CCA/KCCA for more than two views

Canonical Correlation Analysis (CCA) (and its kernel equivalent (KCCA)) can be used to find linear (nonlinear) relationships between two aligned multivariate datasets (or views).

Is there a way to extend this to more than two views? I suppose one way would be to apply CCA/KCCA recursively in a tree structure, but this appears to be rather inefficient. Is there a single optimisation that can achieve this in one step? Or are there any alternative methods that do the same thing?

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If by more than two 'views' you actually mean extending the CCA framework to k-blocks data structure, then you might be interested in

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

The corresponding R package is called RGCCA.

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