相关论文: Spectral Detection on Sparse Hypergraphs

Spectral methods based on the eigenvectors of matrices are widely used in the analysis of network data, particularly for community detection and graph partitioning. Standard methods based on the adjacency matrix and related matrices,…

Community detection is a fundamental problem in network analysis with many methods available to estimate communities. Most of these methods assume that the number of communities is known, which is often not the case in practice. We study a…

Spectral algorithms are classic approaches to clustering and community detection in networks. However, for sparse networks the standard versions of these algorithms are suboptimal, in some cases completely failing to detect communities even…

This article considers spectral community detection in the regime of sparse networks with heterogeneous degree distributions, for which we devise an algorithm to efficiently retrieve communities. Specifically, we demonstrate that a…

Spectral clustering is one of the most popular, yet still incompletely understood, methods for community detection on graphs. This article studies spectral clustering based on the Bethe-Hessian matrix $H_r = (r^2-1)I_n + D-rA$ for sparse…

In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…

We consider the problem of estimating overlapping community memberships in a network, where each node can belong to multiple communities. More than a few communities per node are difficult to both estimate and interpret, so we focus on…

We consider the community detection problem in a sparse $q$-uniform hypergraph $G$, assuming that $G$ is generated according to the Hypergraph Stochastic Block Model (HSBM). We prove that a spectral method based on the non-backtracking…

This article considers the problem of community detection in sparse dynamical graphs in which the community structure evolves over time. A fast spectral algorithm based on an extension of the Bethe-Hessian matrix is proposed, which benefits…

Conventional network data has largely focused on pairwise interactions between two entities, yet multi-way interactions among multiple entities have been frequently observed in real-life hypergraph networks. In this article, we propose a…

Community structures represent a crucial aspect of network analysis, and various methods have been developed to identify these communities. However, a common hurdle lies in determining the number of communities K, a parameter that often…

Local community detection consists of finding a group of nodes closely related to the seeds, a small set of nodes of interest. Such group of nodes are densely connected or have a high probability of being connected internally than their…

We develop a Bayesian hierarchical model to identify communities in networks for which we do not observe the edges directly, but instead observe a series of interdependent signals for each of the nodes. Fitting the model provides an…

We consider the community detection problem in sparse random hypergraphs. Angelini et al. (2015) conjectured the existence of a sharp threshold on model parameters for community detection in sparse hypergraphs generated by a hypergraph…

Complex networks often exhibit community structure, with communities corresponding to denser subgraphs in which nodes are closely linked. When modelling systems where interactions extend beyond node pairs to arbitrary numbers of nodes,…

Hypergraphs are widely adopted tools to examine systems with higher-order interactions. Despite recent advancements in methods for community detection in these systems, we still lack a theoretical analysis of their detectability limits.…

The Bethe-Hessian matrix, introduced by Saade, Krzakala, and Zdeborov\'a (2014), is a Hermitian matrix designed for applying spectral clustering algorithms to sparse networks. Rather than employing a non-symmetric and high-dimensional…

We consider the community detection problem in sparse random hypergraphs under the non-uniform hypergraph stochastic block model (HSBM), a general model of random networks with community structure and higher-order interactions. When the…

Dynamic community detection concerns inferring how community memberships evolve over time, including the emergence, persistence, merging, and dissolution of groups in temporal networks. We propose a Bayesian nonparametric model for…

Community detection is a fundamental problem in the domain of complex-network analysis. It has received great attention, and many community detection methods have been proposed in the last decade. In this paper, we propose a divisive…