Topographic Mapping of Dissimilarity Data

  • Barbara Hammer
  • Andrej Gisbrecht
  • Alexander Hasenfuss
  • Bassam Mokbel
  • Frank-Michael Schleif
  • Xibin Zhu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6731)


Topographic mapping offers a very flexible tool to inspect large quantities of high-dimensional data in an intuitive way. Often, electronic data are inherently non-Euclidean and modern data formats are connected to dedicated non-Euclidean dissimilarity measures for which classical topographic mapping cannot be used. We give an overview about extensions of topographic mapping to general dissimilarities by means of median or relational extensions. Further, we discuss efficient approximations to avoid the usually squared time complexity.


Cost Function Topographic Mapping Dissimilarity Matrix Relational Cluster Median Cluster 
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.
    Bishop, C.: Pattern Recognition and Machine Learning. Springer, Heidelberg (2007)zbMATHGoogle Scholar
  3. 3.
    Bishop, C.M., Williams, C.K.I.: GTM: The generative topographic mapping. Neural Computation 10, 215–234 (1998)CrossRefGoogle 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.
    Boeckmann, B., Bairoch, A., Apweiler, R., Blatter, M.-C., Estreicher, A., Gasteiger, E., Martin, M.J., Michoud, K., O’Donovan, C., Phan, I., Pilbout, S., Schneider, M.: The SWISS-PROT protein knowledgebase and its supplement TrEMBL in 2003. Nucleic Acids Research 31, 365–370 (2003)CrossRefGoogle Scholar
  6. 6.
    Bottou, L., Bengio, Y.: Convergence properties of the k-means algorithm. In: Tesauro, G., Touretzky, D.S., Leen, T.K. (eds.) NIPS 1994, pp. 585–592. MIT, Cambridge (1995)Google Scholar
  7. 7.
    Cottrell, M., Fort, J.C., Pagès, G.: Theoretical aspects of the SOM algorithm. Neurocomputing 21, 119–138 (1999)CrossRefzbMATHGoogle Scholar
  8. 8.
    Cottrell, M., Hammer, B., Hasenfuss, A., Villmann, T.: Batch and median neural gas. Neural Networks 19, 762–771 (2006)CrossRefzbMATHGoogle Scholar
  9. 9.
    Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification. John Wiley & Sons, New York (2001)zbMATHGoogle Scholar
  10. 10.
    Fort, J.-C., Letrémy, P., Cottrell, M.: Advantages and drawbacks of the Batch Kohonen algorithm. In: Verleysen, M. (ed.) ESANN 2002, D Facto, pp. 223–230 (2002)Google Scholar
  11. 11.
    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
  12. 12.
    Frey, B.J., Dueck, D.: Clustering by passing messages between data points. Science 315, 972–976 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    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
  14. 14.
    Gisbrecht, A., Mokbel, B., Hammer, B.: Relational generative topographic map. Neurocomputing 74, 1359–1371 (2011)CrossRefGoogle Scholar
  15. 15.
    Hammer, B., Hasenfuss, A.: Topographic mapping of large dissimilarity datasets. Neural Computation 22(9), 2229–2284 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Hammer, B., Hasenfuss, A., Rossi, F.: Median topographic maps for biological data sets. In: Biehl, M., Hammer, B., Verleysen, M., Villmann, T. (eds.) Similarity-Based Clustering. LNCS, vol. 5400, pp. 92–117. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  17. 17.
    Hathaway, R.J., Bezdek, J.C.: Nerf c-means: Non-Euclidean relational fuzzy clustering. Pattern Recognition 27(3), 429–437 (1994)CrossRefGoogle Scholar
  18. 18.
    Heskes, T.: Self-organizing maps, vector quantization, and mixture modeling. IEEE Transactions on Neural Networks 12, 1299–1305 (2001)CrossRefGoogle Scholar
  19. 19.
    Keim, D.A., Mansmann, F., Schneidewind, J., Thomas, J., Ziegler, H.: Visual analytics: Scope and challenges. In: Simoff, S., Boehlen, M.H., Mazeika, A. (eds.) Visual Data Mining: Theory, Techniques and Tools for Visual Analytics. LNCS, Springer, Heidelberg (2008)Google Scholar
  20. 20.
    Kohonen, T. (ed.): Self-Organizing Maps, 3rd edn. Springer, New York (2001)zbMATHGoogle Scholar
  21. 21.
    Kohonen, T., Somervuo, P.: How to make large self-organizing maps for nonvectorial data. Neural Networks 15, 945–952 (2002)CrossRefGoogle Scholar
  22. 22.
    Lundsteen, C., J-Phillip, Granum, E.: Quantitative analysis of 6985 digitized trypsin g-banded human metaphase chromosomes. Clinical Genetics 18, 355–370 (1980)CrossRefGoogle Scholar
  23. 23.
    Martinetz, T., Berkovich, S., Schulten, K.: Neural-gas Network for Vector Quantization and its Application to Time-Series Prediction. IEEE-Transactions on Neural Networks 4(4), 558–569 (1993)CrossRefGoogle Scholar
  24. 24.
    Mevissen, H., Vingron, M.: Quantifying the local reliability of a sequence alignment. Protein Engineering 9, 127–132 (1996)CrossRefGoogle Scholar
  25. 25.
    Neuhaus, M., Bunke, H.: Edit distance based kernel functions for structural pattern classification. Pattern Recognition 39(10), 1852–1863 (2006)CrossRefzbMATHGoogle Scholar
  26. 26.
    Ontrup, J., Ritter, H.: Hyperbolic self-organizing maps for semantic navigation. In: Dietterich, T., Becker, S., Ghahramani, Z. (eds.) Advances in Neural Information Processing Systems, vol. 14, pp. 1417–1424. MIT Press, Cambridge (2001)Google Scholar
  27. 27.
    Pardalos, P.M., Vavasis, S.A.: Quadratic programming with one negative eigenvalue is NP hard. Journal of Global Optimization 1, 15–22 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Williams, C., Seeger, M.: Using the Nyström method to speed up kernel machines. In: Advances in Neural Information Processing Systems, vol. 13, pp. 682–688. MIT Press, Cambridge (2001)Google Scholar
  29. 29.
    Yin, H.: ViSOM - A novel method for multivariate data projection and structure visualisation. IEEE Trans. on Neural Networks 13(1), 237–243 (2002)CrossRefGoogle Scholar
  30. 30.
    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
  31. 31.
    Zhu, X., Hammer, B.: Patch affinity propagation. In: European Symposium on Artificial Neural Networks (to appear, 2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Barbara Hammer
    • 1
  • Andrej Gisbrecht
    • 1
  • Alexander Hasenfuss
    • 2
  • Bassam Mokbel
    • 1
  • Frank-Michael Schleif
    • 1
  • Xibin Zhu
    • 1
  1. 1.CITEC centre of excellenceBielefeld UniversityGermany
  2. 2.Computing CentreTU ClausthalGermany

Personalised recommendations