A mixture of ellipsoidal densities for 3D data modelling

TL;DR

This paper introduces a novel ellipsoidal mixture model for 3D data, utilizing a new elliptical distribution and an EM algorithm for parameter estimation, with theoretical and empirical validation against existing methods.

Contribution

It presents a new probability density function for ellipsoidal data and a mixture model with an EM algorithm, advancing 3D data modeling techniques.

Findings

The proposed model effectively captures 3D data spread around ellipsoidal surfaces.

The EM algorithm provides reliable parameter estimates, validated theoretically and empirically.

Compared to existing ellipse fitting methods, the new approach shows improved accuracy.

Abstract

In this paper, we propose a new ellipsoidal mixture model. This model is based a new probability density function belonging to the family of elliptical distributions and designed to model points spread around an ellipsoidal surface. Then, we consider a mixture model based on this density, whose parameters are estimated with the help of an EM algorithm. The properties of the estimates are studied theoretically and empirically. The algorithm is compared to a state of the art ellipse fitting method and experimented on 3D data.