RT info:eu-repo/semantics/article
T1 Finding the Number of Normal Groups in Model-Based Clustering via Constrained Likelihoods
A1 Cerioli, Andrea
A1 García Escudero, Luis Ángel
A1 Mayo Iscar, Agustín
A1 Riani, Marco
AB Deciding the number of clusters k is one of the most difficult problems in clus-ter analysis. For this purpose, complexity-penalized likelihood approaches have beenintroduced in model-based clustering, such as the well known BIC and ICL crite-ria. However, the classi cation/mixture likelihoods considered in these approachesare unbounded without any constraint on the cluster scatter matrices. Constraintsalso prevent traditional EM and CEM algorithms from being trapped in (spurious)local maxima. Controlling the maximal ratio between the eigenvalues of the scattermatrices to be smaller than a  xed constant c   1 is a sensible idea for setting suchconstraints. A new penalized likelihood criterion which takes into account the highermodel complexity that a higher value of c entails, is proposed. Based on this criterion,a novel and fully automated procedure, leading to a small ranked list of optimal (k; c)couples is provided. A new plot called \car-bike" which provides a concise summaryof the solutions is introduced. The performance of the procedure is assessed both inempirical examples and through a simulation study as a function of cluster overlap.Supplemental materials for the article are available online.
YR 2018
FD 2018
LK http://uvadoc.uva.es/handle/10324/32023
UL http://uvadoc.uva.es/handle/10324/32023
LA spa
NO Journal of Computational and Graphical Statistics, Vol. 27, 404-416
DS UVaDOC
RD 06-ago-2024