NF: Added alignment of datasets based on STATIS with tests

[swaroopgj]

I implemented simple alignment based on STATIS in the lines of Hyperalignment based on [0].
It also computes similarity of representations across subjects and each subject's contribution to compromise similarity matrix.
I also added unittest for basic functionality similar to hyperalignment.
This could be extended to include bootstrapped permutations to produce MDS-like plots with confidence ellipses as shown in [0].

[0] Abdi, H., Williams, L.J., Valentin, D., & Bennani-Dosse, M. (2012). STATIS and DISTATIS: Optimum multi-table principal component analysis and three way metric multidimensional scaling. Wiley Interdisciplinary Reviews: Computational Statistics, 4, 124-167.

[nno]

can this be a debug statement?

[nno]

Thanks @swaroopgj, this looks very nice. I've added a few minor comments.

[swaroopgj]

Added more tests and incorporated suggestions by @nno

[yarikoptic]

typo: Stati[s]

[yarikoptic]

also list this as new feature in the ChangeLog please

[swaroopgj]

Made changes as suggested by @yarikoptic

[nno]

Thanks @swaroopgj.
However, the coverage has decreased substantially (7.6%), more than I would expect based on the amount of code added (with tests!). At the moment I don't have time to look into this, but it seems that is is not due to your changes; something else might be going on. Before we merge it would be good to figure out why the coverage has gone down by so much. @yarikoptic @Hanke, any ideas on this?

[yarikoptic]

Seems to be some fluke unrelated to these changes... Didn't look into details though to figure it out

On October 26, 2015 8:30:48 PM EDT, "Nikolaas N. Oosterhof" notifications@github.com wrote:

Thanks @swaroopgj.
However, the coverage has decreased substantially (7.6%), more than I
would expect based on the amount of code added (with tests!). At the
moment I don't have time to look into this, but it seems that is is not
due to your changes; something else might be going on. Before we merge
it would be good to figure out why the coverage has gone down by so
much. @yarikoptic @Hanke, any ideas on this?

---

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#362 (comment)

[yarikoptic]

Was about to merge but then -- is this really the Statis or an alignment based on Statis (and thus better be StatisAlignment or smth like that)? also add it to suite.py

[swaroopgj]

It returns mappers for alignment. However, it does pretty much what is in the STATIS paper except plotting the results. The way I envisioned is that it returns mappers, but the object can be used to plot by storing required matrices. Clearly, more work needs to be added for that ;)

Quoting my initial PR description:
"This could be extended to include bootstrapped permutations to produce MDS-like plots with confidence ellipses as shown in [0]."