There is a God!

Amazing when things work the way you think they will the first time around. I posed the CCA promblem as an SDP optimization problem and fed it into SeDuMi and then compared the solution to the spectral solution: In every test case the solution vectors produced by SeDuMi match up with the spectral solution. So it looks like I know what I'm doing after all.

There are a few little details I want to investigate tomorrow. Though corresponding solution vectors have consistent direction, they do not have the same magnitude, so the SDP and the spectral method aren't solving the problem according to the exact same constraints. So far this is a minor detail, since only the direction of a vector is important, but it would be interesting to see why these methods don't add up.

Another question I have concerns the nature of the SDP set up. [Note! Ask Gert about this tomorrow.] I was under the impression that convex SDP's must have inequalities in their contraints (Ax < b ), but SeDuMi solves a problem with equality constraints (Ax = b). What's up with that?

Since the optimization problem is coming along the next step is to add sparsity constraints to the SDP demo I have set up. Once that is taken care of I should run the code past Gert and start thinking about how I am going to run experiments on our audio-text corpus. This is some really great progress, I'm going to sleep happy tonight!