Visualization of Intersecting Groups Based on Hypergraphs

SUMMARY Hypergraphs drawn in the subset standard areuseful to represent group relationships using topographic char-acteristics such as intersection, exclusion and enclosing. How-ever, they present cluttering when dealing with a moderately highnumber of nodes (more than 20) and large hyperedges (connect-ing more than 10 nodes, with three or more overlapping nodes).At this complexity level, a study of the visual encoding of hy-pergraphs is required in order to reduce cluttering and increasethe understanding of moderately larger sets. Here we present agraph model and a visual design that help in the visualization ofgroup relationships represented by hypergraphs. This is done bythe use of superimposed visualization layers with different levelsof abstraction and the help of interaction and navigation throughthe display.key words: information visualization, graph drawing, intersect-ing groups, hypergraphs 1. IntroductionGroups are intrinsic to a large number of data sets. Forexample, data about movies, scientific papers or terror-ism share two levels of data: the individuals (actors, re-searchers, terrorists) and their collaborations (movies,papers, organizations). Usually, these collaborationsoverlap, having individuals in more than one group.In addition, groups can be inferred from almostany data set. This is the case of data clustering, whichusually searches for non-overlapping groups using dis-tance metrics. This is also the case of complex queriesin databases, for example the search for several possiblyoverlapped groups of data, each one fulfilling a differ-ent query. Furthermore, some grouping algorithms con-sider overlappingas essential in the searching of groups,such as biclustering algorithms [1].The ability to represent group relationships is use-ful in a number of ways, for example: to character-ize the nature of group-to-group relationships (non-existent, incidental, extensive), to identify individualsin several groups (’group hubs’), to determine the de-gree of similarity between more than two groups and todetect possible ’supergroups’formed by the intersectionof several groups.Therefore, the analysis of groups and their rela-tionships is an interesting area for graph drawing. Tra-

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