While a conventional CCA generalizes principal component analysis (PCA) to two sets of random variables, a gCCA generalizes PCA to more than two sets of random variables.
The canonical variables represent those common factors that can be found by a large PCA of all of the transformed random variables after each set underwent its own PCA.
They can always be made to vanish by introducing a new regression parameter for each common factor.
The gCCA method can be used for finding those harmful common factors that create cross-correlation between the blocks.
However, no optimal HWB solution exists if the random variables do not contain enough information on all of the new regression parameters.