Shape theory via SVD decomposition I

TL;DR

This paper introduces a novel method for deriving non-isotropic elliptical shape distributions using SVD decomposition, enabling exact density-based inference and practical application in biological landmark data analysis.

Contribution

It develops a new approach to shape distribution modeling via SVD, avoiding invariant polynomials and providing exact densities for non-isotropic models.

Findings

New shape distributions are easily computable.

Exact inference is possible with the proposed densities.

Application to biological data demonstrates model effectiveness.

Abstract

This work finds the non isotropic noncentral elliptical shape distributions via SVD decomposition in the context of zonal polynomials, avoiding the invariant polynomials and the open problems for their computation. The new shape distributions are easily computable and then the inference procedure is based on exact densities instead of the published approximations and asymptotic densities of isotropic models. An application of the technique is illustrated with a classical landmark data in Biology, for this, three models are proposed, the usual Gaussian and two non Gaussian; the best one is chosen by using a modified BIC criterion.