Robust generalized canonical correlation analysis based on scatter matrices

Generalized Canonical Correlation Analysis (GCCA) is a powerful tool for analyzing and understanding linear relationships between multiple sets of variables. However, its classical estimations are highly sensitive to outliers, which can significantly affect the results of the analysis. A functional version of GCCA is proposed, based on scatter matrices, leading to robust and Fisher consistent estimators for appropriate choices of the scatter matrix. In cases where scatter matrices are ill-conditioned, a modification based on an estimation of the precision matrix is introduced. A procedure to identify influential observations is also developed. A simulation study evaluates the finite-sample performance of the proposed methods under clean and contaminated samples. The advantages of the influential data detection approach are demonstrated through an application to a real dataset.