Linear Time Heuristics for Topographic Mapping of Dissimilarity Data

  • Andrej Gisbrecht
  • Frank-Michael Schleif
  • Xibin Zhu
  • Barbara Hammer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6936)


Topographic mapping offers an intuitive interface to inspect large quantities of electronic data. Recently, it has been extended to data described by general dissimilarities rather than Euclidean vectors. Unlike its Euclidean counterpart, the technique has quadratic time complexity due to the underlying quadratic dissimilarity matrix. Thus, it is infeasible already for medium sized data sets. We introduce two approximation techniques which speed up the complexity to linear time algorithms: the Nyström approximation and patch processing, respectively. We evaluate the techniques on three examples from the biomedical domain.


Topographic Mapping Dissimilarity Matrix Biomedical Domain Generalize Linear Regression Model Generative Topographic Mapping 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alex, N., Hasenfuss, A., Hammer, B.: Patch clustering for massive data sets. Neurocomputing 72(7-9), 1455–1469 (2009)CrossRefGoogle Scholar
  2. 2.
    Barbuddhe, S.B., Maier, T., Schwarz, G., Kostrzewa, M., Hof, H., Domann, E., Chakraborty, T., Hain, T.: Rapid identification and typing of listeria species by matrix-assisted laser desorption ionization-time of flight mass spectrometry. Applied and Environmental Microbiology 74(17), 5402–5407 (2008)CrossRefGoogle Scholar
  3. 3.
    Bishop, C., Svensen, M., Williams, C.: The generative topographic mapping. Neural Computation 10(1), 215–234 (1998)CrossRefzbMATHGoogle Scholar
  4. 4.
    Boulet, R., Jouve, B., Rossi, F., Villa-Vialaneix, N.: Batch kernel SOM and related Laplacian methods for social network analysis. Neurocomputing 71(7-9), 1257–1273 (2008)CrossRefGoogle Scholar
  5. 5.
    Cottrell, M., Hammer, B., Hasenfuss, A., Villmann, T.: Batch and median neural gas. Neural Networks 19, 762–771 (2006)CrossRefzbMATHGoogle Scholar
  6. 6.
    Gasteiger, E., Gattiker, A., Hoogland, C., Ivanyi, I., Appel, R.D., Bairoch, A.: ExPASy: the proteomics server for in-depth protein knowledge and analysis. Nucleic Acids Res. 31, 3784–3788 (2003)CrossRefGoogle Scholar
  7. 7.
    Gisbrecht, A., Mokbel, B., Hammer, B.: The Nystrom approximation for relational generative topographic mappings. In: NIPS Workshop on Challenges of Data Visualization (2010)Google Scholar
  8. 8.
    Gisbrecht, A., Mokbel, B., Hammer, B.: Relational Generative Topographic Mapping. Neurocomputing 74, 1359–1371 (2011)CrossRefGoogle Scholar
  9. 9.
    Graepel, T., Obermayer, K.: A stochastic self-organizing map for proximity data. Neural Computation 11, 139–155 (1999)CrossRefGoogle Scholar
  10. 10.
    Hammer, B., Hasenfuss, A.: Topographic Mapping of Large Dissimilarity Data Sets. Neural Computation 22(9), 2229–2284 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Hathaway, R.J., Bezdek, J.C.: Nerf c-means: Non-Euclidean relational fuzzy clustering. Pattern Recognition 27(3), 429–437 (1994)CrossRefGoogle Scholar
  12. 12.
    Kohonen, T. (ed.): Self-Organizing Maps, 3rd edn. Springer-Verlag New York, Inc., Secaucus (2001)zbMATHGoogle Scholar
  13. 13.
    Kohonen, T., Somervuo, P.: How to make large self-organizing maps for nonvectorial data. Neural Networks 15, 945–952 (2002)CrossRefGoogle Scholar
  14. 14.
    Lundsteen, C., Phillip, J., Granum, E.: Quantitative analysis of 6985 digitized trypsin G-banded human metaphase chromosomes. Clinical Genetics 18, 355–370 (1980)CrossRefGoogle Scholar
  15. 15.
    Maier, T., Klebel, S., Renner, U., Kostrzewa, M.: Fast and reliable MALDI-TOF ms–based microorganism identification. Nature Methods 3 (2006)Google Scholar
  16. 16.
    Seo, S., Obermayer, K.: Self-organizing maps and clustering methods for matrix data. Neural Networks 17, 1211–1230 (2004)CrossRefzbMATHGoogle Scholar
  17. 17.
    Williams, C.K.I., Seeger, M.: Using the Nyström method to speed up kernel machines. In: Advances in Neural Information Processing Systems, vol. 13, pp. 682–688 (2001)Google Scholar
  18. 18.
    Yin, H.: On the equivalence between kernel self-organising maps and self-organising mixture density networks. Neural Networks 19(6-7), 780–784 (2006)CrossRefzbMATHGoogle Scholar
  19. 19.
    Lipman, D.J., Pearson, W.R.: Rapid and sensitive protein similarity searches. Science, 227, 1435–1441Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Andrej Gisbrecht
    • 1
  • Frank-Michael Schleif
    • 1
  • Xibin Zhu
    • 1
  • Barbara Hammer
    • 1
  1. 1.CITEC Centre of ExcellenceBielefeld UniversityBielefeldGermany

Personalised recommendations