Abstract
We present angle-uniform parallel coordinates, a data-independent technique that deforms the image plane of parallel coordinates so that the angles of linear relationships between two variables are linearly mapped along the horizontal axis of the parallel coordinates plot. Despite being a common method for visualizing multidimensional data, parallel coordinates are ineffective for revealing positive correlations since the associated parallel coordinates points of such structures may be located at infinity in the image plane and the asymmetric encoding of negative and positive correlations may lead to unreliable estimations. To address this issue, we introduce a transformation that bounds all points horizontally using an angle-uniform mapping and shrinks them vertically in a structure-preserving fashion; polygonal lines become smooth curves and a symmetric representation of data correlations is achieved. We further propose a combined subsampling and density visualization approach to reduce visual clutter caused by overdrawing. Our method enables accurate visual pattern interpretation of data correlations, and its data-independent nature makes it applicable to all multidimensional datasets. The usefulness of our method is demonstrated using examples of synthetic and real-world datasets.
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Acknowledgements
LZ acknowledges support from the Data for Better Health Project of Peking University-Master Kong, YW from the National Natural Science Foundation of China (62132017), and DW from the Deutsche Forschungsgemeinschaft (DFG) Project-ID 251654672-TRR 161.
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Kaiyi Zhang is a third-year master student in the School of Computer Science and Technology, Shandong University. His research interests include text visualization and visual analysis.
Liang Zhou is an assistant professor at the National Institute of Health Data Science, Peking University. His research interests include scientific and information visualization, visual perception, and visual analytics for health science.
Lu Chen is currently a Ph.D. student at the State Key Lab of CAD&CG, Zhejiang University. He obtained his B.Eng. degree in computer science from Shandong University in 2022. His research interests lie primarily in 3D computer vision and information visualization.
Shitong He is a junior student in Taishan College, Shandong University. His research interests include scientific visualization and information visualization.
Daniel Weiskopf is a professor at the Visualization Research Center (VISUS) of the University of Stuttgart, Germany. His research interests include visualization, visual analytics, eye tracking, GPU methods, computer graphics, human—computer interaction, augmented and virtual reality, and special and general relativity.
Yunhai Wang is a professor in the School of Computer Science and Technology at Shandong University. He serves as an associate editor of Computer Graphics Forum. His interests include scientific visualization, information visualization, and computer graphics.
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Zhang, K., Zhou, L., Chen, L. et al. Angle-uniform parallel coordinates. Comp. Visual Media 9, 495–512 (2023). https://doi.org/10.1007/s41095-022-0291-7
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DOI: https://doi.org/10.1007/s41095-022-0291-7