Flux Research Group / School of Computing

Path Boxplots: A Method for Characterizing Uncertainty in Path Ensembles on a Graph

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Mukund Raj, Mahsa Mirzargar, Robert Ricci, Robert Kirby, and Ross Whitaker

Journal of Computational and Graphical Statistics 26(2), 2017.



Graphs are powerful and versatile data structures that can be used to represent a wide range of different types of information. In this article, we introduce a method to analyze and then visualize an important class of data described over a graph—namely, ensembles of paths. Analysis of such path ensembles is useful in a variety of applications, in diverse fields such as transportation, computer networks, and molecular dynamics. The proposed method generalizes the concept of band depth to an ensemble of paths on a graph, which provides a center-outward ordering on the paths. This ordering is, in turn, used to construct a generalization of the conventional boxplot or whisker plot, called a path boxplot, which applies to paths on a graph. The utility of path boxplot is demonstrated for several examples of path ensembles including paths defined over computer networks and roads.