General Projective Maps for Multidimensional Data Projection

• Published in: Computer graphics forum Vol. 35; no. 2; pp. 443 - 453
• Main Authors: Lehmann, Dirk J., Theisel, Holger
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.05.2016
• Subjects: Analysis; Categories and Subject Descriptors (according to ACM CCS); Computer graphics; Degrees of freedom; Distortion; I.3.3 [Computer Graphics]: Picture/Image Generation-Information Visualization; Image processing systems; Mathematical analysis; Mathematical models; Multidimensional data; Projection; Stars; Studies
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.12845

To project high‐dimensional data to a 2D domain, there are two well‐established classes of approaches: RadViz and Star Coordinates. Both are well‐explored in terms of accuracy, completeness, distortions, and interaction issues. We present a generalization of both RadViz and Star Coordinates such that it unifies both approaches. We do so by considering the space of all projective projections. This gives additional degrees of freedom, which we use for three things: Firstly, we define a smooth transition between RadViz and Star Coordinates allowing the user to exploit the advantages of both approaches. Secondly, we define a data‐dependent magic lens to explore the data. Thirdly, we optimize the new degrees of freedom to minimize distortion. We apply our approach to a number of high‐dimensional benchmark datasets.