Regularized Generalized Canonical Correlation Analysis (RGCCA)

What is Regularized Generalized Canonical Correlation Analysis (RGCCA)?

RGCCA is a method introduced by Tenenhaus et al. (2011). It allows to optimize a global function using an algorithm very similar to the PLSPM algorithm.

Unlike the PLS approach, the results of the RGCCA are correlations between latent variables and between manifest variables and their associated latent variables (there is no regression at the end of the algorithm).

The RGCCA is based on a simple iterative algorithm similar to that of the PLS approach. Once the algorithm has converged, we obtain results that optimize specific functions depending on the choice of the tau parameter.

Tau is a parameter that has to be set for each latent variable. It enables you to adjust the “mode” associated to the latent variable. If tau = 0, then we will be in the case of mode B and the results of PLSPM and RGCCA are similar. When tau = 1, we find ourselves in the new mode A (as stated by M. Tenenhaus). This mode is close to the mode A of PLSPM while optimizing a given function. When tau varies between 0 and 1, the latent variable mode stands in between mode A and mode B. XLSTAT-PLSPM offers a special mode called Ridge RGCCA that automatically adjust the tau parameter. For more details on RGCCA see Tenenhaus et al. (2011).

Tenenhaus, M. and Tenenhaus, A. (2011). Regularized Generalized Canonical Correlation Analysis, Psychometrika, 76(2), 257–284.