Community detection in hypergraphs, spiked tensor models, and Sum-of-Squares
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1705.02973.pdf
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Author(s)
Kim, Chiheon
Sousa Bandeira, Afonso Jose
Goemans, Michel X
Date Issued
September 2017
Journal
2017 International Conference on Sampling Theory and Applications (SampTA)
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Kim, Chiheon, Afonso S. Bandeira, and Michel X. Goemans. “Community Detection in Hypergraphs, Spiked Tensor Models, and Sum-of-Squares.” 2017 International Conference on Sampling Theory and Applications (SampTA) (July 2017).
Version
Original manuscript
Abstract
We study the problem of community detection in hypergraphs under a stochastic block model. Similarly to how the stochastic block model in graphs suggests studying spiked random matrices, our model motivates investigating statistical and computational limits of exact recovery in certain spiked tensor models. In contrast with the matrix case, the spiked model naturally arising from community detection in hypergraphs is different from the one arising in the so-called tensor Principal Component Analysis model. We investigate the effectiveness of algorithms in the Sum-of-Squares hierarchy on these models. Interestingly, our results suggest that these two apparently similar models might exhibit very different computational to statistical gaps.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/SAMPTA.2017.8024470
