Suitable tools are needed to explore high-dimensional data spaces and to gain insight into the underlying geoprocesses. Especially interactive, computer-generated representations enrich our perception, so that complex...
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Suitable tools are needed to explore high-dimensional data spaces and to gain insight into the underlying geoprocesses. Especially interactive, computer-generated representations enrich our perception, so that complex phenomena can be comprehended intuitively. Although several helpful visualization techniques are available today, there is a growing demand for more advanced tools and strategies. The latter must ensure that techniques appropriate for the nature of data and suitable for the objectives are applied throughout the whole dataexploration process. This paper outlines the deficits of existing software and requirements for future visualization environments, focusing on the exploration branch in geoscientific visualization. (C) 2000 Elsevier Science Ltd. All rights reserved.
visualization techniques are of increasing importance in exploring and analyzing large amounts of multidimensional information. One important class of visualization techniques which is particularly interesting for vis...
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visualization techniques are of increasing importance in exploring and analyzing large amounts of multidimensional information. One important class of visualization techniques which is particularly interesting for visualizing very large multidimensional data sets is the class of pixel-oriented techniques. The basic idea of pixel-oriented visualization techniques is to represent as many data objects as possible on the screen at the same time by mapping each data value to a pixel of the screen and arranging the pixels adequately. A number of different pixel-oriented visualization techniques have been proposed in recent years and it has been shown that the techniques are useful for visual data exploration in a number of different application contexts. In this paper, we discuss a number of issues which are of high importance in developing pixel-oriented visualization techniques. The major goal of this article is to provide a formal basis of pixel-oriented visualization techniques and show that the design decisions in developing them can be seen as solutions of well-defined optimization problems. This is true for the mapping of the data values to colors, the arrangement of pixels inside the subwindows, the shape of the subwindows, and the ordering of the dimension subwindows. The paper also discusses the design issues of special variants of pixel-oriented techniques for visualizing large spatial data sets. The optimization functions for the mentioned design decisions are important for the effectiveness of the resulting visualizations. We show this by evaluating the optimization functions and comparing the results to the visualizations obtained in a number of different application.
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 o...
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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 R-N is represented by a polygonal line, it is found that a point <-> line duality is induced in the Euclidean plane R-2. This leads to the development in the projective, P-2, rather than the Euclidean plane. Pointers on how to minimize the technical complications and avoid errors are provided. The representation (i.e. visualisation) of 1-dimensional objects is obtained from the envelope of the polygonal lines representing the points on their points. On the plane R-2 there is a inflection-point <-> cusp, conics <-> conics and other potentially useful dualities. A line l subset of R-N 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 greater than or equal to 2 is obtained recursively. Specifically, the representation of a p-flat, a plane of dimension 2 less than or equal to p less than or equal to N - 1 in R-N is obtained from the (p-l)-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 rep
We have developed a methodology that allows integration of microarray data and meta information within a visualization in order to guide the investigator during dataexploration and analysis. A simple mathematical fra...
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