An Algebra for Visual Analysis

Visual analytics that combine analytical techniques with advanced visualization features is fast becoming a standard tool in extracting information from complex data. A number of sophisticated tools have been developed for this purpose, which necessitates formal methods to guide the creation of such tools and also compare them. Further, there is a need for visual analysts to document the steps in their analysis, for reuse, sharing, result justification, and so forth. This calls for a visual analytic framework encapsulated in a formal algebra. In this paper, we develop such an algebra for graph data and introduce its atomic operators, which include selection, aggregation, and labeling. We then build a framework around this algebra, which enables visual exploration of data. We employ visual operators and support dynamic attributes of data to complete this visual analytic framework. We show several visual data analysis examples using the algebra and framework to illustrate its utility.