Visualization of Intersecting Sets

Understanding relationships between sets is an important analysis task that has received widespread attention in the

visualization community. The major challenge in this context is the combinatorial explosion of the number of set intersections if the

number of sets exceeds a trivial threshold. In this paper we introduce UpSet, a novel visualization technique for the quantitative

analysis of sets, their intersections, and aggregates of intersections. UpSet is focused on creating task-driven aggregates, communicating

the size and properties of aggregates and intersections, and a duality between the visualization of the elements in a dataset

and their set membership. UpSet visualizes set intersections in a matrix layout and introduces aggregates based on groupings and

queries. The matrix layout enables the effective representation of associated data, such as the number of elements in the aggregates

and intersections, as well as additional summary statistics derived from subset or element attributes. Sorting according to various

measures enables a task-driven analysis of relevant intersections and aggregates. The elements represented in the sets and their

associated attributes are visualized in a separate view. Queries based on containment in specific intersections, aggregates or driven

by attribute filters are propagated between both views. We also introduce several advanced visual encodings and interaction methods

to overcome the problems of varying scales and to address scalability. UpSet is web-based and open source. We demonstrate its

general utility in multiple use cases from various domains.

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