相关论文: Hypergraph clustering using Ricci curvature: an ed…

Detecting communities in networks is important in various domains of applications. While a variety of methods exists to perform this task, recent efforts propose Optimal Transport (OT) principles combined with the geometric notion of…

In standard graph clustering/community detection, one is interested in partitioning the graph into more densely connected subsets of nodes. In contrast, the "search" problem of this paper aims to only find the nodes in a "single" such…

We present a new curvature condition which is preserved by the Ricci flow in higher dimensions. For initial metrics satisfying this condition, we establish a higher dimensional version of Hamilton's neck-like curvature pinching estimate.…

Hypergraphs, describing networks where interactions take place among any number of units, are a natural tool to model many real-world social and biological systems. In this work we propose a principled framework to model the organization of…

We propose a new local community detection algorithm that finds communities by identifying borderlines between them using boundary nodes. Our method performs label propagation for community detection, where nodes decide their labels based…

Hypergraph-based machine learning methods are now widely recognized as important for modeling and using higher-order and multiway relationships between data objects. Local hypergraph clustering and semi-supervised learning specifically…

We present the class of projection methods for community detection that generalizes many popular community detection methods. In this framework, we represent each clustering (partition) by a vector on a high-dimensional hypersphere. A…

In this survey we describe a recently-developed technique for bounding the number (and controlling the typical structure) of finite objects with forbidden substructures. This technique exploits a subtle clustering phenomenon exhibited by…

In community detection, the exact recovery of communities (clusters) has been mainly investigated under the general stochastic block model with edges drawn from Bernoulli distributions. This paper considers the exact recovery of communities…

Local graph clustering is an important machine learning task that aims to find a well-connected cluster near a set of seed nodes. Recent results have revealed that incorporating higher order information significantly enhances the results of…

Community detection is a discovery tool used by network scientists to analyze the structure of real-world networks. It seeks to identify natural divisions that may exist in the input networks that partition the vertices into coherent…

Community detection and link prediction are both of great significance in network analysis, which provide very valuable insights into topological structures of the network from different perspectives. In this paper, we propose a novel…

Community is a universal structure in various complex networks, and community detection is a fundamental task for network analysis. With the rapid growth of network scale, networks are massive, changing rapidly and could naturally be…

Groups with complex set intersection relations are a natural way to model a wide array of data, from the formation of social groups to the complex protein interactions which form the basis of biological life. One approach to representing…

We present a novel method for detecting communities in bipartite networks. Based on an extension of the $k$-clique community detection algorithm, we demonstrate how modular structure in bipartite networks presents itself as overlapping…

We propose RicciFlowRec, a geometric recommendation framework that performs root cause attribution via Ricci curvature and flow on dynamic financial graphs. By modelling evolving interactions among stocks, macroeconomic indicators, and…

Community detection is considered as a fundamental task in analyzing social networks. Even though many techniques have been proposed for community detection, most of them are based exclusively on the connectivity structures. However, there…

We use the discrete Ollivier-Ricci graph curvature with Ricci flow to examine the intrinsic geometry of financial markets through the empirical correlation graph of the NASDAQ 100 index. Our main result is the development of a technique to…

We develop a theory of Ricci flow for metrics on Courant algebroids which unifies and extends the analytic theory of various geometric flows, yielding a general tool for constructing solutions to supergravity equations. We prove short time…

Many algorithms have been proposed for detecting disjoint communities (relatively densely connected subgraphs) in networks. One popular technique is to optimize modularity, a measure of the quality of a partition in terms of the number of…