Eigenvalues nearly all 1 in canonical correlation analysis

Question

I ran a Canonical Correlation Analysis on about 845 cases with 1000 variables each. (It originally started with 1000 cases and 400 variables but by using a kernel I got a 1000x1000 matrix)

As a result I got mainly eigenvalues very close to 1 (e.g. the highest: 0.9999987616532545), then there were a couple with E-8, five with 0 and some negative ones.

I find especially the nearly 1000 1's quite strange or is that a result that is possible/makes sense? I didn't quite get the results that I was hoping for, so I was wondering if all those nearly 1's could be the cause and if anyone has an idea what might have caused those?

I use EigenDecomposition from Commons Math 3.0 (http://commons.apache.org/math/apidocs/index.html). I also tried some other matrices earlier and then got "MaxCountExceededException: illegal state: convergence failed" error. Not sure if that has anything to do with it, but I thought I'd add it.

Answer 1

I think this is a small n large p problem. If you have more parameters than cases it is very difficult to see much. You could be severely overfitting to the data and creating singularities or near singularities because of some variables being highly correlated with each other. I think that would explain why so many eigenvalues are nearly equal to 1.