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

• Published in: Journal of statistical computation and simulation Vol. 92; no. 16; pp. 3468 - 3487
• Main Authors: Kim, Nam-Hwui, Browne, Ryan P.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02-11-2022; Taylor & Francis Ltd
• Subjects: Clustering; dimension reduction; intrinsic dimension; Mixtures; Model-based clustering; Stress relaxation tests; Subspaces
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949655.2022.2069769

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.