Direct ellipsoidal fitting of discrete multi-dimensional data
Abstract
Multi-dimensional distributions of discrete data that resemble ellipsoids arise in numerous areas of science, statistics, and computational geometry. We describe a complete algebraic algorithm to determine the quadratic form specifying the equation of ellipsoid for the boundary of such multi-dimensional discrete distribution. In this approach, the equation of ellipsoid is reconstructed using a set of matrix equations from low-dimensional projections of the input data. We provide a Mathematica program realizing the full implementation of the ellipsoid reconstruction algorithm in an arbitrary number of dimensions. To demonstrate its many potential uses, the fast reconstruction method is applied to quasi-Gaussian statistical distributions arising in elementary particle production at the Large Hadron Collider.
Cite
@article{arxiv.1901.05511,
title = {Direct ellipsoidal fitting of discrete multi-dimensional data},
author = {Rafey Anwar and Madeline Hamilton and Pavel Nadolsky},
journal= {arXiv preprint arXiv:1901.05511},
year = {2020}
}
Comments
20 pages, 5 figures The Mathematica program implementing the ellipsoid reconstruction algorithm can be found here: https://www.physics.smu.edu/web/research/preprints/SMU-HEP-19-01/