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Computational Visual Media 2023, 9(3): 495-512 https://doi.org/10.1007/s41095-022-0291-7
Research Article | Open Access | Issue | Published: 31 March 2023

Angle-uniform parallel coordinates

Show Author's Information Kaiyi Zhang1,*,  Liang Zhou2,*( ),  Lu Chen1,  Shitong He1,  Daniel Weiskopf3,  Yunhai Wang1
School of Computer Science and Technology, Shandong University, Qingdao 266237, China
National Institute of Health Data Science, Peking University, Beijing 100191, China
Visualization Research Center (VISUS), University of Stuttgart, 70569 Stuttgart, Germany

* Kaiyi Zhang and Liang Zhou contribute equally to this work.

Keywords:
deformation, multidimensional data, parallel coordinates, correlations
Cite this article:
Zhang K, Zhou L, Chen L, et al. Angle-uniform parallel coordinates. Computational Visual Media, 2023, 9(3): 495-512. https://doi.org/10.1007/s41095-022-0291-7
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Abstract Full text About this article

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 parallelcoordinates 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 structuresmay 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 becomesmooth curves and a symmetric representation of data correlations is achieved. We further propose a combinedsubsampling and density visualization approach to reduce visual clutter caused by overdrawing. Ourmethod 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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Angle-uniform parallel coordinates

Show Author's information Kaiyi Zhang1,*, Liang Zhou2,*( ), Lu Chen1, Shitong He1, Daniel Weiskopf3, Yunhai Wang1
School of Computer Science and Technology, Shandong University, Qingdao 266237, China
National Institute of Health Data Science, Peking University, Beijing 100191, China
Visualization Research Center (VISUS), University of Stuttgart, 70569 Stuttgart, Germany

* Kaiyi Zhang and Liang Zhou contribute equally to this work.

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 parallelcoordinates 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 structuresmay 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 becomesmooth curves and a symmetric representation of data correlations is achieved. We further propose a combinedsubsampling and density visualization approach to reduce visual clutter caused by overdrawing. Ourmethod 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.

Keywords: deformation, multidimensional data, parallel coordinates, correlations

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Publication history

Received: 16 December 2021
Accepted: 03 May 2022
Published: 31 March 2023
Issue date: September 2023

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© The Author(s) 2023.

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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