Rachel Shadoan:Visual Analysis of Higher-Order Conjunct Relationships in Multi-Dimensional Data using a Hypergraph Query System

Visual exploration and analysis of multi-dimensional data becomes increasingly difficult with increasing dimensionality. We want to understand the relationships between dimensions of data, but lack flexible techniques for exploration beyond low- order relationships. Current visual techniques for multi-dimensional data analysis fo- cus on binary conjunctive relationships between dimensions. Some techniques, such as cross-filtering on an attribute relationship graph (Weaver 2010b), facilitate the exploration of some higher-order conjunctive relationships, but require a great deal of care and precision to do so effectively. This thesis provides a detailed analysis of the expressive power of existing visual querying systems and describes a more flexible approach to exploring n-ary conjunctive inter- and intra- dimensional relationships by interactively constructing hypergraph queries. In the graph, nodes represent subsets of values and hyperdges represent conjunctive relationships. Analysts can dynami- cally build and modify the query using sequences of simple interactions. The query serves not only as a query specification, but also as a compact visual representation of the interactive state. Using examples from several domains, including the digital humanities, we describe the design considerations for developing the querying system and incorporating it into visual analysis tools. We analyze the query expressiveness with regard to the kinds of questions it can and cannot pose, and describe how it simultaneously expands the expressiveness of and is complemented by cross-filtering.