Optimizing alluvial plots

2025-09-03

AI Summary

Alluvial diagrams for multivariate data visualization suffer from disordered category ordering and inconsistent coloring, impairing structural clarity and perceptual discriminability. Method: We formalize two combinatorial optimization objectives—minimizing flow edge crossings to enhance layout coherence and maximizing inter-class color contrast to improve readability—and adapt the NeighborNet algorithm from evolutionary biology into a novel bi-objective optimization framework. An efficient approximation strategy is designed, enabling fully automated, semantics-aware ordering and coloring implemented in R and integrated into the open-source R package *wompwomp* (GitHub). Contribution/Results: Experiments on multiple real-world multivariate datasets demonstrate significant reductions in visual clutter and substantial improvements in pattern recognition efficiency. This work provides the first systematic, reproducible solution for joint layout and coloring optimization of alluvial diagrams.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization
• Data Mining & Knowledge Management: Data Visualization & Summarization

Application Category

• Web Mining and Content Analysis: Web data visualization
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

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

Problem

• Optimizing ordering of alluvia in multivariate data visualization
• Formalizing challenges in partition ordering and coloring
• Adapting phylogenetics algorithms for alluvial plot optimization

Innovation

• Adapts NeighborNet algorithm for alluvia ordering
• Formulates optimization for ordering and coloring
• Implements solution in open-source R package