A Bayesian Covariance Based Clustering for High-Dimensional Tensors

• Activity Number: 379 - Single and Multi-Object Regression and Clustering with Applications in Neuro-Imaging Data
• Type: Topic Contributed
• Date/Time: Wednesday, August 10, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Mental Health Statistics Section
• Author(s): Aaron Scheffler* and Rene Gutierrez and Rajarshi Guhaniyogi
• Companies: UCSF and UCSC and Texas A & M University
• Keywords: Bayesian statistics; Clustering; Tensor normal distribution; Autism spectrum disorder; Covariance

Abstract

Clustering of high dimensional tensors with limited sample size has become prevalent in a variety of application areas. Existing Bayesian model-based clustering of tensors yields less accurate clusters when the tensor dimensions are sufficiently large, sample size is low and clusters of tensors mainly reveal difference in their variability. We propose a novel clustering technique for high dimensional tensors with limited sample size when the clusters show difference in their covariances, rather than in their means. The proposed approach constructs several matrices from a tensor to adequately estimate its variability along different modes and implements a model-based approximate Bayesian clustering algorithm with the matrices thus constructed, in place with the original tensor data. Although some information in the data is discarded, we gain substantial computational efficiency and accuracy in clustering. A simulation study assesses the proposed approach along with its competitors. The proposed methodology is applied to resting state EEG data collected on children with autism spectrum disorder (ASD) and provides novel insights into neurodevelopmental heterogeneity within ASD.