Visualizing Overlapping Biclusterings and Boolean Matrix Factorizations

TL;DR

This paper addresses the challenge of visualizing overlapping biclusters and Boolean matrix factorizations in bipartite graphs, proposing objective functions and algorithms to improve clarity and interpretability.

Contribution

It introduces a novel heuristic for visualization that balances proximity, large uniform areas, and uninterrupted regions in bipartite graph clusterings.

Findings

The heuristic outperforms existing methods in real-world datasets.

Balancing the three visualization objectives improves interpretability.

The approach effectively visualizes overlapping clusters in bipartite graphs.

Abstract

Finding (bi-)clusters in bipartite graphs is a popular data analysis approach. Analysts typically want to visualize the clusters, which is simple as long as the clusters are disjoint. However, many modern algorithms find overlapping clusters, making visualization more complicated. In this paper, we study the problem of visualizing \emph{a given clustering} of overlapping clusters in bipartite graphs and the related problem of visualizing Boolean Matrix Factorizations. We conceptualize three different objectives that any good visualization should satisfy: (1) proximity of cluster elements, (2) large consecutive areas of elements from the same cluster, and (3) large uninterrupted areas in the visualization, regardless of the cluster membership. We provide objective functions that capture these goals and algorithms that optimize these objective functions. Interestingly, in experiments on real-world datasets, we find that the best trade-off between these competing goals is achieved by a novel heuristic, which locally aims to place rows and columns with similar cluster membership next to each other.