Skip to main content
SpringerLink
Log in

Graph-Based Visualisation of High Dimensional Data

  • Chapter
  • First Online:
Book cover Graph-Based Clustering and Data Visualization Algorithms

Part of the book series: SpringerBriefs in Computer Science ((BRIEFSCOMPUTER))

  • 3535 Accesses

Abstract

In this chapter we give an overview of classical dimensionality reduction and graph based visualisation methods that are able to uncover hidden structure of high dimensional data and visualise it in a low-dimensional vector space.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 49.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Tukey, J.: Exploratory Data Analysis. Addison-Wesley, New York (1977)

    MATH  Google Scholar 

  2. McQueen, J.: Some methods for classification and analysis of multivariate observations. Proceedings of fifth Berkeley symposium on mathematical statistics and probability, pp. 281–297 (1967)

    Google Scholar 

  3. Martinetz, T.M., Shulten, K.J.: A neural-gas network learns topologies. In: Kohonen, T., Mäkisara, K., Simula, O., Kangas, J. (eds.) Artificial Neural Networks, pp. 397–402. Elsevier Science Publishers B.V, North-Holland (1991)

    Google Scholar 

  4. Johannes, M., Brase, J.C., Fröhlich, H., Gade, S., Gehrmann, M., Fälth, M., Sültmann, H., Beißbarth, T.: Integration of pathway knowledge into a reweighted recursive feature elimination approach for risk stratification of cancer patients. Bioinformatics 26(17), 2136–2144 (2010)

    Article  Google Scholar 

  5. Lai, C., Reinders, M.J.T., Wessels, L.: Random subspace method for multivariate feature selection. Pattern Recognit. Lett. 27(10), 1067–1076 (2006)

    Article  Google Scholar 

  6. Nguyen, M.H., de la Torre, F.: Optimal feature selection for support vector machines. Pattern Recognit. 43(3), 584–591 (2010)

    Article  MATH  Google Scholar 

  7. Rong, J., Li, G., Chen, Y.P.P.: Acoustic feature selection for automatic emotion recognition from speech. Inf. Process. Manag. 45(3), 315–328 (2009)

    Article  Google Scholar 

  8. Tsang, I.W., Kocsor, A., Kwok, J.T.: Efficient kernel feature extraction for massive data sets. Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining, pp. 724–729 (2006)

    Google Scholar 

  9. Wang, J., Zhang, B., Wang, S., Qi, M., Kong, J.: An adaptively weighted sub-pattern locality preserving projection for face recognition. J. Netw. Comput. Appl. 332(3), 323–332 (2010)

    Article  Google Scholar 

  10. Blum, A.L., Langley, P.: Selection of relevant features and examples in machine learning. Artif. Intell. 97(12), 245271 (1997)

    MathSciNet  Google Scholar 

  11. Guyon, I., Elisseeff, A.: An introduction to variable and feature selection. J. Mach. Learn. Res. 3, 1157–1182 (2003)

    MATH  Google Scholar 

  12. Jain, A., Zongker, D.: Feature selection: Evaluation, application, and small sample performance. IEEE Trans. Pattern Anal. Mach. Intell. 192, 153–158 (1997)

    Article  Google Scholar 

  13. Weston, J., et al.: Feature selection for SVMs. In: Leen, T.K., Dietterich, T.G., Tresp, V. (eds.) Advances in Neural Information Processing Systems, vol. 13, pp. 668–674. The MIT Press, Cambride (2001)

    Google Scholar 

  14. Narendra, P., Fukunaga, K.: A branch and bound algorithm for feature subset selection. IEEE Trans. Comput. C–26(9), 917–922 (1977)

    Article  Google Scholar 

  15. Pudil, P., Novovičová, J., Kittler, J.: Floating search methods in feature selection. Pattern Recognit. Lett. 15(1), 1119–1125 (1994)

    Article  Google Scholar 

  16. Hotelling, H.: Analysis of a complex of statistical variables into principal components. J. Educ. Psychol. 24, 417–441 (1933)

    Article  Google Scholar 

  17. Jolliffe, T.: Principal Component Analysis. Springer, New York (1996)

    Google Scholar 

  18. Sammon, J.W.: A non-linear mapping for data structure analysis. IEEE Trans. Comput. 18(5), 401–409 (1969)

    Article  Google Scholar 

  19. Tenenbaum, J.B., Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000)

    Article  Google Scholar 

  20. Comon, P.: Independent component analysis: a new concept? Signal Process. 36(3), 287–317 (1994)

    Article  MATH  Google Scholar 

  21. Fisher, R.A.: The use of multiple measurements in taxonomic problems. Ann. Eugen. 7, 179–188 (1936)

    Article  Google Scholar 

  22. Kohonen, T.: Self-organized formation of topologically correct feature maps. Biol. Cybern. 43, 59–69 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  23. Kohonen, T.: Self-Organizing maps, 3rd edn. Springer, New York (2001)

    Book  MATH  Google Scholar 

  24. Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000)

    Article  Google Scholar 

  25. Saul, L.K., Roweis, S.T.: Think globally, fit locally: unsupervised learning of low dimensional manifolds. J. Mach. Learn. Res. 4, 119–155 (2003)

    MathSciNet  Google Scholar 

  26. Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15(6), 1373–1396 (2003)

    Article  MATH  Google Scholar 

  27. Borg, I.: Modern multidimensional scaling: theory and applications. Springer, New York (1977)

    Google Scholar 

  28. Kruskal, J.B., Carroll, J.D.: Geometrical models and badness-of-fit functions. In: Krishnaiah, R. (ed.) Multivariate Analysis II, vol. 2, pp. 639–671. Academic Press Pachuri, New York (1969)

    Google Scholar 

  29. Kaski, S., Nikkilä, J., Oja, M., Venna, J., Törönen, J., Castrén, E.: Trustworthiness and metrics in visualizing similarity of gene expression. BMC Bioinformatics 4, 48 (2003)

    Article  Google Scholar 

  30. Venna, J., Kaski, S.: Local multidimensional scaling with controlled tradeoff between trustworthiness and continuity, In: Proceedings of the workshop on self-organizing maps, pp. 695–702 (2005)

    Google Scholar 

  31. Venna, J., Kaski, S.: Local multidimensional scaling. Neural Netw. 19(6), 889–899 (2006)

    Article  MATH  Google Scholar 

  32. Kiviluoto, K.: Topology preservation in self-organizing maps. Proceedings of IEEE international conference on neural networks, pp. 294–299 (1996)

    Google Scholar 

  33. Bauer, H.U., Pawelzik, K.R.: Quantifying the neighborhood preservation of selforganizing feature maps. IEEE Trans. Neural Netw. 3(4), 570–579 (1992)

    Article  Google Scholar 

  34. Duda, R.O., Hart, P.E., Stork, D.: Pattern classification. Wiley, New York (2000)

    Google Scholar 

  35. Mika, S., Schölkopf, B., Smola, A.J., Müller, K.-R., Scholz, M., Rätsch, G.: Kernel PCA and de-noising in feature spaces. In: Advances in neural information processing systems, vol. 11, Cambridge, USA (1999)

    Google Scholar 

  36. Schölkopf, B., Smola, A.J., Müller, K.-R.: Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput. 10(5), 1299–1319 (1998)

    Article  Google Scholar 

  37. Mao, J., Jain, A.K.: Artifical neural networks for feature extraction and multivariate data projection. IEEE Trans. Neural Netw 6(2), 629–637 (1995)

    Google Scholar 

  38. Pal, N.R., Eluri, V.K.: Two efficient connectionist schemes for structure preserving dimensionality reduction. IEEE Trans. Neural Netw. 9, 1143–1153 (1998)

    Article  Google Scholar 

  39. Young, G., Householder, A.S.: Discussion of a set of points in terms of their mutual distances. Psychometrika 3(1), 19–22 (1938)

    Article  MATH  Google Scholar 

  40. Naud, A.: Neural and statistical methods for the visualization of multidimensional data. Technical Science Katedra Metod Komputerowych Uniwersytet Mikoaja Kopernika w Toruniu (2001)

    Google Scholar 

  41. Kruskal, J.B.: Multidimensional scaling by optimizing goodness-of-fit to a nonmetric hypothesis. Psychometrika 29, 1–29 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  42. He, X., Niyogi, P.: Locality preserving projections. In: Lawrence, K., Saul, Weiss, Y., Bottou, L., (eds.) Advances in Neural Information Processing Systems 17. Proceedings of the 2004 Conference, MIT Press, vol. 16, p. 37 (2004) http://mitpress.mit.edu/books/advances-neural-information-processing-systems-17

  43. UC Irvine Machine Learning Repository www.ics.uci.edu/ mlearn/ Cited 15 Oct 2012

    Google Scholar 

  44. Haykin, S.: Neural Networks: A Comprehensive Foundation. Prentice Hall, Upper Saddle River (1999)

    MATH  Google Scholar 

  45. Ultsch, A.: Self-organization neural networks for visualization and classification. In: Opitz, O., Lausen, B., Klar, R. (eds.) Information and Classification, pp. 307–313. Springer, Berlin (1993)

    Chapter  Google Scholar 

  46. Blackmore, J., Miikkulainen, R.: Incremental grid growing: encoding high-dimensional structure into a two-dimensional feature map. In: Proceedong on IEEE international conference on neural networks, vol. 1, pp. 450–455 (1993)

    Google Scholar 

  47. Merkl, D., He, S.H., Dittenbach, M., Rauber, A.: Adaptive hierarchical incremental grid growing: an architecture for high-dimensional data visualization. In: Proceeding of the workshop on SOM, Advances in SOM, pp. 293–298 (2003)

    Google Scholar 

  48. Lee, J.A., Lendasse, A., Donckers, N., Verleysen, M.: A robust nonlinear projection method. Proceedings of ESANN’2000, 8th european symposium on artificial, neural networks, pp. 13–20 (2000)

    Google Scholar 

  49. Estévez, P.A., Figueroa, C.J.: Online data visualization using the neural gas network. Neural Netw. 19, 923–934 (2006)

    Article  MATH  Google Scholar 

  50. Estévez, P.A., Chong, A.M., Held, C.M., Perez, C.A.: Nonlinear projection using geodesic distances and the neural gas network. Lect. Notes Comput. Sci. 4131, 464–473 (2006)

    Article  Google Scholar 

  51. Wu, Y., Chan, K.L.: An extended isomap algorithm for learning multi-class manifold. Proceeding of IEEE international conference on machine learning and, cybernetics (ICMLC2004), vol. 6, pp. 3429–3433 (2004)

    Google Scholar 

  52. Lee, J.A., Verleysen, M.: Nonlinear projection with the isotop method. Proceedings of ICANN’2002, international conference on artificial, neural networks, pp. 933–938 (2002)

    Google Scholar 

  53. Lee, J.A., Archambeau, C., Verleysen, M.: Locally linear embedding versus isotop. In: ESANN’2003 proceedings: European symposium on artificial neural networks Bruges (Belgium), pp. 527–534 (2003)

    Google Scholar 

  54. Demartines, P., Herault, J.: Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets. IEEE Trans. Neural Netw. 8, 148–154 (1997)

    Article  Google Scholar 

  55. Lee, J.A., Lendasse, A., Verleysen, M.: Curvilinear distance analysis versus isomap. Proceedings of ESANN’2002, 10th European symposium on artificial, neural networks, pp. 185–192 (2000)

    Google Scholar 

  56. Lee, J.A., Lendasse, A., Verleysen, M.: Nonlinear projection with curvilinear distances: isomap versus curvilinear distance analysis. Neurocomputing 57, 49–76 (2004)

    Article  Google Scholar 

  57. Vathy-Fogarassy, A., Kiss, A., Abonyi, J.: Topology representing network map—a new tool for visualization of high-dimensional data. Trans. Comput. Sci. I. 4750, 61–84 (2008) (Springer)

    Google Scholar 

  58. Vathy-Fogarassy, A., Abonyi, J.: Local and global mappings of topology representing networks. Inf. Sci. 179, 3791–3803 (2009)

    Article  MathSciNet  Google Scholar 

  59. Dijkstra, E.W.: A note on two problems in connection with graphs. Numer. Math. 1, 269–271 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  60. Martinetz, T.M., Shulten, K.J.: Topology representing networks. Neural Netw. 7(3), 507–522 (1994)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science and Systems Technology, University of Pannonia, Egyetem u.10, Veszprém, 8200, Hungary

    Ágnes Vathy-Fogarassy

  2. Department of Process Engineering, University of Pannonia, Egyetem u. 10, Veszprém, 8200, Hungary

    János Abonyi

Authors
  1. Ágnes Vathy-Fogarassy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. János Abonyi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ágnes Vathy-Fogarassy .

Rights and permissions

Reprints and permissions

Copyright information

© 2013 János Abonyi

About this chapter

Cite this chapter

Vathy-Fogarassy, Á., Abonyi, J. (2013). Graph-Based Visualisation of High Dimensional Data. In: Graph-Based Clustering and Data Visualization Algorithms. SpringerBriefs in Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-5158-6_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-5158-6_3

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5157-9

  • Online ISBN: 978-1-4471-5158-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation