Advertisement

Application of Perspective-Based Observational Tunnels Method to Visualization of Multidimensional Fractals

  • Dariusz JamrozEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10842)

Abstract

Methods of multidimensional data visualization are frequently applied in the qualitative analysis allowing to state some properties of this data. They are based only on using the transformation of the multidimensional space into a two-dimensional one which represents the screen in a way ensuring not to lose important properties of the data. Thanks to this it is possible to observe some searched data properties in the most natural way for human beings–through the sense of sight. In this way, the whole analysis is conducted excluding applications of complex algorithms serving to get information about these properties. The example of a multidimensional data visualization method is a relatively new method of perspective-based observational tunnels. It was proved earlier that this method is efficient in the analysis of real data located in a multidimensional space of features obtained by characters recognition. Its efficiency was also shown by the analysis of multidimensional real data describing coal samples. In this paper, another aspect of using this method was shown–to visualize artificially generated five-dimensional fractals located in a five-dimensional space. The purpose of such a visualization can be to obtain views of such multidimensional objects as well as to adapt and teach our mind to percept, recognize and perhaps understand objects of a higher number of dimensions than 3. Our understanding of such multidimensional data could significantly influence the way of perceiving complex multidimensional relations in data and the surrounding world. The examples of obtained views of five-dimensional fractals were shown. Such a fractal looks like a completely different object from different perspectives. Also, views of the same fractal obtained using the PCA, MDS and autoassociative neural networks methods are presented for comparison.

Keywords

Multidimensional data analysis Data mining Multidimensional visualization Observational tunnels method Multidimensional perspective Fractals 

References

  1. 1.
    Jamroz, D.: The perspective-based observational tunnels method: a new method of multidimensional data visualization. Inf. Vis. 16(4), 346–360 (2017)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Jamroz, D., Niedoba, T.: Comparison of selected methods of multi-parameter data visualization used for classification of coals. Physicochem. Probl. Mineral Process. 51(2), 769–784 (2015)Google Scholar
  3. 3.
    Hotelling, H.: Analysis of a complex of statistical variables into principal components. J. Educ. Psychol. 24, 417–441, 498–520 (1933)CrossRefGoogle Scholar
  4. 4.
    Jolliffe, I.T.: Principal Component Analysis, Series. Springer Series in Statistics, 2nd edn. Springer, New York (2002).  https://doi.org/10.1007/b98835CrossRefzbMATHGoogle Scholar
  5. 5.
    Kruskal, J.B.: Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika 29, 1–27 (1964)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Kim, S.S., Kwon, S., Cook, D.: Interactive visualization of hierarchical clusters using MDS and MST. Metrika 51, 39–51 (2000)CrossRefGoogle Scholar
  7. 7.
    Assa, J., Cohen-Or, D., Milo, T.: RMAP: a system for visualizing data in multidimensional relevance space. Vis. Comput. 15(5), 217–234 (1999)CrossRefGoogle Scholar
  8. 8.
    Niedoba, T.: Application of relevance maps in multidimensional classification of coal types. Arch. Min. Sci. 60(1), 93–107 (2015)Google Scholar
  9. 9.
    Inselberg, A.: Parallel Coordinates: VISUAL Multidimensional Geometry and its Applications. Springer, New York (2009).  https://doi.org/10.1007/978-0-387-68628-8CrossRefzbMATHGoogle Scholar
  10. 10.
    Akers, S.B., Horel, D., Krisnamurthy, B.: The star graph: an attractive alternative to the n-cube. In: Proceedings of International Conference On Parallel Processing, pp. 393–400. Pensylvania State University Press (1987)Google Scholar
  11. 11.
    Aldrich, C.: Visualization of transformed multivariate data sets with autoassociative neural networks. Pattern Recogn. Lett. 19(8), 749–764 (1998)CrossRefGoogle Scholar
  12. 12.
    Jamroz, D.: Application of multi-parameter data visualization by means of autoassociative neural networks to evaluate classification possibilities of various coal types. Physicochem. Probl. Mineral Process. 50(2), 719–734 (2014)Google Scholar
  13. 13.
    Kohonen, T.: Self Organization and Associative Memory. Springer, Heidelberg (1989).  https://doi.org/10.1007/978-3-642-88163-3CrossRefzbMATHGoogle Scholar
  14. 14.
    Jamroz, D., Niedoba, T.: Application of multidimensional data visualization by means of self-organizing Kohonen maps to evaluate classification possibilities of various coal types. Arch. Min. Sci. 60(1), 39–51 (2015)Google Scholar
  15. 15.
    Fisher, Y.: Fractal Image Compression. Springer, New York (1995).  https://doi.org/10.1007/978-1-4612-2472-3CrossRefzbMATHGoogle Scholar
  16. 16.
    Kouzani, A.Z.: Classification of face images using local iterated function systems. Mach. Vis. Appl. 19, 223–248 (2008)CrossRefGoogle Scholar
  17. 17.
    Mozaffari, S., Facz, K., Faradji, F.: One dimensional fractal coder for online signature recognition. In: International Conference on Pattern Recognition, pp. 857–860 (2008)Google Scholar
  18. 18.
    Gdawiec, K.: Shape recognition using partitioned iterated function systems. In: Cyran, K.A., Kozielski, S., Peters, J.F., Stańczyk, U., Wakulicz-Deja, A. (eds.) Man-Machine Interactions. AISC, vol. 59, pp. 451–458. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-642-00563-3_48CrossRefGoogle Scholar
  19. 19.
    Barnsley, M.: Fractals Everywhere. Academic Press, Boston (1988)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied Computer ScienceAGH University of Science and TechnologyKrakowPoland

Personalised recommendations