minor cosmetic changes to follow the work of Mairal, 2009

[laurentperrinet]

In the paper from Mairal et al referenced in the script, the set of possible dictionary vectors is not the ball but the convex set of dictionaries whose norm is inferior or equal to one.
This is simply implemented in the normalization step in the function updating the script + corresponding changes in the documentation.

[amueller]

This is a behavior change, so it is not really cosmetic, right?

[agramfort]

this will have no effect in practice as at the optimum all atoms will be of norm 1.

[laurentperrinet]

right, it is not only cosmetic due to the modified normalization step (see my comment on the commit). I was able to test the behavior on the http://scikit-learn.org/stable/auto_examples/decomposition/plot_image_denoising.html example with qualitatively similar results.

[laurentperrinet]

this will have no effect in practice as at the optimum all atoms will be of norm 1.

right, but is seems important during learning.

[agramfort]

can you show results with and without?

[laurentperrinet]

I have compared with and without and the results are very similar (I based myself on ?? examples/decomposition/plot_image_denoising_mod.py). I am kind of surprised since the original paper is insisting on that point.
Since the code is already quite complicated, I'll close this PR - if anybody really wants to re-open I'll be glad to assist.

[GaelVaroquaux]

Hi Laurent, Thanks a lot for this thorough analysis. This is very useful. I agree that closing the PR was probably the right choice.