Cluster-Faithful Graph Visualization: New Metrics and Algorithms

The cluster faithfulness metrics CQ measure how faithfully the ground truth clustering of a graph is represented as the geometric clustering in a drawing of the graph. Existing CQ metrics use k-means clustering, which effectively compute a geometric clustering when the cluster sizes are even, resulting in accurate CQ metrics. However, k-means clustering tends to compute clusters of even sizes and thus often fails to compute an accurate geometric clustering when the cluster sizes are uneven, leading to inaccurate CQ metrics.In this paper, we present a new cluster faithfulness metric CQ-HAC, using HAC (Hierarchical Agglomerative Clustering). HAC can compute a more accurate geometric clustering for uneven cluster sizes than k-means clustering. Consequently, CQ-HAC can more accurately measure cluster faithfulness, regardless of whether the sizes of clusters are even or uneven. Moreover, we present two algorithms, Cluster-kmeans and Cluster-HAC, for optimizing cluster faithfulness of graph drawings. Extensive experiments show that in practice, both algorithms always compute perfectly cluster-faithful drawings (i.e., CQ = 1) in our experiments using various graphs with both even and uneven cluster sizes, achieving significant improvement over existing graph layouts, including cluster-focused layouts.