3/18/2023 0 Comments Hyper graph(2007), were among the earliest to look at learning on non-uniform hypergraphs. Within the machine learning community, Zhou et al. However, most of the real-world hypergraphs have arbitrary-sized hyperedges, which makes these methods unsuitable for several practical applications. 2010) are confined to k-uniform hypergraphs where each hyperedge connects exactly k number of nodes. A few early works on hypergraph clustering ( Leordeanu and Sminchisescu 2012 Bulo and Pelillo 2013 Agarwal et al. 2011), de-clustering for parallel databases ( Liu and Wu 2001) and modeling eco-biological systems ( Estrada and Rodriguez-Velazquez 2005), among others. This has been the subject of several research works by various communities with applications to various problems such as VLSI placement ( Karypis and Kumar 1998), discovering research groups ( Kamiński et al. 2018 Chodrow and Mellor 2019).Īnalogous to the graph clustering task, Hypergraph clustering seeks to discover densely connected components within a hypergraph ( Schaeffer 2007). Indeed, there is a recently expanding interest in research in learning on hypergraphs ( Zhang et al. This suggests that the hypergraph representation is not only more information-rich but is also conducive to higher-order learning tasks by virtue of its structure. If this were modeled as a graph, we would be able to see which two authors are collaborating, but would not see if multiple authors worked on the same paper. A hyperedge can capture a multi-way relation for example, in a co-authorship network, where nodes represent authors, a hyperedge could represent a group of authors who collaborated for a common paper. These systems can be more precisely modeled using hypergraphs where nodes represent the interacting components, and hyperedges capture higher-order interactions ( Bretto and et al. The representational power of pairwise graph models is insufficient to capture higher-order information and present it for analysis or learning tasks. In such systems, modeling all relations as pairwise can lead to a loss of information. While most graph clustering approaches assume pairwise relationships between entities, many real-world network systems involve entities that engage in more complex, multi-way relations. The graph clustering problem involves dividing a graph into multiple sets of nodes, such that the similarity of nodes within a cluster is higher than the similarity of nodes belonging to different clusters ( Schaeffer 2007 Sankar et al. We demonstrate both the efficacy and efficiency of our methods on several real-world datasets. We additionally propose an iterative technique that provides refinement over the obtained clusters. The modularity function can be defined on a thus reduced graph, which can be maximized using any standard modularity maximization method, such as the Louvain method. The proposed graph reduction technique preserves the node degree sequence from the original hypergraph. In doing so, we introduce a null model for graphs generated by hypergraph reduction and prove its equivalence to the configuration model for undirected graphs. Our primary contribution in this article is to provide a generalization of the modularity maximization framework for clustering on hypergraphs. For the problem of clustering on graphs, modularity maximization has been known to work well in the pairwise setting. Especially, hypergraph clustering is gaining attention because of its enormous applications such as component placement in VLSI, group discovery in bibliographic systems, image segmentation in CV, etc. Learning on hypergraphs has thus been garnering increased attention with potential applications in network analysis, VLSI design, and computer vision, among others. Such super-dyadic relations are more adequately modeled using hypergraphs rather than graphs. Many of these systems involve higher-order interactions (super-dyadic) rather than mere pairwise (dyadic) relationships examples of these are co-authorship, co-citation, and metabolic reaction networks. Learning on graphs is a subject of great interest due to the abundance of relational data from real-world systems.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |