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

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, specifically noting that the correlation dimension variants perform favorably to the maximum likelihood method in terms of accuracy and computational efficiency.