Visualization and knowledge discovery for high dimensional data
Inselberg, A.
User Interfaces to Data Intensive Systems, 2001. UIDIS 2001. Proceedings. Second International Workshop on
Volume , Issue , 2001 Page(s):5 - 24
Digital Object Identifier 10.1109/UIDIS.2001.929921
Summary:The goal of the article is to present a multidimensional
visualization methodology and its applications to visual and automatic
knowledge discovery. Visualization provides insight through images and
can be considered as a collection of application specific mappings:
ProblemDomain→VisuaLRange. For the visualization of multivariate
problems, a multidimensional system of parallel coordinates
(||-coords) is constructed which induces a one-to-one mapping between
subsets of N-space and subsets of 2-space. The result is a rigorous
methodology for doing and seeing N-dimensional geometry. We start with
an overview of the mathematical foundations where it is seen that from
the display of high-dimensional datasets, the search for multivariate
relations among the variables is transformed into a 2D pattern
recognition problem. This is the basis for the application to visual
knowledge discovery which is illustrated in the second part with a real
dataset of VLSI production. Then a recent geometric classifier is
presented and applied to 3 real datasets. The results compared to those
of 23 other classifiers have the least error. The algorithm has
quadratic computational complexity in the size and number of parameters,
provides comprehensible and explicit rules, does dimensionality
selection, and orders these variables so as to optimize the clarity of
separation between the designated set and its complement. Finally a
simple visual economic model of a real country is constructed and
analyzed in order to illustrate the special strength of ||-coords in
modeling multivariate relations by means of hypersurfaces
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