In the pursuit of sparseness: A new rank-preserving penalty for a finite mixture of factor analyzers

A finite mixture of factor analyzers is an effective method for achieving parsimony in model-based clustering. Introducing a penalization term for the factor loading can lead to sparse estimates. However, in the pursuit of sparseness, one can end up with rank-deficient solutions regardless of the number of factors assumed. In light of this issue, a new penalty-based method that can fit a finite mixture of sparse factor analyzers with full-rank factor loading estimates is developed. In addition, the extension of an existing penalized factor analyzer model to a finite mixture is introduced. (C) 2021 Elsevier B.V. All rights reserved.