Question about the CCA

[Super-1123]

Hi,

I noticed that in the paper, it is said: " In this framework, CCA components are iteratively identified conditional on the previous components, which encourages uncorrelated components that explain sequentially and stochastically less variation in the original observations". Is it means that the components were obtained in descending order, in which the first component has the largest correlation? If so, how to realize this? In the PMA toolbox, the components obtained from the SCCA seems are not rank in order. Hope you can kindly help me. Many thanks.

[daniel-munro]

Hello, you are correct that the components are not strictly ordered by correlation, but I believe they are in the order they were found in the iterative process. Without sparseness penalties, the d vector of the output ($u'X'Zv$) should be in descending order. For example, trying this example from the docs but passing K=20 to get more components, out$d is roughly ordered, but if you remove the sparseness constraints by passing penaltyx=1, penaltyz=1,, out$d becomes completely ordered. The correlations in out$cors are sometimes roughly ordered and sometimes not, and I've forgotten how it relates to d. In short, I would recommend keeping the output order, which is what we did.