Cluster-Flow Parallel Coordinates: Tracing Clusters Across Subspaces

Abstract

We present a novel variant of parallel coordinates plots (PCPs) in which we show clusters in 2D subspaces of multivariate data and emphasize flow between them. We achieve this by duplicating and stacking individual axes vertically. On a high level, our clusterflow layout shows how data points move from one cluster to another in different subspaces. We achieve cluster-based bundling and limit plot growth through the reduction of available vertical space for each duplicated axis. Although we introduce space between clusters, we preserve the readability of intra-cluster correlations by starting and ending with the original slopes from regular PCPs and drawing Hermite spline segments in between. Moreover, our rendering technique enables the visualization of small and large data sets alike. Cluster-flow PCPs can even propagate the uncertainty inherent to fuzzy clustering through the layout and rendering stages of our pipeline. Our layout algorithm is based on A*. It achieves an optimal result with regard to a novel set of cost functions that allow us to arrange axes horizontally (dimension ordering) and vertically (cluster ordering).