Optimizing alluvial plots

Alluvial plots can be effective for visualization of multivariate data, but rely on ordering of alluvia that can be non-trivial to arrange. We formulate two optimization problems that formalize the challenge of ordering and coloring partitions in alluvial plots. While solving these optimization problems is challenging in general, we show that the NeighborNet algorithm from phylogenetics can be adapted to provide excellent results in typical use cases. Our methods are implemented in a freely available R package available on GitHub at https://github.com/pachterlab/wompwomp