View Composition Algebra for Ad Hoc Comparison

TL;DR

This paper introduces a View Composition Algebra (VCA) enabling users to perform ad hoc comparisons in visual data analysis by composing and manipulating visualization elements through a set of algebraic operators.

Contribution

The paper presents a novel algebraic framework for composing and comparing visualization elements during exploratory data analysis, supporting ad hoc comparison tasks.

Findings

VCA supports flexible ad hoc comparison operations.

Interaction design based on VCA facilitates intuitive visual comparisons.

Use cases demonstrate the algebra's utility in real-world scenarios.

Abstract

Comparison is a core task in visual analysis. Although there are numerous guidelines to help users design effective visualizations to aid known comparison tasks, there are few techniques available when users want to make ad hoc comparisons between marks, trends, or charts during data exploration and visual analysis. For instance, to compare voting count maps from different years, two stock trends in a line chart, or a scatterplot of country GDPs with a textual summary of the average GDP. Ideally, users can directly select the comparison targets and compare them, however what elements of a visualization should be candidate targets, which combinations of targets are safe to compare, and what comparison operations make sense? This paper proposes a conceptual model that lets users compose combinations of values, marks, legend elements, and charts using a set of composition operators that summarize, compute differences, merge, and model their operands. We further define a View Composition Algebra (VCA) that is compatible with datacube-based visualizations, derive an interaction design based on this algebra that supports ad hoc visual comparisons, and illustrate its utility through several use cases.