Source-linked AI summary
Dynamic Tree Colors: Adaptive Discriminable Hierarchies with Minimum Instability
Tobias Mertz, Steven Lamarr Reynolds, Jörn Kohlhammer
TL;DR
Large hierarchical visualizations need dynamic color adjustment for discriminability without sacrificing users’ orientation through unstable color changes. The paper presents Dynamic Tree Colors, metrics for both criteria, and a qualitative study; DTC performs well across many scenarios but trails Cuttlefish in its target scenario.
Problem
Dynamic color maps can improve discriminability in large hierarchies, but incremental color changes may cause users to lose orientation.
Method
The paper presents Dynamic Tree Colors, defines metrics for discriminative power and color stability, and compares DTC with Cuttlefish in a qualitative user study.
Results
DTC achieves a flexible tradeoff between discriminative power and color stability and generally performs well across application scenarios.
Takeaways & Limitations
DTC is applicable to many analysis scenarios, while scenario-specific algorithms may perform better in the settings they target.
Takeaways & Limitations
DTC does not reach Cuttlefish’s performance in the multiscale visualization scenario for which Cuttlefish was designed.
Abstract
from arXiv · showhide
Hierarchical color maps can support users in the analysis of hierarchical data. For large hierarchies, dynamic color maps can improve discriminability upon user interactions, but the incremental color changes may cause users to lose their orientation in the data set. To address this challenge, we present Dynamic Tree Colors, a dynamic hierarchical color map that can be configured to a suitable tradeoff between discriminability and color stability. We also define quality metrics for both criteria and investigate our algorithm's performance with respect to these metrics as well as a user study with 18 participants. Our results indicate that Dynamic Tree Colors yields good results in a wide range of application scenarios, but it does not achieve the performance of the state-of-the-art algorithm Cuttlefish in the specific scenario that algorithm was designed for.
1 INTRODUCTION
Dynamic Tree Colors addresses the tension between improving discriminability during interaction and preserving color stability in hierarchical visualizations. It combines an adaptive algorithm with quality metrics and a qualitative user study.
- Dynamic color adjustment can improve discriminability, but iterative color changes may undermine users’ orientation in the data.
- Dynamic Tree Colors combines Tree Colors and Cuttlefish to support dynamic color mapping for entire hierarchies.
- Discriminability and color stability are competing goals, requiring an application-dependent tradeoff.
- The paper contributes quantitative metrics for discriminative power and color stability in hierarchical color maps.
- A qualitative user study compares Dynamic Tree Colors with Cuttlefish across diverse application scenarios.
2 RELATED WORK
Prior hierarchical color-map research progressed from static hue-assignment methods to dynamic algorithms for improving discriminability in large or multiscale hierarchies. This paper extends limited quality-metric work for hierarchical color maps.
- Early hierarchical color maps assigned equidistant or structurally derived hues to hierarchy nodes and leaves.
- Tree Colors became a state-of-the-art static method through recursive hue subdivision, but static maps have poor discriminability for large hierarchies.
- Chameleon and Cuttlefish introduced dynamic approaches, while later work explored linear optimization with color harmony as an additional objective.
- Research on hierarchical color-map quality remains limited compared with work on one- and two-dimensional quantitative color maps.
- The paper defines hierarchical color-map metrics by building on prior design rules and color-map metric proposals, focusing on discriminative power.
3 THE ALGORITHM
DTC computes static and interaction-specific Tree Colors, aligns the incremental map with a static reference, and interpolates between them using a stability ratio. It uses rigid hue rotation and offset interpolation to preserve discriminability while controlling instability.
- Pipeline: DTC computes a static reference map once and recomputes incremental colors for the currently visible hierarchy after interaction.
- Pipeline: Incremental coloring can allocate more hue range to visible nodes because invisible nodes occupy no color space.
- Applying Color Rotation: A weighted rigid hue rotation aligns incremental colors with reference colors without reducing inter-node distances or discriminability.
- Configuring the Tradeoff: The stability ratio interpolates between fully stable reference colors at 1 and unconstrained incremental colors at 0.
- Configuring the Tradeoff: Naive hue interpolation can rotate nodes in opposite directions, so DTC interpolates parent-child offsets and reconstructs colors down the hierarchy.
4 APPLICATION EXAMPLES
DTC is demonstrated across treemap, node-link, and icicle-plot applications with different hierarchy representations and interaction or filtering modalities.
- The experiments use three application examples that differ in visual hierarchy representation and filtering modality.
- Treemap: The treemap encodes population by rectangle area and supports zooming through a hierarchy of 229 countries.
- Node-Link Diagram: The node-link example uses geometric zoom and pan, recomputing incremental colors as the viewport changes.
- Icicle Plot: The icicle plot lets users hide sub-trees, colors them gray, and recomputes incremental colors for the remaining hierarchy.
5 COLOR MAP QUALITY
Dynamic Tree Colors is evaluated with metrics that quantify discriminative power and two forms of color instability, enabling analysis of the tradeoff between distinguishability and stability. Across datasets, higher stability ratios reduce discriminative power, while Cuttlefish generally has lower discriminative power but greater reference instability; dataset balance produces important exceptions.
- Quality metrics: The evaluation defines quantitative metrics for discriminative power and color stability, then applies them to compare Dynamic Tree Colors with Cuttlefish.The study also examines whether the stability ratio flexibly controls the tradeoff between the two quality criteria.
- Discriminative power: Global discriminative power averages pairwise color differences across the hierarchy, whereas local discriminative power considers only sibling-node differences.The global metric can decrease as nodes become invisible because within-subtree pairs receive greater relative weight; the local metric avoids this effect.
- Discriminative power: Higher stability ratios produce lower discriminative power, with equidistant ratios yielding equidistant curves as the fraction of invisible nodes increases.The curves remain tightly bundled for low fractions of invisible nodes and diverge as that fraction grows.
- Discriminative power: Cuttlefish achieves consistently lower discriminative power than every DTC configuration across both metrics, but its performance varies by dataset.It scores lower on the World Population dataset and higher on the less balanced Goldmessenger dataset.
- Dataset effects: Goldmessenger exposes a tradeoff: Cuttlefish distributes hues more evenly and achieves greater global discriminative power, but can repeat hues across unrelated hierarchy levels.Those inconsistencies are not captured by discriminative-power magnitude and were less relevant to Cuttlefish’s original multi-scale application.
- Color instability: Reference instability increases with invisible nodes and lower stability ratios, while a ratio of 1 produces a static color map with zero instability.Across all datasets, Cuttlefish has greater reference instability than DTC, whereas incremental instability is less clear.
6 USER STUDY
The user study examined how stability ratio affects perceived discriminative power and confusion across three analysis scenarios, comparing DTC configurations with Cuttlefish. Results indicate that the preferred tradeoff depends on the scenario, and DTC outperforms Cuttlefish in two scenarios but not the treemap.
- Study design: The exploratory study evaluated DTC and Cuttlefish across three analysis scenarios using perceived discriminability and confusion ratings.Participants assessed four color-map configurations: Cuttlefish and DTC with stability ratios 0, 0.4, and 0.8, using five-point Likert scales.
- Study design: The study tasks required participants to identify hierarchy nodes by color, change the interaction state, and re-identify those nodes.The scenarios used treemap, node-link, and icicle-plot visualizations with different interaction methods and analysis tasks.
- User perceptions: Perceived discriminative power decreased with higher stability ratios in the treemap and node-link scenarios, but not consistently in the icicle plot.In the icicle plot, positive responses decreased overall while very positive responses increased, contrary to the hypothesis.
- User perceptions: Perceived confusion from color instability showed a slight decreasing trend in the node-link and icicle-plot scenarios, while treemap configurations performed almost identically.These results only partially supported the expected relationship between higher stability ratios and lower confusion.
- Scenario differences: The best stability ratio was 0 for treemap, 0.4 for icicle plot, and unclear for the node-link diagram.For node-link, ratio 0.4 produced the most positive responses, while ratio 0 produced more very high ratings.
- Algorithm comparison: DTC outperformed Cuttlefish in the icicle-plot and node-link scenarios, whereas Cuttlefish performed better in the treemap scenario.The comparison used Cuttlefish against the best DTC stability ratio in each scenario.
- User perceptions: Participants reported little trouble with color changes, reflected in overall low perceived-confusion ratings.Participants described strategies such as relying on position rather than attempting to remember changing colors.
7 DISCUSSION
The discussion concludes that DTC provides a flexible discriminability–stability tradeoff and performs well across most tested scenarios. However, Cuttlefish remains superior for the treemap-like multiscale scenario, and the study leaves important questions about user strategies and mental-map preservation unresolved.
- Main findings: DTC allows flexible adjustment of the tradeoff between discriminative power and color stability, although some expected trends differed across scenarios.The relationship between stability ratio and user perception may not be linear, and further research is needed.
- Main findings: DTC outperformed Cuttlefish in measured quality and user perception in most application scenarios.DTC also achieved lower reference and, unexpectedly, lower incremental color instability than Cuttlefish.
- Limitation and scope: Cuttlefish was superior in the treemap scenario, showing that an algorithm tuned to a specific application scenario can outperform DTC.The authors recommend Cuttlefish for multiscale visualizations that display one hierarchy level at a time and support zooming into individual branches.
- Limitations: Participants’ strategies for avoiding color reliance and short task durations limited conclusions about color instability and mental-map preservation.These factors introduced measurement inaccuracy and prevented measurement of instability’s impact on mental-map preservation.
8 CONCLUSION
Dynamic Tree Colors provides a flexible approach for dynamically generating hierarchical color maps, with quality metrics and user-study evaluation. It performs well across many analysis scenarios but trails Cuttlefish in Cuttlefish’s target scenario, while leaving avenues for future improvement.
- DTC combines quantitative metrics for discriminative power and color instability with a qualitative user study comparing it against Cuttlefish.
- DTC is flexible across many analysis scenarios and delivers good results overall.
- DTC does not reach Cuttlefish’s performance in the specific scenario for which Cuttlefish was designed.
- Because DTC relies on rigid rotation and interpolation, it is compatible with other static color map algorithms and supports future improvements.
- The quality analysis should add color-map uniformity, and the user-study design should be improved to yield conclusive evidence.
SUPPLEMENTAL MATERIALS
Supplemental materials are available on OSF under a CC-BY 4.0 license and include screenshots, datasets, and study results.
- The supplemental materials are available on OSF under a CC-BY 4.0 license.
- They include additional DTC screenshots, code-structure datasets, and results from the quality analysis and user study.