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Selecting the aspect ratio of a scatter plot based on its delaunay triangulation
Martin Fink1, Jan-Henrik Haunert, Joachim Spoerhase
1Lehrstuhl I, Institut für Informatik, Universit¨at Würzburg.
IEEE Transactions on Visualization and Computer Graphics
|September 21, 2013
Summary
Optimizing scatter plot aspect ratios using Delaunay triangulation properties improves data visualization. Minimizing total edge length and triangle uncompactness yielded results closest to user preferences.
Area of Science:
- Data Visualization
- Computational Geometry
- Human-Computer Interaction
Background:
- Scatter plots are crucial for visualizing two-dimensional data, enabling correlation and cluster detection.
- The effectiveness of scatter plots is highly dependent on the chosen aspect ratio.
- Existing methods for selecting optimal aspect ratios are limited.
Purpose of the Study:
- To develop an algorithm for optimizing scatter plot aspect ratios based on geometric properties of Delaunay triangulations.
- To identify aspect ratios that enhance the interpretability of scatter plots.
- To compare algorithm-generated aspect ratios with human preferences.
Main Methods:
- Formulated an optimization problem to find a scale factor that improves Delaunay triangulation properties (e.g., minimum angle, total edge length).
- Developed an efficient algorithm to solve this optimization problem.
- Conducted an empirical study with 64 participants evaluating 18 scatter plots with algorithm-optimized aspect ratios.
Main Results:
- The algorithm efficiently finds optimal aspect ratios by optimizing geometric properties of the Delaunay triangulation.
- Tested six quality measures for optimization, finding that minimizing total edge length and 'uncompactness' were most effective.
- Algorithm-optimized aspect ratios showed high similarity to those chosen by human participants.
Conclusions:
- Optimizing scatter plot aspect ratios via Delaunay triangulation geometric properties is a viable approach for enhancing data visualization.
- Minimizing total edge length and triangle uncompactness are promising metrics for automated aspect ratio selection.
- The proposed method provides a data-driven approach to improve scatter plot interpretability and aligns with user perception.
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