text: Social networks are now ubiquitous and most of them contain interactions involving multiple actors (groups) like author collaborations, teams or emails in an organizations, etc. Hypergraphs are natural structures to effectively capture multi-actor interactions which conventional dyadic graphs fail to capture. In this work the problem of predicting collaborations is addressed while modeling the collaboration network as a hypergraph network. The problem of predicting future multi-actor collaboration is mapped to hyperedge prediction problem. Given that the higher order edge prediction is an inherently hard problem, in this work we restrict to the task of predicting edges (collaborations) that have already been observed in past. In this work, we propose a novel use of hyperincidence temporal tensors to capture time varying hypergraphs and provides a tensor decomposition based prediction algorithm. We quantitatively compare the performance of the hypergraphs based approach with the conventional dyadic graph based approach. Our hypothesis that hypergraphs preserve the information that simple graphs destroy is corroborated by experiments using author collaboration network from the DBLP dataset. Our results demonstrate the strength of hypergraph based approach to predict higher order collaborations (size>4) which is very difficult using dyadic graph based approach. Moreover, while predicting collaborations of size>2 hypergraphs in most cases provide better results with an average increase of approx. 45 in F-Score for different sizes = 3,4,5,6,7 .
  @cite_18: We study both @math and @math -eigenvalues of the adjacency tensor of a uniform multi-hypergraph and give conditions for which the largest positive @math or @math -eigenvalue corresponds to a strictly positive eigenvector. We also investigate when the @math -spectrum of the adjacency tensor is symmetric.
  @cite_14: The signless Laplacian tensor and its H-eigenvalues for an even uniform hypergraph are introduced in this paper. Some fundamental properties of them for an even uniform hypergraph are obtained. In particular, the smallest and the largest H-eigenvalues of the signless Laplacian tensor for an even uniform hypergraph are discussed, and their relationships to hypergraph bipartition, minimum degree, and maximum degree are described. As an application, the bounds of the edge cut and the edge connectivity of the hypergraph involving the smallest and the largest H-eigenvalues are presented.
  @cite_8: Database schemes (winch, intuitively, are collecuons of table skeletons) can be wewed as hypergraphs (A hypergraph Is a generalization of an ordinary undirected graph, such that an edge need not contain exactly two nodes, but can instead contain an arbitrary nonzero number of nodes.) A class of "acychc" database schemes was recently introduced. A number of basic desirable propemes of database schemes have been shown to be equivalent to acyclicity This shows the naturalness of the concept. However, unlike the situation for ordinary, undirected graphs, there are several natural, noneqmvalent notions of acyclicity for hypergraphs (and hence for database schemes). Various desirable properties of database schemes are constdered and it is shown that they fall into several equivalence classes, each completely characterized by the degree of acycliclty of the scheme The results are also of interest from a purely graph-theoretic viewpomt. The original notion of aeyclicity has the countermtmtive property that a subhypergraph of an acychc hypergraph can be cyclic. This strange behavior does not occur for the new degrees of acyelicity that are considered.
  @cite_21: 
  @cite_1: Clustering of data in a large dimension space is of a great interest in many data mining appli cations In this paper we propose a method for clustering of data in a high dimensional space based on a hypergraph model In this method the relationship present in the original data in high dimensional space are mapped into a hypergraph A hyperedge represents a relationship a n ity among subsets of data and the weight of the hyperedge re ects the strength of this a nity A hypergraph partitioning algorithm is used to nd a partitioning of the vertices such that the corresponding data items in each partition are highly related and the weight of the hyperedges cut by the partitioning is minimized We present results of experiments on two di erent data sets S P stock data for the period of and protein coding data These experiments demonstrate that our approach is applicable and e ective in high dimensional datasets
  @cite_24: 
  @cite_19: This paper quantitatively explores the social and socio-semantic patterns of constitution of academic collaboration teams. To this end, we broadly underline two critical features of social networks of knowledge-based collaboration: first, they essentially consist of group-level interactions which call for team-centered approaches. Formally, this induces the use of hypergraphs and n-adic interactions, rather than traditional dyadic frameworks of interaction such as graphs, binding only pairs of agents. Second, we advocate the joint consideration of structural and semantic features, as collaborations are allegedly constrained by both of them. Considering these provisions, we propose a framework which principally enables us to empirically test a series of hypotheses related to academic team formation patterns. In particular, we exhibit and characterize the influence of an implicit group structure driving recurrent team formation processes. On the whole, innovative production does not appear to be correlated with more original teams, while a polarization appears between groups composed of experts only or non-experts only, altogether corresponding to collectives with a high rate of repeated interactions.
  @cite_23: 
  @cite_15: 
  @cite_13: Motivation: Incorporating biological prior knowledge into predictive models is a challenging data integration problem in analyzing high-dimensional genomic data. We introduce a hypergraph-based semi-supervised learning algorithm called HyperPrior to classify gene expression and array-based comparative genomic hybridization (arrayCGH) data using biological knowledge as constraints on graph-based learning. HyperPrior is a robust two-step iterative method that alternatively finds the optimal labeling of the samples and the optimal weighting of the features, guided by constraints encoding prior knowledge. The prior knowledge for analyzing gene expression data is that cancer-related genes tend to interact with each other in a protein–protein interaction network. Similarly, the prior knowledge for analyzing arrayCGH data is that probes that are spatially nearby in their layout along the chromosomes tend to be involved in the same amplification or deletion event. Based on the prior knowledge, HyperPrior imposes a consistent weighting of the correlated genomic features in graph-based learning. Results: We applied HyperPrior to test two arrayCGH datasets and two gene expression datasets for both cancer classification and biomarker identification. On all the datasets, HyperPrior achieved competitive classification performance, compared with SVMs and the other baselines utilizing the same prior knowledge. HyperPrior also identified several discriminative regions on chromosomes and discriminative subnetworks in the PPI, both of which contain cancer-related genomic elements. Our results suggest that HyperPrior is promising in utilizing biological prior knowledge to achieve better classification performance and more biologically interpretable findings in gene expression and arrayCGH data. Availability: http: compbio.cs.umn.edu HyperPrior Contact: kuang@cs.umn.edu Supplementary information:Supplementary data are available at bioinformatics online.
  @cite_20: Many real-world social interactions involve multiple people, for e.g., authors collaborating on a paper, email exchanges made in a company and task-oriented teams in workforce. Simple graph representation of these activities destroys the group structure present in them. Hypergraphs have recently emerged as a better tool for modeling group interactions. However, methods in social hypernetwork analysis haven't kept pace. In this work, we extend the concept of node degree centrality to hypergraphs. We validate our proposed measures using alternate measures of influence available to us using two datasets namely, the DBLP dataset of scientific collaborations and the group network in a popular Chinese multi-player online game called CR3. We discuss several schemes for assigning weights to hyperedges and compare them empirically. Finally, we define separate weak and strong tie node degree centralities which improves performance of our models. Weak tie degree centrality is found to be a better predictor of influence in hypergraphs than strong tie degree centrality.
summary: Hypergraphs can easily capture the higher-order relationships while incorporating both group and node level attributes. Moreover, research has shown that several social, biological, ecological and technological systems can be better modeled using hypergraphs than using dyadic proxies @cite_21 . There is an abundant literature of hypergraph theory in past @cite_15 and many work in the spectral theory of hypergraphs recently @cite_18 @cite_14 . The past decade has also seen an increasing interest for hypergraphs in machine learning community @cite_24 @cite_13 . Hypergraphs have been used to model complex networks in different fields including biology @cite_23 , databases @cite_8 and data mining @cite_1 . In the domain of social sciences, Kapoor et a.l @cite_20 have proposed with centrality metrics for weighted hypergraphs. @cite_19 propose hypergraphs based metrics to evaluate various hypothesis, both semantic and structural, regarding team formation.