Add Panther algorithm per #3849

[mrecachinas]

This addresses #3849.

A couple remaining questions:

• Is there a better home for generate_random_paths? It’s a generic Markovian random walk that could be used elsewhere. Alternatively, if this already exists or there's a more efficient approach, I'm all ears.
• I used numpy for a bit of this. Is there a desire to have a pure Python version as well (like simrank_similarity vs simrank_similarity_numpy)?
• Should n_choose_k be elsewhere or perhaps should we use scipy.special.binom instead?
• Do we want Panther++ added (requires a KD-tree, which we can use from scipy.spatial)?

[pep8speaks]

Hello @mrecachinas! Thanks for updating this PR.

• In the file networkx/algorithms/similarity.py:

Line 1460:1: W293 blank line contains whitespace
Line 1516:89: E501 line too long (92 > 88 characters)
Line 1517:54: W605 invalid escape sequence '\p'
Line 1518:47: W605 invalid escape sequence '\s'
Line 1642:89: E501 line too long (98 > 88 characters)

Please install and run psf/black.

Comment last updated at 2020-09-05 14:56:05 UTC

[dschult]

n_choose_k is nicely expressed in Python 3.8+ as math.comb(n, k).
But we probably need to keep something around until we stop supporting Python 3.7.

There is only a reason to keep a numpy version and plain python if there is an advantage to each approach. For example, the algorithm used might be different with one using matrix manipulations and one using graph search techniques, or similar.

Thanks for this! I think there could be demand for Panther++. Let me think about where generate_random_paths might fit better.

small tweaks -- typo "ictionary" in docs for generate_random_paths. And could the example do soemthing with random_path to show that it has two outputs and what someone might want to do with them? Perhaps you could return just the paths and have an optional argument index_map that could be filled if supplied. ??

[mrecachinas]

@dschult Fixed the typo and moved index_map to be an optional kwarg that, if provided, will be populated. I also added an example in the docstring illustrating that.

Let me know if there's anything else. In the meantime, I'll finish my implementation of Panther++.

[storopoli]

Any news guys? Will it be released in the next version?

[mrecachinas]

@dschult Think I addressed everything. Let me know if there's anything else you would like changed!

Also, I'll submit another PR for Panther++ once I finish it.

[storopoli]

@mrecachinas great job! Waiting for the panther++ algorithm also...

[dschult]

Quick question: In the docs, delta is:
The probability that 𝑆 is not an epsilon-approximation to (R, phi)

What are R and phi?

You can answer here-- but if you prefer, you can add more to that doc string.

[storopoli]

@dschult according to the original Panther article, $R$ is the number of random paths and $\phi$ is the probability that an element sampled from a set A $\subseteq$ D, where D is the domain.

ref: Zhang, J., Tang, J., Ma, C., Tong, H., Jing, Y., & Li, J. (2015). Panther: Fast Top-k Similarity Search on Large Networks. Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 1445–1454. https://doi.org/10.1145/2783258.2783267

[dschult]

Good Thanks!

But what is S... ? I don't think these symbols are defined in the doc_string.... only in the article.
The code refers to "S", but it is an array of values, which is hard to see how to be epsilon close to a 2-tuple (R, phi)...

[mrecachinas]

Sorry - S is just the similarity adjacency matrix. Updating the docstring.

[mrecachinas]

@jarrodmillman Let me know if I've addressed your change requests.

[jarrodmillman]

@mrecachinas Sorry for the delay. Ross or I will take a look very soon! We are planning to release 2.6 soonish and I want to get this in first. Thanks for your patience.

Despite our slow response time, we would also like to get Panther++ in soon. So I hope you are still interested in contributing it!

[rossbar]

I went ahead an made some small touch-ups in rossbar/networkx@0973646c. I tried to push these to your branch (to spare you the spam via the github suggestion feature) but was unable to do so, likely because it seems like your fork originated from somewhere other than networkx/networkx. I wasn't able to PR against your fork either, so if you could apply those changes via cherry-pick that'd be great. If you're not comfortable doing so, you can either:

1. Add rossbar as a collaborator to your fork and I'll open a PR against your fork or
2. We just put this in and I can make a follow-on PR

Generally this LGTM - I'm not very familiar with the algorithm so my opinion shouldn't be weighted too heavily but the implementation seems good! I too was struck by the question of whether there is a better place for generate_random_paths, but I don't have any ideas and I don't think that should be a sticking point. Thanks @mrecachinas !

[mrecachinas]

@jarrodmillman I'll dust off and finish the Panther++ I started a few months ago (but I'll put it in a separate PR).

@rossbar Ahh, I think I forked someone else's fork for a previous PR (adding SimRank, IIRC), so yeah that's probably the issue. I'll cherry-pick if you're good with it.