Mixed Membership Models for Multilevel Functional Data

2026-04-10

AI Summary

This study addresses the challenge of modeling mixed membership of observational units across multiple pure categories in multilevel functional data. The authors propose a Bayesian hierarchical mixed-membership model grounded in multivariate Karhunen–Loève decomposition. By incorporating a hierarchical repulsive prior defined on the unit simplex, the model substantially enhances identifiability of the underlying mixture structure. Furthermore, it seamlessly integrates classical functional data analysis techniques into a Bayesian framework, enabling flexible representation and scalable inference for complex functional observations. The proposed method is successfully applied to EEG functional imaging data from children with autism spectrum disorder, effectively uncovering latent multilevel mixed-membership patterns embedded in the data.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Mining of Visual, Multimedia & Multimodal Data

Application Category

• Web Mining and Content Analysis: Mining multimedia, multimodal, multilingual, cross-lingual Web data
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Mixed membership models extend classical clustering by substituting the notion of uncertain membership with the notion of mixed membership. In particular, these models allow each observation to partially belong to multiple pure membership classes. We discuss mixed membership models for functional data by extending the framework to multilevel functional observations. We show how the classical multivariate Karhunen-Loeve decomposition can be translated into a simple hierarchical model for scalable and flexible expressivity of the underlying stochastic processes. The identifiability of partial membership structures is aided by the definition of a hierarchical repulsive prior on the unitary simplex. Our work is motivated and illustrated by applications to a study on functional brain imaging through electroencephalography (EEG) of children with autism spectrum disorder (ASD).

Problem

• mixed membership
• multilevel functional data
• functional data analysis
• identifiability
• hierarchical modeling

Innovation

• mixed membership models
• multilevel functional data
• Karhunen-Loeve decomposition
• hierarchical repulsive prior
• functional brain imaging