Fix/normalized hypergraph laplacian

[kaiser-dan]

Summary

Rewrote normalized_hypergraph_laplacian implementation to match reference implementation. Fixes #647 .

Description

Rewrote the matrix calculations in normalized_hypergraph_laplacian to match the implementation referenced here: #647 (comment). Also adds a weighted Boolean parameter to allow for differentially weighting edges in the Laplacian calculation, drawn from each edge's "weight" attribute if available (default to 1 if unavailable).

Concerns

I have only added barebone unit tests for the effect of edge weights (only on their acceptable definition). I am unsure how or what the expected behavior would be for non-uniform edge weights.

Other

Currently only supports strictly positive weights - a weight of zero would cause some issues with rank. That said, an edge weight of 0 could be interpreted as the subgraph with that edge removed and could be a nice way to handle zero weights in the future? Deprecated with latest commit 573eaad.

[codecov]

Codecov Report

Attention: Patch coverage is 73.91304% with 6 lines in your changes missing coverage. Please review.

Project coverage is 93.35%. Comparing base (b86da86) to head (4881074).

Files with missing lines	Patch %	Lines
xgi/linalg/laplacian_matrix.py	73.91%	6 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #648      +/-   ##
==========================================
- Coverage   93.45%   93.35%   -0.11%     
==========================================
  Files          64       64              
  Lines        4993     5008      +15     
==========================================
+ Hits         4666     4675       +9     
- Misses        327      333       +6     

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[maximelucas]

Thanks for the PR!

It looks good, I only left a few comments to check that everything is okay in the sparse case, and to simplify a few lines.

About the weights, I'm thinking maybe we want the argument to be boolean instead: weighted=False. When it's True, we could just get the weights from the "weight" attribute of the hyperedges encoded in the hypergraph.
What do you think? Or do you see a case where one would want to use other weights?

That's how we have it for the adjacency matrix now.

[kaiser-dan]

Thanks for the PR!

It looks good, I only left a few comments to check that everything is okay in the sparse case, and to simplify a few lines.

About the weights, I'm thinking maybe we want the argument to be boolean instead: weighted=False. When it's True, we could just get the weights from the "weight" attribute of the hyperedges encoded in the hypergraph. What do you think? Or do you see a case where one would want to use other weights?

That's how we have it for the adjacency matrix now.

Thanks for the feedback!

I agree, I can't think of any use cases where the weights would want to be different than the edge attributes than cannot also be handled with edge attributes. I can make those adjustments soon. I will also implement your suggestions, thank you!

I will ping this for a rereview when those changes are made.

[kaiser-dan]

Okie I believe this is ready for re-review. I have addressed most of your comments @maximelucas by directly implementing the suggestions, however, to clarify on the remaining, here are two observations:

• the np.transpose of a SciPy sparse array is still a sparse array
• np.sum of a sparse matrix is not sparse, so in the middle of the De calculations a dense array is made, then cast back into a sparse diagonal matrix. This is introducing an additional memory allocation of $\Theta(m)$, where m is the number of hyperedges. These default to 64-bit floats in each entry.

[maximelucas]

Thanks a lot @kaiser-dan!

Just added a few more comments for consistency and simplicity:

• eye and identity are usually almost equivalent, so better to use only one of them
• SciPy made the switch a few months ago from sparse matrices to sparse arrays, so we update code to use the latter when we can

After these small changes we should be good to go!

[maximelucas]

Great, thanks a lot! Thanks for bearing with me :)
I just left a last tiny comment (the diags_array is already a sparse matrix), but approved the PR already.
Once you made the tiny change I'll squash and merge (I don't think you can, but if you can feel free to do it yourself).
Congrats on your first approved PR!

[kaiser-dan]

Great, thanks a lot! Thanks for bearing with me :) I just left a last tiny comment (the diags_array is already a sparse matrix), but approved the PR already. Once you made the tiny change I'll squash and merge (I don't think you can, but if you can feel free to do it yourself). Congrats on your first approved PR!

Thank you! It's been fun, I hope to contribute as much as I can moving forward as well.