Cluster Visualization in Parallel Coordinates Using Curve Bundles

The polygonal lines traditionally used in parallel coordinates have two substantial limitations. First, they possess only C0 continuity, which causes the “cross-over” problem. Second, for large datasets, the lines become cluttered, obscuring inherent structure in the data. We introduce a model for curve bundles in parallel-coordinates plots to overcome these problems. The C0 polygonal lines are replaced by C1 continuous piecewise Bézier curves to alleviate cross-overs. The Bézier curves can then be bundled to visualize data with given cluster structures and hierarchies. The curve bundles are efficient to compute, provide visual separation between data clusters, reduce visual clutter, and present a clearer overview of the dataset. A controlled user study with 14 participants confirmed the effectiveness of curve bundling for parallel-coordinates visualization: 1) compared to polygonal lines, it is equally capable of revealing correlations between neighboring data attributes; 2) its geometric cues are as effective as color coding of polylines in displaying cluster information. Curve bundling thus allows the color perceptual channel to be applied to other data attributes.