Skip to main content
SpringerLink
Log in

Topographic Mapping of Dissimilarity Data

  • Conference paper
Advances in Self-Organizing Maps (WSOM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6731))

Included in the following conference series:

Abstract

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.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alex, N., Hasenfuss, A., Hammer, B.: Patch clustering for massive data sets. Neurocomputing 72(7-9), 1455–1469 (2009)

    Article  Google Scholar 

  2. Bishop, C.: Pattern Recognition and Machine Learning. Springer, Heidelberg (2007)

    MATH  Google Scholar 

  3. Bishop, C.M., Williams, C.K.I.: GTM: The generative topographic mapping. Neural Computation 10, 215–234 (1998)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. Cottrell, M., Fort, J.C., Pagès, G.: Theoretical aspects of the SOM algorithm. Neurocomputing 21, 119–138 (1999)

    Article  MATH  Google Scholar 

  8. Cottrell, M., Hammer, B., Hasenfuss, A., Villmann, T.: Batch and median neural gas. Neural Networks 19, 762–771 (2006)

    Article  MATH  Google Scholar 

  9. Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification. John Wiley & Sons, New York (2001)

    MATH  Google Scholar 

  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. 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)

    Article  Google Scholar 

  12. Frey, B.J., Dueck, D.: Clustering by passing messages between data points. Science 315, 972–976 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  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. Gisbrecht, A., Mokbel, B., Hammer, B.: Relational generative topographic map. Neurocomputing 74, 1359–1371 (2011)

    Article  Google Scholar 

  15. Hammer, B., Hasenfuss, A.: Topographic mapping of large dissimilarity datasets. Neural Computation 22(9), 2229–2284 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  17. Hathaway, R.J., Bezdek, J.C.: Nerf c-means: Non-Euclidean relational fuzzy clustering. Pattern Recognition 27(3), 429–437 (1994)

    Article  Google Scholar 

  18. Heskes, T.: Self-organizing maps, vector quantization, and mixture modeling. IEEE Transactions on Neural Networks 12, 1299–1305 (2001)

    Article  Google Scholar 

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

    MATH  Google Scholar 

  21. Kohonen, T., Somervuo, P.: How to make large self-organizing maps for nonvectorial data. Neural Networks 15, 945–952 (2002)

    Article  Google Scholar 

  22. Lundsteen, C., J-Phillip, Granum, E.: Quantitative analysis of 6985 digitized trypsin g-banded human metaphase chromosomes. Clinical Genetics 18, 355–370 (1980)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  24. Mevissen, H., Vingron, M.: Quantifying the local reliability of a sequence alignment. Protein Engineering 9, 127–132 (1996)

    Article  Google Scholar 

  25. Neuhaus, M., Bunke, H.: Edit distance based kernel functions for structural pattern classification. Pattern Recognition 39(10), 1852–1863 (2006)

    Article  MATH  Google Scholar 

  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. Pardalos, P.M., Vavasis, S.A.: Quadratic programming with one negative eigenvalue is NP hard. Journal of Global Optimization 1, 15–22 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  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. Yin, H.: ViSOM - A novel method for multivariate data projection and structure visualisation. IEEE Trans. on Neural Networks 13(1), 237–243 (2002)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  31. Zhu, X., Hammer, B.: Patch affinity propagation. In: European Symposium on Artificial Neural Networks (to appear, 2011)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CITEC centre of excellence, Bielefeld University, Germany

    Barbara Hammer, Andrej Gisbrecht, Bassam Mokbel, Frank-Michael Schleif & Xibin Zhu

  2. Computing Centre, TU Clausthal, Germany

    Alexander Hasenfuss

Authors
  1. Barbara Hammer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrej Gisbrecht
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alexander Hasenfuss
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Bassam Mokbel
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Frank-Michael Schleif
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Xibin Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Information and Computer Science, Aalto University School of Science, 00076, Aalto, Finland

    Jorma Laaksonen  & Timo Honkela  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hammer, B., Gisbrecht, A., Hasenfuss, A., Mokbel, B., Schleif, FM., Zhu, X. (2011). Topographic Mapping of Dissimilarity Data. In: Laaksonen, J., Honkela, T. (eds) Advances in Self-Organizing Maps. WSOM 2011. Lecture Notes in Computer Science, vol 6731. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21566-7_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-21566-7_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21565-0

  • Online ISBN: 978-3-642-21566-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation