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General Projective Maps for Multidimensional Data Projection
Author(s) -
Lehmann Dirk J.,
Theisel Holger
Publication year - 2016
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.12845
Subject(s) - computer science , subspace topology , projection (relational algebra) , star (game theory) , completeness (order theory) , degrees of freedom (physics and chemistry) , domain (mathematical analysis) , generalization , projective test , algorithm , theoretical computer science , artificial intelligence , mathematics , pure mathematics , mathematical analysis , physics , quantum mechanics
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.