[ENH] Contribute Distortion Index (Olteanu and al. 2019)

[ceciledebezenac]

Hello I am just opening this issue following a discussion with @darribas to contribute into segregation the statistic proposed in the following paper:
(Olteanu and al. 2019)
I have a working version in another repository here I and I just wanted to kick off the discussion on how to integrate it in, and have your advice on the process.

[ljwolf]

Yes! Rad! This would be wonderful; I'm a big fan of the paper 😁

Taking a look at some small things that might help w/ maintenance, integration, & api consistency, we might want to make a few adjustments? It's real well documented & the code is very clean, so I think it should be simple to change a few things over.

Not sure how @renanxcortes or @knaaptime feel, but I spot these things we'd wanna do for integration/consistency. Renan/Eli, you know better about the actual API of the functions, which we might want to also make consistent w/ the other measures.

• Use scipy more fully
  • This distance could use scipy.spatial.distance.pdist or sklearn.metrics.pairwise_distances?, allowing us to use a more generic metric='euclidean' specification & use faster vectorized distance computations.
  • Again should be similar for the for dissimilarity calculation, which I think would apply in the method argument of set_neighborhood_type
  • Also for the kl_div, which might use scipy.special.kl_divfor nan filtering & vectorized computation
• Use pysal where possible
  • Adjacency computations definitely would become a pysal.weights.Rook if when we integrate, or hit the geodata.sindex at least?
• smaller stuff
  • print generally should use warnings.warn when showing warnings.
  • Maybe we should pull graphics imports inside of the plot methods & try/catch to avoid crashing? Most folks have these installed I think, but it's technically not necessary for the statistical functions, so that might be nice to avoid a hard dependency there?
  • Unittests would be needed
  • documentation/examples should be made generic, so the data would have to be published or examples changed.

[knaaptime]

agree with Levi's points. also,

1. is pickle really required? if so, what for?
2. we have gini and lorenz implementations (but we might prefer your lorenz implementation) so we might want to think about how reconfigure these pieces to fit together without duplication

[knaaptime]

matplotlib is already a dependency, but might be good to move seaborn into the function

[ceciledebezenac]

Hello all,
Thank you for going through the code so quickly! I totally agree with all that has been said, I paid very little attention to performance for computing the neighbourhood structure... I used pickle for my own analysis, but left it in the cleaner version for no particular reason.
The scipy.special.kl_div method is great and would make the code a lot simpler. 
Please let me know if there are other parts of it that are obscure...

[ljwolf]

Happy to help get this done :) this would be an awesome addition to the library!

[knaaptime]

also i just realized seaborn is a dependency elsewhere in the pysal stack (spvcm) so i'd be fine including it as a hard dependency here as well