical considerations on nonparametric methods for estimating intrinsic dimensions of nonlinear data structures.', International journal of pattern recognition and artificial intelligence., 34 (9). p. 29782.

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.

Item Type:Article
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Full text:(VoR) Version of Record
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1142/S0218001420580100
Publisher statement: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.
Date accepted:09 September 2019
Date deposited:04 December 2019
Date of first online publication:20 November 2019
Date first made open access:04 December 2019

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