Optimizing Feature Ordering in Radar Charts for Multi-Profile Comparison

TL;DR

This paper presents a permutation optimization method to reorder features in radar charts, enhancing visual clarity and accurate comparison of multiple profiles by minimizing abrupt changes in feature values.

Contribution

It introduces a combinatorial optimization approach that improves radar chart readability by globally balancing feature orderings, unlike previous methods that alter visualization or learn orderings.

Findings

Significant reduction in visual spikiness of radar charts.

Enhanced accuracy in multi-profile feature comparison.

Method applicable to moderate feature sets with manageable complexity.

Abstract

Radar charts are widely used to visualize multivariate data and compare multiple profiles across features. However, the visual clarity of radar charts can be severely compromised when feature values alternate drastically in magnitude around the circle, causing areas to collapse, which misrepresents relative differences. In the present work we introduce a permutation optimization strategy that reorders features to minimize polygon ``spikiness'' across multiple profiles simultaneously. The method is combinatorial (exhaustive search) for moderate numbers of features and uses a lexicographic minimax criterion that first considers overall smoothness (mean jump) and then the largest single jump as a tie-breaker. This preserves more global information and produces visually balanced arrangements. We discuss complexity, practical bounds, and relations to existing approaches that either change the visualization (e.g., OrigamiPlot) or learn orderings (e.g., Versatile Ordering Network). An example with two profiles and $p=6$ features (before/after ordering) illustrates the qualitative improvement. Keywords: data visualization, radar charts, combinatorial optimization, minimax optimization, feature ordering