Dual Formulations, Demos, Plans

This week was a little short on work thanks to a Vegas trip last weekend and Bats Day up in Disneyland this weekend. But I did get a little done. I finished a SDP formulation of the sparse CCA dual. I'm fairly certain it's correct, however its formulation ultimately leads to some problems in recovering the canonical correlation directions. I have emailed my advisor, Gert, about this and await his reply soon. (Note: I wanna look at formulating some of the quadratic constraints using the Schur complement instead of the straightforward method I used.)

I started a little matlab demo of CCA do get some more intuition about the technique. I think I have a logical bug in my code cause my canonical directions seem to be exactly 90 degrees off from what they should be. I'll poke around that a little bit more tomorrow on that.

As for the next steps in the project:

1. As soon as I finished up this little demo (should only take another hour or two of playing around with it) I want to demo sparse CCA (sCCA), first on matlab, using matlab's QCQP or SDP solvers. I would like to play around with the primal and dual formulations to see how similar I can get the results to be. It will be a good sanity check that my dual formulation is correct. But like I said, there may be an issue regarding the recovery of the correlation directions.
   
   
2. Once I'm done playing around in matlab land I may take a crack at using a standard mathematical solver, just to get acquainted with it. Using a solver written in a lower level language should outperform matlab in terms of speed.
   
   
3. Next step is to run a sCCA test with the Audio-Text data set that will be the subject of the main experiment. I can take a few songs and text and see what output I can get. I don't expect to see any signal in these results. This step will serve mostly to cement the implementation details of the experiment.
   
   
4. After the previous steps are done I should be ready to run the complete test on our test data. The faster I can get these babies going the better. With a little luck, early results could translate into a quick and dirty paper deadline at the end of the month.
   

here goes nothing...