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  • 1
    Electronic Resource
    Electronic Resource
    Bingley : Emerald
    Kybernetes 34 (2005), S. 151-166 
    ISSN: 0368-492X
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Computer Science
    Notes: Purpose - To discuss some of the work of Heinz von Foerster with regard to multidimensional visualization. Design/methodology/approach - An introduction to multidimensional visualization, followed with the connections derived from the Biological Computer Laboratory. Findings - Visualization provides insight through images. Considers the steps involved in interacting and learning so that this will lead the individual into their own "concept formation". Originality/value - Studies aspects of Heinz von Foerster's work that are of importance for understanding multidimensional visualization.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    The visual computer 1 (1985), S. 69-91 
    ISSN: 1432-2315
    Keywords: Convexity ; Duality ; Parallel coordinates ; Intelligent control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract By means ofParallel Coordinates planar “graphs” of multivariate relations are obtained. Certain properties of the relationship correspond tothe geometrical properties of its graph. On the plane a point ←→ line duality with several interesting properties is induced. A new duality betweenbounded and unbounded convex sets and hstars (a generalization of hyperbolas) and between Convex Unions and Intersections is found. This motivates some efficient Convexity algorithms and other results inComputational Geometry. There is also a suprising “cusp” ←→ “inflection point” duality. The narrative ends with a preview of the corresponding results inR N .
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Computational statistics 14 (1999), S. 53-77 
    ISSN: 1613-9658
    Keywords: Key words: Multidimensional Visualization, Parallel Coordinates, Visual Data Exploration, Nonlinear Models, Blessings for Dimensionality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Parallel coordinates is a methodology for visualizing N-dimensional geometry and multivariate problems. In this self-contained up-to-date overview the aim is to clarify salient points causing difficulties, and point out more sophisticated applications and uses in statistics which are marked by **. Starting from the definition of the parallel-axes multidimensional coordinate system, where a point in Euclidean N-space RN is represented by a polygonal line, it is found that a point↔line duality is induced in the Euclidean plane R2. This leads to the development in the projective, P2, rather than the Euclidean plane. Pointers on how to minimize the technical complications and avoid errors are provided. The representation (i.e. visualization) of 1-dimensional objects is obtained from the envelope of the polygonal lines representing the points on their points. On the plane R2 there is a inflection-point ↔ cusp, conics ↔ conics and other potentially useful dualities. A line ?⊂ RN is represented by N – 1 points with a pair of indices in [1, 2, ..., N]. This representation also enables the visualization and computation of proximity properties like the minimum distance between pairs of lines [18]. The representation of objects of dimension ≥ 2 is obtained recursively. Specifically, the representation of a p-flat, a plane of dimension 2 ≤ p ≤ N–1 in RN is obtained from the (p-1)-flats it contains, and which are obtained from the (p-2)-flats and so on all the way down from the points (0-dimensional); hence the recursion. A p-flat is represented by p-points each with (p+1) indices. This is the key message: **high-dimensional objects may be visualized recursively, in terms of their higher dimensional components, rather than directly from their points. Further, this process is robust so that “near” p-flats are also detected in the same way and very useful tight error bounds are available. The representation of a smooth hypersurface in RN is obtained as the envelope of the tangent hyperplanes. The set of points obtained in this way visually reveal properties like convexity, whether the surface is developable, or ruled. A simpler but ambiguous representation for hypersurfaces is also given together with modeling applications of an algorithm for computing and displaying interior, exterior or surface points.
    Type of Medium: Electronic Resource
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  • 4
    Title: Parallel coordinates : visual multidimensional geometry and its applications
    Author: Inselberg, Alfred
    Edition: 1. Aufl.
    Publisher: New York, NY :Springer New York,
    Year of publication: 2009
    Pages: 100 schw.-w. Abb., 100 schw.-w. Zeichn +
    ISBN: 0-387-21507-7 , 978-0-387-21507-5
    Type of Medium: Book
    Language: English
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