Anderson relaxation test for intrinsic dimension selection in model-based clustering

Abstract

Parsimonious finite mixture models often require the a priori selection of desired model dimensionality. For example, projection-based parsimonious models demand the dimension of the subspace for projection. Other models ask for their own structural restrictions on parameters. The subspace clustering framework is a projection-based parsimonious model for various finite mixtures, including the Gaussian variant. The existing dimension selection methods for subspace clustering are ad-hoc or potentially computationally prohibitive, creating a need for a principled, yet computationally lightweight, approach. In light of this problem, a hypothesis test-based intrinsic dimension estimation method called the Anderson Relaxation Test (ART) is introduced, and its performance is examined in both simulated and real data settings.