Eigenvalues and constraints in mixture modeling: geometric and computational issues

This paper presents a review about the usage of eigenvalues restrictions for constrained parameter estimation in mixtures of elliptical distributions according to the likelihood approach. These restrictions serve a twofold purpose: to avoid convergence to degenerate solutions and to reduce the onset of non interesting (spurious) maximizers, related to complex likelihood surfaces. The paper shows how the constraints may play a key role in the theory of Euclidean data clustering. The aim here is to provide a reasoned review of the constraints and their applications, along the contributions of many authors, spanning the literature of the last thirty years.
Spanish Ministerio de Economía y Competitividad (grant MTM2017-86061-C2-1-P)
Junta de Castilla y León - Fondo Europeo de Desarrollo Regional (grant VA005P17 and VA002G18)