Feature/spectral clustering #665
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Add module boilerplate. Add `_kmeans` function with naive signature. Add test class and trivial clustering test case.
Add `spectral_clustering` function. Add test class and test overabundant cluster exception.
Add `numpy.random.default_rng` to `_kmeans` for random number sampling. Fixes bug with test cases where clusters could get merged from rare random conditions.
Add perfectly separable `spectral_clustering` test.
| return clusters | ||
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| def _kmeans(X, k, seed=37): |
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Add docstring. Also, is there a reason to specify the seed by default instead of seed=None like in other functions?
| H : Hypergraph | ||
| Hypergraph | ||
| k : int, optional | ||
| Number of clusters to find. If unspecified, computes spectral gap. |
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How would this work, the spectral gap is not an integer in general?
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Ah, sorry I meant the location of the spectral gap. I will expand on this later this week with updates to the PR.
| if k is None: | ||
| raise NotImplementedError( | ||
| "Choosing a number of clusters organically is currently unsupported. Please specify an integer value for paramater 'k'!" | ||
| ) |
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I'd say either we implement this k=None default option, or we remove the default value and these lines (until it's maybe implemented).
| "spectral_clustering", | ||
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| MAX_ITERATIONS = 10_000 |
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Unless this parameter is planned to be used in other functions, I'd define it in _kmeans(), the only function using it? Maybe even as a parameter of the function?
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Thanks! @thomasrobiglio is probably best placed to review the method, I just made quick general comments more about the formatting |
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Thank you @kaiser-dan! I will have a look over the week |
Sure thing, I will also be working on some better tests when I get a chance. Unclear when that will be, unfortunately. |
Summary
Partially addresses #604.
Add
xgi.communitiesmodule.Add
spectral_clusteringmethod to cluster a given hypergraph into K-many groups.Description
Added a new module to begin resolving #604 and adding community detection capabilities.
Added a simple version of spectral clustering, clustering the given hypergraph into a specified number of communities based on a single K-means application of the hypergraph embedding given by the spectra as computed with
normalized_hypergraph_laplacian- a heuristic suggested in [1].Notes
If the user is agnostic to the number of groups, there is reason to believe to spectral gap may give a nice default number of groups. However, I am unsure how to handle the case of a hypergraph having no discernible community structure. The spectral gap would be uninformative there. For this reason, I have not yet added that functionality and instead an error is raised if
kis unspecified.Concerns
The tests do depend on a random seed being fixed - I am unsure how the underlying OS affects this. Furthermore, I am unsure if the tests I've written, specifically this one, are an ideal way to test the correctness of the clustering method.
References
[1] D. Zhou, J. Huang, and B. Schölkopf, “Learning with Hypergraphs: Clustering, Classification, and Embedding,” in Advances in Neural Information Processing Systems, MIT Press, 2006. Accessed: Nov. 10, 2023. [Online]. Available: https://proceedings.neurips.cc/paper_files/paper/2006/hash/dff8e9c2ac33381546d96deea9922999-Abstract.html