Contrastive Latent Functional Model

Area of Science:

• Statistics
• Functional Data Analysis
• Machine Learning

Background:

• Functional Principal Component Analysis (FPCA) is widely used for dimensionality reduction of functional data.
• Existing methods often struggle to disentangle shared and unique variation patterns in multi-group functional data.
• Understanding group-specific temporal dynamics is crucial in many biomedical applications.

Purpose of the Study:

• To extend FPCA to contrastive settings for multi-group functional data analysis.
• To develop a model that captures both shared and sample-unique temporal variation.
• To apply the novel framework to real-world biomedical datasets for enhanced interpretation.

Main Methods:

• Proposed the Contrastive Latent Functional Model (cLFM) integrating FPCA with contrastive learning principles.
• Employed an Expectation-Maximization (EM) algorithm for efficient parameter estimation.
• Ensured orthogonality between shared and unique functional components.

Main Results:

• Simulation studies validated cLFM's efficacy across various scenarios of shared/unique variation, sample sizes, and error variances.
• Application to EEG data revealed group differences in neurodevelopment (autism vs. neurotypical).
• Analysis of kidney function data identified distinct patterns among chronic kidney disease subgroups.

Conclusions:

• cLFM effectively disentangles shared and unique variation in multi-group functional data.
• The model provides novel insights into group-specific temporal dynamics in biomedical research.
• This framework advances the analysis of complex functional data in comparative studies.