Multivariate Sparse Functional Linear Discriminant Analysis: An Application to Inflammatory Bowel Disease Classification

2025-03-17

AI Summary

This study addresses the dynamic multiclass discrimination problem among Crohn’s disease (CD), ulcerative colitis (UC), and non-IBD controls—a challenge inadequately tackled by existing methods restricted to single-time-point snapshots, univariate analysis, or binary classification. We propose the first discriminant analysis framework tailored for sparsely sampled, multivariate functional time-series data. Methodologically, we innovatively integrate sparse regularization—via an L₁/L₂ mixed penalty—into multivariate functional linear discriminant analysis, enabling simultaneous multiclass temporal discrimination and automatic selection of discriminative “time–pathway” interaction features. Applied to longitudinal microbial pathway abundance data, our approach identifies dynamically dysregulated pathways—including mucin degradation, amino acid metabolism, and peptidoglycan recognition—and, for the first time, uncovers a temporally evolving role of vitamin B deficiency in IBD pathogenesis and progression.

Technology Category

• Machine Learning: Multi-instance/Multi-view Learning
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Natural Language Processing: Discourse, Pragmatics & Argument Mining

Application Category

• Web Mining and Content Analysis: Interdisciplinary science discovery with web data mining
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Search and Retrieval-Augmented AI: Multilingual and cross-lingual Web search

Abstract

Inflammatory Bowel Disease (IBD), including Crohn's Disease (CD) and Ulcerative Colitis (UC), presents significant public health challenges due to its complex etiology. Motivated by the IBD study of the Integrative Human Microbiome Project, our objective is to identify microbial pathways that distinguish between CD, UC and non-IBD over time. Most current research relies on simplistic analyses that examine one variable or time point at a time, or address binary classification problems, limiting our understanding of the dynamic interactions within the microbiome over time. To address these limitations, we develop a novel functional data analysis approach for discriminant analysis of multivariate functional data that can effectively handle multiple high-dimensional predictors, sparse time points, and categorical outcomes. Our method seeks linear combinations of functions (i.e., discriminant functions) that maximize separation between two or more groups over time. We impose a sparsity-inducing penalty when estimating the discriminant functions, allowing us to identify relevant discriminating variables over time. Applications of our method to the motivating data identified microbial features related to mucin degradation, amino acid metabolism, and peptidoglycan recognition, which are implicated in the progression and development of IBD. Furthermore, our method highlighted the role of multiple vitamin B deficiencies in the context of IBD. By moving beyond traditional analytical frameworks, our innovative approach holds the potential for uncovering clinically meaningful discoveries in IBD research.

Problem

• Develops multivariate functional linear discriminant analysis for IBD classification
• Identifies microbial pathways distinguishing Crohn's, colitis and non-IBD over time
• Handles multiple high-dimensional predictors with sparse time points

Innovation

• Multivariate functional data analysis for discriminant analysis
• Sparsity-inducing penalty to identify relevant variables
• Handles multiple high-dimensional predictors and sparse time points