Abstract
This chapter introduces geometrical projection surfaces to provide a stable ‘stage’ for subsequent visual analysis of locations, positions, and pathways. It proposes methods for link erosion, planar projection (with monotonic convergence!), kernel smoothening, and a hypsometric colour scheme for tile colouring in order to help create conceptual landscape visualizations. The means presented here complement the analytical processes introduced in the previous chapter with a powerful visual instrument. When combined, the two provide means to analyse social semantic performance networks.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Proximity between all eigenvectors times the eigenvalue stretch factor.
- 2.
Kamada and Kawai (1989) propose to use \( L = {L}_0/\ max\left({d}_{ij}\right) \) to calculate the desirable length in the plane, with L 0 being the length of a side of the square (!) plane. Since hardly any digital display surfaces are quadratic, this would offer room for further improvement, e.g., by determining L 0 through the length of the display diagonal and subsequently using adapted perturbations for x and y coordinates.
- 3.
Equations 6.6–6.9 were taken from the C code implemented in Butts et al. (2012).
- 4.
The R implementation uses |V|2 as k.
- 5.
Instead of the originally proposed Newton–Raphson method, the R implementation uses Gaussian perturbation with (per default): \( {\mathrm{y}}_{\mathrm{j}}{}^{\prime }=\mathrm{rnorm}\Big({\mathrm{y}}_{\mathrm{j}},\left(\frac{\mathrm{n}}{4}\right)\cdot \left(10\cdot \frac{0.99^{\mathrm{iteration}}}{10}\right) \) and \( {\mathrm{x}}_{\mathrm{j}}{}^{\prime }=\mathrm{rnorm}\Big({\mathrm{x}}_{\mathrm{j}},\left(\frac{\mathrm{n}}{4}\right)\cdot \left(10\cdot \frac{0.{99}^{\mathrm{iteration}}}{10}\right). \)
- 6.
See Butts et al. (2012), in the function network_layout_kamadakawai_R in layout.c for more details.
References
Blanc, C., Schlick, C.: X-Splines: a spline model designed for the end-user. In: Proceedings of the SIGGRAPH’95, pp. 377–386 (1995)
Butts, C.T.: network: a package for managing relational data in R. J. Stat. Softw. 24(2), (2008)
Butts, C.T., Hunter, D., Handcock, M.S.: network: classes for relational data. R package version 1.7-1, Irvine, CA. http://statnet.org/ (2012)
De Leeuw, J.: Convergence of the majorization method for multidimensional scaling. J. Classif. 5(2), 163–180 (1988)
Eades, P.: A heuristics for graph drawing. Congressus. Numerantium. 42, 149–160 (1984)
Fabrikant, S., Montello, D., Mark, D.: The natural landscape metaphor in information visualization: the role of commonsense geomorphology. J. Am. Soc. Inf. Sci. Technol. 61(2), 253–270 (2010)
Fruchterman, T., Reingold, E.: Graph drawing by force-directed placement. Softw. Pract. Experience 21(11), 1129–1164 (1991)
Furrer, R., Nychka, D., Sain, S.: Fields: Tools for Spatial Data, R Package Version 6.8. http://CRAN.R-project.org/package=fields (2013)
Gronemann, M., Gutwenger, C., Jünger, M., Mutzel, P.: Algorithm engineering im Graphenzeichnen. Informatik. Spektrum. 36(2), 162–173 (2013)
Juenger, M., Mutzel, P.: Technical foundations. In: Juenger, M., Mutzel, P. (eds.) Graph Drawing Software. Springer, Berlin (2004)
Kamada, T., Kawai, S.: An algorithm for drawing general undirected graphs. Inf. Process. Lett. 31(1989), 7–15 (1989)
Patterson, T., Kelso, N.: Hal Shelton revisited: designing and producing natural-color maps with satellite land cover data. Cartogr. Perspect. 47, 28–55 (2004)
Thomas, J., Kielman, J.: Challenges for visual analytics. Inf. Vis. 8(4), 309–314 (2009)
Thomas, J.J., Cook, K.A.: Illuminating the path: the research and development agenda for visual analytics. IEEE Computer Society Press, Los Alamitos, CA (2005)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Wild, F. (2016). Visual Analytics Using Vector Maps as Projection Surfaces. In: Learning Analytics in R with SNA, LSA, and MPIA. Springer, Cham. https://doi.org/10.1007/978-3-319-28791-1_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-28791-1_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-28789-8
Online ISBN: 978-3-319-28791-1
eBook Packages: Computer ScienceComputer Science (R0)