Visualizing multivariate network on the surface of a sphere

A multivariate network is a graph whose nodes contain multi-dimensional attributes. We propose a method to visualize such a network using spherical Self-Organizing Map (SOM) and circular layout. The spherical SOM produced an initial graph layout by grouping nodes with similar attributes to adjacent areas on the sphere. The circular layout algorithm fine tunes the position of each node to avoid node-node/node-edge overlap and minimize the number of edge crossings. We also implement an interface to project the spherical image onto a 2D plane such that the user can have a global view of the data set. The user is allowed to select any point of interest to be the center of the 2D projection.

[1]  H. Hotelling.  Analysis of a complex of statistical variables into principal components. , 1933 .

[2]  M. V. Velzen,et al.  Self-organizing maps , 2007 .

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

[4]  Masahiro Takatsuka,et al.  The Geodesic Self-Organizing Map and Its Error Analysis , 2005, ACSC.

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

[6]  Vladimir Batagelj,et al.  Exploratory Social Network Analysis with Pajek , 2005 .

[7]  Juha Vesanto,et al.  Data exploration process based on the self-organizing map , 2002 .

[8]  Bernd Meyer,et al.  Self-Organizing Graphs - A Neural Network Perspective of Graph Layout , 1998, GD.

[9]  Helge Ritter.  Asymptotic level density for a class of vector quantization processes , 1991, IEEE Trans. Neural Networks.

[10]  Ivan Herman,et al.  Graph Visualization and Navigation in Information Visualization: A Survey , 2000, IEEE Trans. Vis. Comput. Graph..

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

[12]  E. Kreyszig.  Introduction to Differential Geometry and Riemannian Geometry , 1968 .

[13]  Andreas Buja,et al.  Exploratory Visual Analysis of Graphs in GGOBI , 2004 .

[14]  Frank Canters,et al.  The World in Perspective: A Directory of World Map Projections , 1989 .

[15]  David S. Johnson,et al.  Crossing Number is NP-Complete , 1983 .

[16]  K. Wampler,et al.  Non-Euclidean Spring Embedders , 2004 .