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RESEARCH PRODUCT
On the problem of visualizing point distributions in high dimensional spaces
Peter E. Beckmannsubject
Theoretical computer scienceDynamical systems theoryFrame (networking)General EngineeringStructure (category theory)Computer Graphics and Computer-Aided DesignVisualizationHuman-Computer InteractionComputer graphicsProjection (mathematics)GraphicsDynamical system (definition)AlgorithmMathematicsdescription
Abstract Exploring dynamical systems with the aid of computer graphics requires that the relevant structures can be seen and be noticed. This poses special problems if the system is multidimensional, and it has to be decided which kind of projection serves the purpose. I propose using the mathematical frame of categories and functors to describe the process of visualization. This allows detecting and analyzing possible sources of misinterpretation in a formal way. The distribution of distances of embedded electroencephalographic data from a fixed reference point is used as an example for discussing some aspects of the visualization process. The multidimensional p-norms are an example of a property with a semigroup structure that can be visualized easily.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1995-07-01 | Computers & Graphics |