optimization doesn't appear to run currently

[stanleyjs]

I've forked pygsp and started implementing the tikhonov optimization on my branch, but it appears that

1. The current implementation of optimization.prox_tv does not work because
2. pyunlocbox does not yet support the non-tight frame problem.
   Regardless, I think I've fixed prox_tv up to this error with pyunlocbox. Once I get prox_tik done/documented, i'll switch over to pyunlocbox and see what I can do about the non-tight frame case.

[nperraud]

Hi stanlejys,
Thanks for contributing to the pygsp. I have implemented the tikonov case in this branch
https://github.com/epfl-lts2/pygsp/tree/semi-supervised-learning
For the Tikonov case, it not worth using proximal splitting optimization. It is better to directly compute the solution.
For the TV case, the best would be to use a primal dual scheme with the gradient operator and not directly the prox_tv. I have a matlab implementation using the unlocbox in case you want to implement it for the pygsp.

[stanleyjs]

ah, ok - I was just going based on the matlab/gspbox implementation of prox_tik which uses prox when a forward operator is supplied. Of course, when the forward operator is identity the Chebyshev approximation is often faster.

Where is your matlab prox_tv implementation?

[nperraud]

It is there:
https://github.com/epfl-lts2/gspbox/blob/master/graph_ml/gsp_regression_tv.m
The MATLAB unlocbox does not have the most intuitive design and it is mostly my fault. Sorry for that.

I see 3 different ways to implement the TV version

• Using the prox_tv is probably the easiest way to implement it. However, it results in an algorithm with two levels of iterations.
• Using the solver mlfbf of the pyunlocbox with the norm_l1 of the pyunlocbox. This will result in an algorithm that has only one iteration. However, mlfbf is not the best solver for that problem.
• Implementing Chambolle-Pock algorithm in the pyunlocbox and using it with the norm_l1. Probably the best way, but also require more work... (https://hal.archives-ouvertes.fr/hal-00490826/document)

Maybe you should rebase the semi-supervised-learning branch and start from there. @mdeff what do you think?

Good luck

[mdeff]

Yes please do base your work on the semi-supervised-learning branch. It should be merged in #19 once some cleanup is done (I don't have time for it now though).

Maybe @rodrigo-pena has some thoughts on this as well.