Paper Review—Hierarchical Edge Bundles: Visualization of Adjacency Relations in Hierarchical Data

Main Contribution

The research problem in this paper is data visualization at scale for compound graphs. For visualizing a hierarchical organization of large data sets, prior works often use tree visualization methods, which easily lead to visual clutter when displaying adjacency relations. This work proposes a generic technique for the visualization of compound (di)graphs by bundling adjacent edges together.

The main contributions include the introduction of hierarchical edge bundling to reduce visual clutter in complex networks and visualize implicit adjacency edges between parent nodes with varying bundling strength. Additionally, it can be utilized in conjunction with existing tree visualization techniques for better flexibility and straightforward integration.

Method

The author aims to have this method compatible with tree visualization techniques, thus in the problem setup, he uses a tree visualization layout as a guide for bundling the adjacency edges. Using the concept of parametric curves from computer graphics, the two adjacent nodes and the tree path are used to locate the control polygon of a spline curve, which visualizes this adjacency relation. Bundling ambiguity can be reduced by controlling a parameter adjusting the amount of bundling by straightening the spline curve.

Then, the author discussed design decisions around the spline model including determining the spline representation and the straightening procedure. The author chooses a piecewise cubic B-spline representation for better local control and a relatively low degree for feasible computation. Then, to straighten a spline curve, the author straightens the control points of a polygon and uses the new points to find a new control polygon to generate the spline curve. This is preferable to straightening each spline point due to fewer straightening operations.

Another step towards a clean visualization is the rendering of curves of varying lengths. Since short curves tend to be occluded by the long curves, the author proposes to draw the short curves on top of the long curves and it can be further emphasized by alpha blending where the long curves are drawn in a more transparent color. Lastly, the direction of an edge is signified using an RGB interpolated color gradient which is commutative (identical results drawing from the opposite order).

From the figures given in the paper, the alpha blending and color encoding are good approaches to highlight any sparse case that possibly contains key information but was previously buried in the majority of other cases.

What do I think?

In the user feedback section, the author added valuable observation from a user perspective. Compared to non-bundled visualizations where the data hotspots are clustered, this approach shows how bundling could reduce visual clutter and occlusion of implicit information so that the actual connections among the complex network could stand out. However, bundling, as a way of compression, can lead to lossy information and bring about ambiguity into the node structure.

To balance this trade-off between readability and the richness of information, we can collect several visualization states by manipulating the bundling strength, as visualization moves from a low-level view towards a high-level view where the bundling strength is close to 1. Besides, this (moving along the bundle strength axis) can facilitate the human perception for hierarchical understanding.

Overall, this paper shows that the edge bundling technique is great for visualizing datasets consisting of hierarchical structures and adjacency relations. But it’s actually more than that - edge bundling has proven to be a general approach to reduce visual clusters in node-link diagrams, it has been used in graph visualization [1] to bring down the overall edge crossings, and parallel coordinates for multidimensional data [2].

Reference

[1] Holten, D., & Van Wijk, J. J. (2009, June). Force‐directed edge bundling for graph visualization. In Computer graphics forum (Vol. 28, No. 3, pp. 983-990). Oxford, UK: Blackwell Publishing Ltd.

[2] Zhou, H., Yuan, X., Qu, H., Cui, W., & Chen, B. (2008, May). Visual clustering in parallel coordinates. In Computer Graphics Forum (Vol. 27, No. 3, pp. 1047-1054). Oxford, UK: Blackwell Publishing Ltd.