Functional Generalized Canonical Correlation Analysis for studying multiple longitudinal variables

TL;DR

This paper introduces FGCCA, a robust framework for analyzing associations among multiple irregularly observed longitudinal variables, with extensions for prediction and Bayesian estimation, demonstrated through simulations and real data.

Contribution

It presents a novel Functional Generalized Canonical Correlation Analysis framework based on RGCCA, incorporating Bayesian estimation and response integration for predictive analysis.

Findings

Framework is robust to sparse and irregular data

Bayesian approach effectively estimates canonical components

Method performs well in simulations and real data applications

Abstract

In this paper, we introduce Functional Generalized Canonical Correlation Analysis (FGCCA), a new framework for exploring associations between multiple random processes observed jointly. The framework is based on the multiblock Regularized Generalized Canonical Correlation Analysis (RGCCA) framework. It is robust to sparsely and irregularly observed data, making it applicable in many settings. We establish the monotonic property of the solving procedure and introduce a Bayesian approach for estimating canonical components. We propose an extension of the framework that allows the integration of a univariate or multivariate response into the analysis, paving the way for predictive applications. We evaluate the method's efficiency in simulation studies and present a use case on a longitudinal dataset.