An Exact No Free Lunch Theorem for Community Detection

A precondition for a No Free Lunch theorem is evaluation with a loss function which does not assume a priori superiority of some outputs over others. A previous result for community detection by Peel et al. (2017) relies on a mismatch between the loss function and the problem domain. The loss functi...

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Bibliographic Details
Published inarXiv.org
Main Authors McCarthy, Arya D, Chen, Tongfei, Ebner, Seth
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 25.03.2019
Subjects
Clustering
Communities
Computer Science - Discrete Mathematics
Computer Science - Social and Information Networks
Literature reviews
Partitioning
Theorems
Universe
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Summary:A precondition for a No Free Lunch theorem is evaluation with a loss function which does not assume a priori superiority of some outputs over others. A previous result for community detection by Peel et al. (2017) relies on a mismatch between the loss function and the problem domain. The loss function computes an expectation over only a subset of the universe of possible outputs; thus, it is only asymptotically appropriate with respect to the problem size. By using the correct random model for the problem domain, we provide a stronger, exact No Free Lunch theorem for community detection. The claim generalizes to other set-partitioning tasks including core/periphery separation, \(k\)-clustering, and graph partitioning. Finally, we review the literature of proposed evaluation functions and identify functions which (perhaps with slight modifications) are compatible with an exact No Free Lunch theorem.
ISSN:2331-8422
DOI:10.48550/arxiv.1903.10092