在网络中发现社区(称为社区检测/发现)是网络科学中的一个基本问题,在过去的几十年中引起了很多关注。 近年来,随着对大数据的大量研究,另一个相关但又不同的问题(称为社区搜索)旨在寻找包含查询节点的最有可能的社区,这已引起了学术界和工业界的广泛关注,它是社区检测问题的依赖查询的变体。

最新论文

In network analysis, how to estimate the number of communities $K$ is a fundamental problem. We consider a broad setting where we allow severe degree heterogeneity and a wide range of sparsity levels, and propose Stepwise Goodness-of-Fit (StGoF) as a new approach. This is a stepwise algorithm, where for $m = 1, 2, \ldots$, we alternately use a community detection step and a goodness-of-fit (GoF) step. We adapt SCORE \cite{SCORE} for community detection, and propose a new GoF metric. We show that at step $m$, the GoF metric diverges to $\infty$ in probability for all $m < K$ and converges to $N(0,1)$ if $m = K$. This gives rise to a consistent estimate for $K$. Also, we discover the right way to define the signal-to-noise ratio (SNR) for our problem and show that consistent estimates for $K$ do not exist if $\mathrm{SNR} \goto 0$, and StGoF is uniformly consistent for $K$ if $\mathrm{SNR} \goto \infty$. Therefore, StGoF achieves the optimal phase transition. Similar stepwise methods (e.g., \cite{wang2017likelihood, ma2018determining}) are known to face analytical challenges. We overcome the challenges by using a different stepwise scheme in StGoF and by deriving sharp results that are not available before. The key to our analysis is to show that SCORE has the {\it Non-Splitting Property (NSP)}. Primarily due to a non-tractable rotation of eigenvectors dictated by the Davis-Kahan $\sin(\theta)$ theorem, the NSP is non-trivial to prove and requires new techniques we develop.

0
0
下载
预览
参考链接
Top
微信扫码咨询专知VIP会员