Fractal dimension, approximation and data sets
Statistics Theory
2022-09-27 v1 Classical Analysis and ODEs
Statistics Theory
Abstract
The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the salient underlying fractal features of the data set. Instead, we employ the discrete energy, a technique borrowed from geometric measure theory, to limit the number of points of a given data set that lie near a -dimensional hyperplane, or, more generally, near a set of a given upper Minkowski dimension. Concrete motivations stemming from naturally arising data sets are described and future directions outlined.
Cite
@article{arxiv.2209.12079,
title = {Fractal dimension, approximation and data sets},
author = {L. Betti and I. Chio and J. Fleischman and A. Iosevich and F. Iulianelli and S. Kirila and M. Martino and A. Mayeli and S. Pack and Z. Sheng and C. Taliancic and A. Thomas and N. Whybra and E. Wyman and U. Yildirim and K. Zhao},
journal= {arXiv preprint arXiv:2209.12079},
year = {2022}
}