Functional Generalized Canonical Correlation Analysis for studying multiple longitudinal variables

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.