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arXiv · 1705.02973

Community Detection in Hypergraphs, Spiked Tensor Models, and Sum-of-Squares

Chiheon Kim·Afonso S. Bandeira·Michel X. Goemans
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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 a certain spiked tensor model. 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 exhibit significantly different computational to statistical gaps.

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Chiheon Kim, Afonso S. Bandeira, Michel X. Goemans. 2017-05-08. Community Detection in Hypergraphs, Spiked Tensor Models, and Sum-of-Squares. https://arxiv.org/abs/1705.02973

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