Visualizing Overlapping Biclusterings and Boolean Matrix Factorizations
Thibault Marette Pauli Miettinen Stefan Neumann
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.