Heterogeneous Dense Subhypergraph Detection

Sharp detection boundaries on testing dense subhypergraph

We study the problem of testing the existence of a dense subhypergraph. The null hypothesis is an Erdos-Renyi uniform random hypergraph and the alternative hypothesis is a uniform random hypergraph that contains a dense subhypergraph. We establish sharp detection boundaries in both scenarios: (1) the edge probabilities are known; (2) the edge probabilities are unknown. In both scenarios, sharp detectable boundaries are characterized by the appropriate model parameters. Asymptotically powerful tests are provided when the model parameters fall in the detectable regions. Our results indicate that…

通过低次多项式检测稠密子超图

Detection of Dense Subhypergraphs by Low-Degree Polynomials

本文研究随机超图中植入稠密子超图的检测问题，利用低次多项式检验确定了容易与困难区域的精确阈值，并在图情形下给出了新结果。

A practical test for a planted community in heterogeneous networks

One of the fundamental task in graph data mining is to find a planted community(dense subgraph), which has wide application in biology, finance, spam detection and so on. For a real network data, the existence of a dense subgraph is generally unknown. Statistical tests have been devised to testing the existence of dense subgraph in a homogeneous random graph. However, many networks present extreme heterogeneity, that is, the degrees of nodes or vertexes don't concentrate on a typical value. The existing tests designed for homogeneous random graph are not straightforwardly applicable to the het…

Spectral community detection in heterogeneous large networks

In this article, we study spectral methods for community detection based on $ α$-parametrized normalized modularity matrix hereafter called $ {\bf L}_α$ in heterogeneous graph models. We show, in a regime where community detection is not asymptotically trivial, that $ {\bf L}_α$ can be well approximated by a more tractable random matrix which falls in the family of spiked random matrices. The analysis of this equivalent spiked random matrix allows us to improve spectral methods for community detection and assess their performances in the regime under study. In particular, we prove the existenc…