The LloydRelaxer: An Approach to Minimize Scaling Effects for Multivariate Projections

• Published in: IEEE transactions on visualization and computer graphics Vol. 24; no. 8; pp. 2424 - 2439
• Main Authors: Lehmann, Dirk Joachim, Theisel, Holger
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.08.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Computational geometry; Data analysis; Data visualization; Information visualization; Multidimensional data; Online analytical processing; Optimization; Projection; projections; Scaling; star coordinates; Temperature measurement; Two dimensional displays; Voronoi graphs
• ISSN: 1077-2626; 1941-0506
• DOI: 10.1109/TVCG.2017.2705189

Star Coordinates are a popular projection technique in order to analyze and to disclose characteristic patterns of multidimensional data. Unfortunately, the shape, appearance, and distribution of such patterns are strongly affected by the given scaling of the data and can mislead the projection-based data analysis. In an extreme case, patterns might be more related to the choice of scaling than to the data themselves. Thus, we present the LloydRelaxer : a tool to minimize scaling-based effects in Star Coordinates. Our algorithm enforces a scaling configuration for which the data explains the observed patterns better than any scaling of them could do. It does so by an iterative minimizing and optimization process based on Voronoi diagrams and on the Lloyd relaxation within the projection space. We evaluate and test our approach by real benchmark multidimensional data of the UCI data repository.