Advertisement

Aesthetic Discrimination of Graph Layouts

  • Moritz Klammler
  • Tamara MchedlidzeEmail author
  • Alexey Pak
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11282)

Abstract

This paper addresses the following basic question: given two layouts of the same graph, which one is more aesthetically pleasing? We propose a neural network-based discriminator model trained on a labeled dataset that decides which of two layouts has a higher aesthetic quality. The feature vectors used as inputs to the model are based on known graph drawing quality metrics, classical statistics, information-theoretical quantities, and two-point statistics inspired by methods of condensed matter physics. The large corpus of layout pairs used for training and testing is constructed using force-directed drawing algorithms and the layouts that naturally stem from the process of graph generation. It is further extended using data augmentation techniques. Our model demonstrates a mean prediction accuracy of 96.48%, outperforming discriminators based on stress and on the linear combination of popular quality metrics by a small but statistically significant margin.

The full version of the paper including the appendix with additional illustrations is available at https://arxiv.org/abs/1809.01017.

Keywords

Graph drawing Graph drawing aesthetics Machine learning Neural networks Graph drawing syndromes 

References

  1. 1.
    Barbosa, H.J.C., Barreto, A.M.S.: An interactive genetic algorithm with coevolution of weights for multiobjective problems. In: Spector, L., Goodman, E.D., Wu, A., Langdon, W.B., Voigt, H.M. (eds.) An Interactive Genetic Algorithm With Co-evolution of Weights for Multiobjective Problems, GECCO 2001, pp. 203–210. Morgan Kaufmann Publishers Inc. (2001)Google Scholar
  2. 2.
    Boisvert, R.F., Pozo, R., Remington, K., Barrett, R.F., Dongarra, J.J.: Matrix market: a web resource for test matrix collections. In: Boisvert, R.F. (ed.) Quality of Numerical Software: Assessment and enhancement, pp. 125–137. Springer, Heidelberg (1997).  https://doi.org/10.1007/978-1-5041-2940-4_9CrossRefGoogle Scholar
  3. 3.
    Bromley, J., Guyon, I., LeCun, Y., Säckinger, E., Shah, R.: Signature verification using a “Siamese" time delay neural network. In: Advances in Neural Information Processing Systems, pp. 737–744 (1994).  https://doi.org/10.1142/S0218001493000339CrossRefGoogle Scholar
  4. 4.
    Dev, K., Villar, N., Lau, M.: Polygons, points, or voxels?: Stimuli selection for crowdsourcing aesthetics preferences of 3d shape pairs. In: Gooch, B., Gingold, Y.I., Winnemoeller, H., Bartram, L., Spencer, S.N. (eds.) Proceedings of the symposium on Computational Aesthetics, CAE 2017, Los Angeles, California, USA, pp. 2:1–2:7. ACM (2017).  https://doi.org/10.1145/3092912.3092918
  5. 5.
    Eades, P.: A heuristic for graph drawing. Congr. Numer. 24, 149–160 (1984)MathSciNetGoogle Scholar
  6. 6.
    Eades, P., Hong, S., Nguyen, A., Klein, K.: Shape-based quality metrics for large graph visualization. J. Graph Algorithms Appl. 21(1), 29–53 (2017).  https://doi.org/10.7155/jgaa.00405MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Findenegg, G.H., Hellweg, T.: Statistische Thermodynamik, 2nd edn. Springer, Darmstadt (2015).  https://doi.org/10.1007/978-3-642-37872-0CrossRefGoogle Scholar
  8. 8.
    Fredrickson, B.L.: What good are positive emotions. Rev. Gen. Psychol. 2, 300–319 (1998)CrossRefGoogle Scholar
  9. 9.
    Fruchterman, T.M.J., Reingold, E.M.: Graph drawing by force-directed placement. Softw. Pract. Exper. 21(11), 1129–1164 (1991).  https://doi.org/10.1002/spe.4380211102CrossRefGoogle Scholar
  10. 10.
    Hachul, S., Jünger, M.: Drawing large graphs with a potential-field-based multilevel algorithm. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 285–295. Springer, Heidelberg (2005).  https://doi.org/10.1007/978-3-540-31843-9_29CrossRefzbMATHGoogle Scholar
  11. 11.
    Hahnloser, R.H.R., Sarpeshkar, R., Mahowald, M.A., Douglas, R.J., Seung, H.S.: Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit. Nature 405, 947–951 (2000).  https://doi.org/10.1038/35016072CrossRefGoogle Scholar
  12. 12.
    Huang, W., Eades, P.: How people read graphs. In: Hong, S. (ed.) Asia-Pacific Symposium on Information Visualisation, APVIS 2005, pp. 51–58, Australia, Sydney (2005)Google Scholar
  13. 13.
    Huang, W., Eades, P., Hong, S.H., Lin, C.C.: Improving multiple aesthetics produces better graph drawings. J. Vis. Lang. Comput. 24(4), 262–272 (2013).  https://doi.org/10.1016/j.jvlc.2011.12.002CrossRefGoogle Scholar
  14. 14.
    Huang, W., Hong, S., Eades, P.: Effects of crossing angles. In: IEEE VGTC Pacific Visualization Symposium 2008, PacificVis 2008, Kyoto, Japan, pp. 41–46 (2008).  https://doi.org/10.1109/PACIFICVIS.2008.4475457
  15. 15.
    Huang, W., Huang, M.L., Lin, C.C.: Evaluating overall quality of graph visualizations based on aesthetics aggregation. Inf. Sci. 330, 444–454 (2016).  https://doi.org/10.1016/j.ins.2015.05.028, SI: Visual Info CommunicationCrossRefGoogle Scholar
  16. 16.
    Huang, W., Huang, M.: Exploring the relative importance of crossing number and crossing angle. In: Dai, G., et al. (eds.) Proceedings of the 3rd International Symposium on Visual Information Communication, VINCI 2010, pp. 1–8, ACM (2010).  https://doi.org/10.1145/1865841.1865854
  17. 17.
    Kamada, T., Kawai, S.: An algorithm for drawing general undirected graphs. Inf. Process. Lett. 31(1), 7–15 (1989).  https://doi.org/10.1016/0020-0190(89)90102-6MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
  19. 19.
    Klammler, M.: Aesthetic value of graph layouts: investigation of statistical syndromes for automatic quantification. Master’s thesis, Karlsruhe Institute of Technology (2018). http://klammler.eu/msc/
  20. 20.
    Klammler, M., et al.: Source code for aesthetic discrimination of graph layouts. https://github.com/5gon12eder/msc-graphstudy
  21. 21.
    Kohavi, R.: A study of cross-validation and bootstrap for accuracy estimation and model selection. In: Proceedings of the 14thInternational Joint Conference on Artificial Intelligence, IJCAI 1995, Montréal Québec, Canada, vol. 2, pp. 1137–1145. Morgan Kaufmann (1995)Google Scholar
  22. 22.
    Kwon, O.H., Crnovrsanin, T., Ma, K.L.: What would a graph look like in this layout? A machine learning approach to large graph visualization. IEEE Trans. Vis. Comput. Graph. 24(1), 478–488 (2018).  https://doi.org/10.1109/TVCG.2017.2743858CrossRefGoogle Scholar
  23. 23.
    Masui, T.: Evolutionary learning of graph layout constraints from examples. In: Szekely, P.A. (ed.) Proceedings of the 7th Annual ACM Symposium on User Interface Software and Technology, pp. 103–108. UIST 1994. ACM (1994).  https://doi.org/10.1145/192426.192468
  24. 24.
    Nishiyama, M., Okabe, T., Sato, Y., Sato, I.: Sensation-based photo cropping. In: Gao, W., et al. (eds.) Proceedings of the 17th ACM International Conference on Multimedia. pp. 669–672. MM 2009, ACM (2009).  https://doi.org/10.1145/1631272.1631384
  25. 25.
    Norman, D.A.: Emotion & design: attractive things work better. Interactions 9(4), 36–42 (2002).  https://doi.org/10.1145/543434.543435CrossRefGoogle Scholar
  26. 26.
    Press, W., Teukolsky, S., Vetterling, W., Flannery, B.: Numerical Recipes: The Art of Scientific Computing, 3 edn. Cambridge University Press (2007)Google Scholar
  27. 27.
    Prusinkiewicz, P., Lindenmayer, A.: The Algorithmic Beauty of Plants. Springer, New York (1990).  https://doi.org/10.1007/978-1-4613-8476-2CrossRefzbMATHGoogle Scholar
  28. 28.
    Purchase, H.: Which aesthetic has the greatest effect on human understanding? In: DiBattista, G. (ed.) GD 1997. LNCS, vol. 1353, pp. 248–261. Springer, Heidelberg (1997).  https://doi.org/10.1007/3-540-63938-1_67CrossRefGoogle Scholar
  29. 29.
    Purchase, H.C.: Performance of layout algorithms: comprehension, not computation. J. Vis. Lang. Comput. 9(6), 647–657 (1998).  https://doi.org/10.1006/jvlc.1998.0093CrossRefGoogle Scholar
  30. 30.
    Purchase, H.C., Cohen, R.F., James, M.: Validating graph drawing aesthetics. In: Brandenburg, F.J. (ed.) GD 1995. LNCS, vol. 1027, pp. 435–446. Springer, Heidelberg (1996).  https://doi.org/10.1007/BFb0021827CrossRefGoogle Scholar
  31. 31.
    Purchase, H.C., Hamer, J., Nöllenburg, M., Kobourov, S.G.: On the usability of Lombardi graph drawings. In: Didimo, W., Patrignani, M. (eds.) GD 2012. LNCS, vol. 7704, pp. 451–462. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-36763-2_40CrossRefzbMATHGoogle Scholar
  32. 32.
    Rosete-Suarez, A., Sebag, M., Ochoa-Rodriguez, A.: A study of evolutionary graph drawing: laboratoire de Recherche en Informatique (LRI), Universite Paris-Sud XI, p. 1228. Technical report (1999)Google Scholar
  33. 33.
    dos Santos Vieira, R., do Nascimento, H.A.D., da Silva, W.B.: The application of machine learning to problems in graph drawing – a literature review. In: Proceedings of the 7th International Conference on Information, Process, and Knowledge Management,eKNOW 2015, Lisbon, Portugal, pp. 112–118 (2015)Google Scholar
  34. 34.
    Schaefer, S., McPhail, T., Warren, J.: Image deformation using moving least squares. ACM Trans. Graph. 25(3), 533–540 (2006).  https://doi.org/10.1145/1141911.1141920CrossRefGoogle Scholar
  35. 35.
    Scott, D.W.: On optimal and data-based histograms. Biometrika 66(3), 605–610 (1979).  https://doi.org/10.1093/biomet/66.3.605MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27(4), 623–656 (1948).  https://doi.org/10.1002/j.1538-7305.1948.tb00917.xMathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Spönemann, M., Duderstadt, B., von Hanxleden, R.: Evolutionary meta layout of graphs. In: Dwyer, T., Purchase, H., Delaney, A. (eds.) Diagrams 2014. LNCS (LNAI), vol. 8578, pp. 16–30. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-44043-8_3CrossRefGoogle Scholar
  38. 38.
    Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I., Salakhutdinov, R.: Dropout: a simple way to prevent neural networks from overfitting. J. Mach. Learn. Res. 15(1), 1929–1958 (2014)MathSciNetzbMATHGoogle Scholar
  39. 39.
    Tamassia, R.: Handbook of Graph Drawing and Visualization. Discrete Mathematics and Its Applications. CRC Press (2013)Google Scholar
  40. 40.
  41. 41.
    Tractinsky, N., Katz, A.S., Ikar, D.: What is beautiful is usable. Interact. Comput. 13(2), 127–145 (2000).  https://doi.org/10.1016/S0953-5438(00)00031-XCrossRefGoogle Scholar
  42. 42.
    Ware, C., Purchase, H.C., Colpoys, L., McGill, M.: Cognitive measurements of graph aesthetics. Inf. Vis. 1(2), 103–110 (2002).  https://doi.org/10.1057/palgrave.ivs.9500013CrossRefGoogle Scholar
  43. 43.
    Welch, E., Kobourov, S.: Measuring symmetry in drawings of graphs. Comput. Graph. Forum 36(3), 341–351 (2017).  https://doi.org/10.1111/cgf.13192CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Moritz Klammler
    • 1
  • Tamara Mchedlidze
    • 1
    Email author
  • Alexey Pak
    • 2
  1. 1.Karlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.Fraunhofer Institute of Optronics, System Technologies and Image ExploitationKarlsruheGermany

Personalised recommendations