Data Visualization through Graph Drawing
George Michailidis,Jan de Leeuw +1 more
TL;DR: A general graph drawing framework is introduced, the corresponding mathematical problem defined and an algorithmic approach for solving the necessary optimization problem discussed.
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Abstract: In this paper the problem of visualizing categorical multivariate data sets is considered. By representing the data as the adjacency matrix of an appropriately defined bipartite graph, the problem is transformed to one of graph drawing. A general graph drawing framework is introduced, the corresponding mathematical problem defined and an algorithmic approach for solving the necessary optimization problem discussed. The new approach is illustrated through several examples.
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Citations
Local Multidimensional Scaling for Nonlinear Dimension Reduction, Graph Drawing, and Proximity Analysis
Lisha Chen,Andreas Buja +1 more
TL;DR: This work applies the force paradigm to create localized versions of MDS stress functions with a tuning parameter to adjust the strength of nonlocal repulsive forces and solves the problem of tuning parameter selection with a meta-criterion that measures how well the sets of K-nearest neighbors agree between the data and the embedding.
Gifi Methods for Optimal Scaling in R: The Package homals
Jan de Leeuw,Patrick Mair +1 more
TL;DR: In this article, the authors present methodological and practical issues of the R package homals which performs homogeneity analysis and various extensions, such as nonlinear principal component analysis, nonlinear canonical correlation analysis, and predictive models which emulate discriminant analysis and regression models.
An Experimental Study on Distance-Based Graph Drawing
Ulrik Brandes,Christian Pich +1 more
- 05 Feb 2009
TL;DR: An extensive experimental study is presented showing that, if the goal is to represent the distances in a graph well, a combination of two simple algorithms based on variants of multidimensional scaling is to be preferred because of their efficiency, reliability, and even simplicity.
Regional collaborations and indigenous innovation capabilities in China: A multivariate method for the analysis of regional innovation systems
TL;DR: In this article, the emerging patterns of regional collaboration for innovation projects in China, using official government statistics of 30 Chinese regions, were analyzed using Ordinal Multidimensional Scaling and Cluster analysis as a robust method to study regional innovation systems.
116
High-dimensional data visualisation: The textile plot
Natsuhiko Kumasaka,Ritei Shibata +1 more
TL;DR: The textile plot is a parallel coordinate plot in which the ordering, locations and scales of the axes are simultaneously chosen so that the connecting lines are aligned as horizontally as possible.
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References
Validating Graph Drawing Aesthetics
Helen C. Purchase,Robert F. Cohen,Murray James +2 more
- 20 Sep 1995
TL;DR: In this paper, the authors present a graph drawing algorithm that minimizes edge crossings and bends in polyline edges of a graph, where the number of edge crossings in the display should be minimized.
Block-relaxation Algorithms in Statistics
Jan de Leeuw
- 01 Jan 1994
TL;DR: This paper discusses a single class of algorithms, and it is shown how some well-known classes of statistical algorithms fit in this common class.
Multilevel homogeneity analysis with differential weighting
George Michailidis,Jan de Leeuw +1 more
TL;DR: In this article, the authors extend homogeneity analysis and nonlinear principal components analysis to a multilevel sampling design framework and propose a model that differentially weights the groups of objects, and thus allows them to make within-and between-groups comparisons.
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Graph Layout Techniques and Multidimensional Data Analysis
Jan de Leeuw,George Michailidis +1 more
- 01 Jan 2000
TL;DR: The relationship between multivariate data analysis and techniques for graph drawing or graph layout is explored and many common principles and implementations are found.
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