Graph Layout Techniques and Multidimensional Data Analysis

In this paper we explore the relationship between multivariate data analysis and techniques for graph drawing or graph layout. Although both classes of techniques were created for quite different purposes, we find many common principles and implementations. We start with a discussion of the data analysis techniques, in particular multiple correspondence analysis, multidimensional scaling, parallel coordinate plotting, and seriation. We then discuss parallels in the graph layout literature.

[1]  Brian Everitt,et al.  Homogeneity analysis of incomplete data , 1986 .

[2]  C. Burt.  THE FACTORIAL ANALYSIS OF QUALITATIVE DATA , 1950 .

[3]  George Michailidis,et al.  CONSTRAINED HOMOGENEITY ANALYSIS WITH APPLICATIONS TO HIERARCHICAL DATA , 1998 .

[4]  Susanne Prediger,et al.  Symbolic objects in formal concept analysis , 1997 .

[5]  J. Meulman.  A Distance Approach to Nonlinear Multivariate Analysis , 1986 .

[6]  Robert H. Whittaker,et al.  Ordination of Plant Communities , 1978, Handbook of Vegetation Science.

[7]  Ioannis G. Tollis,et al.  Algorithms for automatic graph drawing: an annotated bibliography , 1994 .

[8]  Michael Jünger,et al.  Journal of Graph Algorithms and Applications 2-layer Straightline Crossing Minimization: Performance of Exact and Heuristic Algorithms , 2022 .

[9]  Alfred Inselberg,et al.  Parallel coordinates: a tool for visualizing multi-dimensional geometry , 1990, Proceedings of the First IEEE Conference on Visualization: Visualization `90.

[10]  William J. Stewart,et al.  Algorithm 570: LOPSI: A Simultaneous Iteration Method for Real Matrices [F2] , 1981, TOMS.

[11]  M. Hill,et al.  Nonlinear Multivariate Analysis. , 1990 .

[12]  Peter Eades,et al.  A Heuristic for Graph Drawing , 1984 .

[13]  Prabhakar Raghavan,et al.  Sparse matrix reordering schemes for browsing hypertext , 1996 .

[14]  A. D. Gordon,et al.  Correspondence Analysis Handbook. , 1993 .

[15]  J. Kruskal.  Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis , 1964 .

[16]  J. Leeuw.  Applications of Convex Analysis to Multidimensional Scaling , 2000 .

[17]  J. Leeuw.  Convergence of the majorization method for multidimensional scaling , 1988 .

[18]  Robert Joseph Fowler,et al.  A Spring Modeling Algorithm to Position Nodes of an Undirected Graph in Three Dimensions , 1994 .

[19]  W. T. Tutte.  How to Draw a Graph , 1963 .

[20]  Alfred Inselberg,et al.  Parallel coordinates for visualizing multi-dimensional geometry , 1987 .

[21]  S. Benzer.  The fine structure of the gene. , 1962, Scientific American.

[22]  Jan de Leeuw,et al.  Multilevel homogeneity analysis with differential weighting , 2000 .

[23]  Roberto Tamassia,et al.  Advances in Graph Drawing , 1994, CIAC.

[24]  R. Clarke,et al.  Theory and Applications of Correspondence Analysis , 1985 .

[25]  Ioannis G. Tollis,et al.  Graph Drawing , 1994, Lecture Notes in Computer Science.

[26]  M. J. R. Healy,et al.  An approach to the scaling of categorized attributes , 1976 .

[27]  Edward M. Reingold,et al.  Graph drawing by force‐directed placement , 1991, Softw. Pract. Exp..

[28]  I. Jolliffe,et al.  Nonlinear Multivariate Analysis , 1992 .

[29]  J. Leeuw,et al.  The Gifi system of descriptive multivariate analysis , 1998 .

[30]  J. Meulman.  The integration of multidimensional scaling and multivariate analysis with optimal transformations , 1992 .

[31]  Satoru Kawai,et al.  An Algorithm for Drawing General Undirected Graphs , 1989, Inf. Process. Lett..

[32]  Bernhard Ganter,et al.  Formale Begriffsanalyse - mathematische Grundlagen , 1996 .

[33]  Bruce Hendrickson,et al.  A Spectral Algorithm for Seriation and the Consecutive Ones Problem , 1999, SIAM J. Comput..

[34]  L. Guttman.  A general nonmetric technique for finding the smallest coordinate space for a configuration of points , 1968 .

[35]  L. Guttman.  The principal components of scale analysis , 1950 .

[36]  E. Wegman.  Hyperdimensional Data Analysis Using Parallel Coordinates , 1990 .

[37]  J. Kruskal.  Nonmetric multidimensional scaling: A numerical method , 1964 .

[38]  Jan de Leeuw,et al.  Interpreting multiple correspondence analysis as a multidimensional scaling method , 1992 .

[39]  P. Groenen,et al.  Modern multidimensional scaling , 1996 .

[40]  Kozo Sugiyama,et al.  A Simple and Unified Method for Drawing Graphs: Magnetic-Spring Algorithm , 1994, GD.

[41]  Subir Ghosh,et al.  Multivariate analysis, design of experiments, and survey sampling , 2000 .

[42]  Victor E. McGee,et al.  THE MULTIDIMENSIONAL ANALYSIS OF ‘ELASTIC’ DISTANCES , 1966 .

[43]  C. Coombs.  A theory of data. , 1965, Psychology Review.

[44]  John W. Sammon,et al.  A Nonlinear Mapping for Data Structure Analysis , 1969, IEEE Transactions on Computers.

[45]  M. Hill.  Correspondence Analysis: A Neglected Multivariate Method , 1974 .

[46]  Deborah F. Swayne,et al.  Higher Dimensional Representations of Graphs , 1995 .