On the Concept of Mixed Membership in Functional Data Analysis
Conference
64th ISI World Statistics Congress - Ottawa, Canada
Format: IPS Abstract
Keywords: "bayesian, bayesian, fda
Session: IPS 108 - Recent Advances in Bayesian Methodology for Complex Models
Thursday 20 July 2 p.m. - 3:40 p.m. (Canada/Eastern)
Abstract
Mixed membership models, or partial membership models, are a flexible unsupervised learning method that allows each observation to belong to multiple clusters. In this paper, we propose a Bayesian mixed membership model for functional data. By using the multivariate Karhunen-Loève theorem, we are able to derive a scalable representation of Gaussian processes that maintains data-driven learning of the covariance structure. Within this framework we discuss covariate adjustment and phase variability as possible extensions to a fully unsupervised analysis. Our work is motivated by studies in functional brain imaging through electroencephalography (EEG) of children with autism spectrum disorder (ASD). In this context, our work formalizes the clinical notion of ``spectrum'' in terms of feature membership proportions.