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How Many Dissimilarity/Kernel Self Organizing Map Variants Do We Need?

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Advances in Self-Organizing Maps and Learning Vector Quantization

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 295))

Abstract

In numerous applicative contexts, data are too rich and too complex to be represented by numerical vectors. A general approach to extend machine learning and data mining techniques to such data is to really on a dissimilarity or on a kernel that measures how different or similar two objects are.

This approach has been used to define several variants of the Self Organizing Map (SOM). This paper reviews those variants in using a common set of notations in order to outline differences and similarities between them. It discuss the advantages and drawbacks of the variants, as well as the actual relevance of the dissimilarity/kernel SOM for practical applications.

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References

  1. Ambroise, C., Govaert, G.: Analyzing dissimilarity matrices via Kohonen maps. In: Proceedings of 5th Conference of the International Federation of Classification Societies (IFCS 1996), Kobe (Japan), vol. 2, pp. 96–99 (March 1996)

    Google Scholar 

  2. Andras, P.: Kernel-Kohonen networks. International Journal of Neural Systems 12, 117–135 (2002)

    Article  Google Scholar 

  3. Aronszajn, N.: Theory of reproducing kernels. Transactions of the American Mathematical Society 68(3), 337–404 (1950)

    Article  MathSciNet  Google Scholar 

  4. Becker, A., Cleveland, S.: Brushing scatterplots. Technometrics 29(2), 127–142 (1987)

    Article  MathSciNet  Google Scholar 

  5. Boulet, R., Jouve, B., Rossi, F., Villa, N.: Batch kernel SOM and related Laplacian methods for social network analysis. Neurocomputing 71(7-9), 1257–1273 (2008)

    Article  Google Scholar 

  6. Buhmann, J.M., Hofmann, T.: A maximum entropy approach to pairwise data clustering. In: Proceedings of the International Conference on Pattern Recognition, Hebrew University, Jerusalem, Israel, vol. II, pp. 207–212. IEEE Computer Society Press (1994)

    Google Scholar 

  7. Conan-Guez, B., Rossi, F.: Speeding up the dissimilarity self-organizing maps by branch and bound. In: Sandoval, F., Prieto, A.G., Cabestany, J., Graña, M. (eds.) IWANN 2007. LNCS, vol. 4507, pp. 203–210. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  8. Conan-Guez, B., Rossi, F.: Accélération des cartes auto-organisatrices sur tableau de dissimilarités par séparation et évaluation. Revue des Nouvelles Technologies de l’Information, pp. 1–16 (June 2008), RNTI-C-2 Classification: points de vue croisés. Rédacteurs invités : Mohamed Nadif et François-Xavier Jollois

    Google Scholar 

  9. Conan-Guez, B., Rossi, F.: Dissimilarity clustering by hierarchical multi-level refinement. In: Proceedings of the XXth European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN 2012), Bruges, Belgique, pp. 483–488 (March 2012)

    Google Scholar 

  10. Conan-Guez, B., Rossi, F., El Golli, A.: Fast algorithm and implementation of dissimilarity self-organizing maps. Neural Networks 19(6-7), 855–863 (2006)

    Article  Google Scholar 

  11. Cottrell, M., Hammer, B., Hasenfuß, A., Villmann, T.: Batch and median neural gas. Neural Networks 19(6), 762–771 (2006)

    Article  Google Scholar 

  12. El Golli, A., Conan-Guez, B., Rossi, F.: Self organizing map and symbolic data. Journal of Symbolic Data Analysis 2(1) (November 2004)

    Google Scholar 

  13. El Golli, A., Conan-Guez, B., Rossi, F.: A self organizing map for dissimilarity data. In: Banks, D., House, L., McMorris, F.R., Arabie, P., Gaul, W. (eds.) Classification, Clustering, and Data Mining Applications (Proceedings of IFCS 2004), Chicago, Illinois, pp. 61–68. IFCS, Springer (2004)

    Google Scholar 

  14. Fort, J.C., Letremy, P., Cottrell, M.: Advantages and drawbacks of the batch kohonen algorithm. In: Proceedings of Xth European Symposium on Artificial Neural Networks (ESANN 2002), vol. 2, pp. 223–230 (2002)

    Google Scholar 

  15. Gärtner, T., Lloyd, J.W., Flach, P.A.: Kernels and distances for structured data. Machine Learning 57(3), 205–232 (2004)

    Article  Google Scholar 

  16. Gisbrecht, A., Mokbel, B., Schleif, F.M., Zhu, X., Hammer, B.: Linear time relational prototype based learning. Int. J. Neural Syst. 22(5) (2012)

    Google Scholar 

  17. Graepel, T., Burger, M., Obermayer, K.: Self-organizing maps: Generalizations and new optimization techniques. Neurocomputing 21, 173–190 (1998)

    Article  Google Scholar 

  18. Graepel, T., Obermayer, K.: A stochastic self-organizing map for proximity data. Neural Computation 11(1), 139–155 (1999)

    Article  Google Scholar 

  19. Hammer, B., Gisbrecht, A., Hasenfuss, A., Mokbel, B., Schleif, F.-M., Zhu, X.: Topographic mapping of dissimilarity data. In: Laaksonen, J., Honkela, T. (eds.) WSOM 2011. LNCS, vol. 6731, pp. 1–15. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  21. Hammer, B., Hasenfuss, A., Rossi, F., Strickert, M.: Topographic processing of relational data. In: Proceedings of the 6th International Workshop on Self-Organizing Maps (WSOM 2007), Bielefeld, Germany (September 2007)

    Google Scholar 

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

    Article  Google Scholar 

  23. Hathaway, R.J., Davenport, J.W., Bezdek, J.C.: Relational duals of the c-means clustering algorithms. Pattern Recognition 22(2), 205–212 (1989)

    Article  MathSciNet  Google Scholar 

  24. Hendrickson, B., Leland, R.: A multilevel algorithm for partitioning graphs. In: Proceedings of the 1995 ACM/IEEE Conference on Supercomputing (CDROM), Supercomputing 1995. ACM, New York (1995), http://doi.acm.org/10.1145/224170.224228

    Google Scholar 

  25. Heskes, T., Kappen, B.: Error potentials for self-organization. In: Proceedings of 1993 IEEE International Conference on Neural Networks (Joint FUZZ-IEEE 1993 and ICNN 1993 [IJCNN 1993]), vol. III, pp. 1219–1223. IEEE/INNS, San Francisco (1993)

    Google Scholar 

  26. Hofmann, T., Buhmann, J.M.: Pairwise data clustering by deterministic annealing. IEEE Transactions on Pattern Analysis and Machine Intelligence 19(1), 1–14 (1997)

    Article  Google Scholar 

  27. Kohonen, T.: Self-organizing maps of symbol strings. Technical report A42, Laboratory of computer and information science, Helsinki University of Technology, Finland (1996)

    Google Scholar 

  28. Kohonen, T.: Self-Organizing Maps, 3rd edn. Springer Series in Information Sciences, vol. 30. Springer (2001)

    Google Scholar 

  29. Kohonen, T., Somervuo, P.J.: Self-organizing maps of symbol strings. Neurocomputing 21, 19–30 (1998)

    Article  Google Scholar 

  30. Kohonen, T., Somervuo, P.J.: How to make large self-organizing maps for nonvectorial data. Neural Networks 15(8), 945–952 (2002)

    Article  Google Scholar 

  31. Mac Donald, D., Fyfe, C.: The kernel self organising map. In: Proceedings of 4th International Conference on Knowledge-Based Intelligence Engineering Systems and Applied Technologies, pp. 317–320 (2000)

    Google Scholar 

  32. Martín-Merino, M., Muñoz, A.: Extending the SOM algorithm to non-euclidean distances via the kernel trick. In: Pal, N.R., Kasabov, N., Mudi, R.K., Pal, S., Parui, S.K. (eds.) ICONIP 2004. LNCS, vol. 3316, pp. 150–157. Springer, Heidelberg (2004), http://dx.doi.org/10.1007/978-3-540-30499-9_22

    Chapter  Google Scholar 

  33. Müllner, D.: Modern hierarchical, agglomerative clustering algorithms. Lecture Notes in Computer Science 3918(1973), 29 (2011), http://arxiv.org/abs/1109.2378

  34. Olteanu, M., Villa-Vialaneix, N., Cottrell, M.: On-line relational SOM for dissimilarity data. In: Estévez, P.A., Príncipe, J.C., Zegers, P. (eds.) Advances in Self-Organizing Maps. AISC, vol. 198, pp. 13–22. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  35. Rose, K.: Deterministic annealing for clustering, compression,classification, regression, and related optimization problems. Proceedings of the IEEE 86(11), 2210–2239 (1998)

    Article  Google Scholar 

  36. Rossi, F.: Model collisions in the dissimilarity SOM. In: Proceedings of XVth European Symposium on Artificial Neural Networks (ESANN 2007), Bruges (Belgium), pp. 25–30 (April 2007)

    Google Scholar 

  37. Rossi, F., Hasenfuss, A., Hammer, B.: Accelerating relational clustering algorithms with sparse prototype representation. In: Proceedings of the 6th International Workshop on Self-Organizing Maps (WSOM 2007), Bielefeld, Germany (September 2007)

    Google Scholar 

  38. Rossi, F., Villa-Vialaneix, N.: Optimizing an organized modularity measure for topographic graph clustering: a deterministic annealing approach. Neurocomputing 73(7-9), 1142–1163 (2010)

    Article  Google Scholar 

  39. Rossi, F., Villa-Vialaneix, N.: Représentation d’un grand réseau à partir d’une classification hiérarchique de ses sommets. Journal de la Société Française de Statistique 152(3), 34–65 (2011)

    MathSciNet  MATH  Google Scholar 

  40. Schleif, F.-M., Gisbrecht, A.: Data analysis of (non-)metric proximities at linear costs. In: Hancock, E., Pelillo, M. (eds.) SIMBAD 2013. LNCS, vol. 7953, pp. 59–74. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  41. Schölkopf, B., Smola, A., Müller, K.R.: Kernel principal component analysis. In: Gerstner, W., Hasler, M., Germond, A., Nicoud, J.-D. (eds.) ICANN 1997. LNCS, vol. 1327, pp. 583–588. Springer, Heidelberg (1997)

    Google Scholar 

  42. Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press (2004)

    Google Scholar 

  43. Somervuo, P.J.: Self-organizing map of symbol strings with smooth symbol averaging. In: Workshop on Self-Organizing Maps (WSOM 2003), Hibikino, Kitakyushu, Japan (September 2003)

    Google Scholar 

  44. Somervuo, P.J.: Online algorithm for the self-organizing map of symbol strings. Neural Networks 17, 1231–1239 (2004)

    Article  Google Scholar 

  45. Ultsch, A., Siemon, H.P.: Kohonen’s self organizing feature maps for exploratory data analysis. In: Proceedings of International Neural Network Conference (INNC 1990), pp. 305–308 (1990)

    Google Scholar 

  46. Ultsch, A., Mörchen, F.: Esom-maps: tools for clustering, visualization, and classification with emergent som. Tech. Rep. 46, Department of Mathematics and Computer Science, University of Marburg, Germarny (2005)

    Google Scholar 

  47. Vesanto, J.: Som-based data visualization methods. Intelligent Data Analysis 3(2), 111–126 (1999)

    Article  Google Scholar 

  48. Vesanto, J.: Data Exploration Process Based on the Self–Organizing Map. Ph.D. thesis, Helsinki University of Technology, Espoo (Finland) (May 2002), Acta Polytechnica Scandinavica, Mathematics and Computing Series No. 115

    Google Scholar 

  49. Villa, N., Rossi, F.: A comparison between dissimilarity som and kernel som for clustering the vertices of a graph. In: Proceedings of the 6th International Workshop on Self-Organizing Maps (WSOM 2007), Bielefeld, Germany (September 2007)

    Google Scholar 

  50. Williams, C., Seeger, M.: Using the nyström method to speed up kernel machines. In: Advances in Neural Information Processing Systems 13 (2001)

    Google Scholar 

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Author information

Authors and Affiliations

  1. SAMM (EA 4543), Université Paris 1, 90, rue de Tolbiac, 75634, Paris Cedex 13, France

    Fabrice Rossi

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  1. Fabrice Rossi
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Correspondence to Fabrice Rossi .

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Editors and Affiliations

  1. Department of Mathematics, University of Applied Sciences Mittweida, Mittweida, Sachsen, Germany

    Thomas Villmann

  2. University of Applied Sciences Mittweida, Mittweida, Germany

    Frank-Michael Schleif

  3. University of Applied Sciences Mittweida, Mittweida, Germany

    Marika Kaden

  4. University of Applied Sciences Mittweida, Mittweida, Germany

    Mandy Lange

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Rossi, F. (2014). How Many Dissimilarity/Kernel Self Organizing Map Variants Do We Need?. In: Villmann, T., Schleif, FM., Kaden, M., Lange, M. (eds) Advances in Self-Organizing Maps and Learning Vector Quantization. Advances in Intelligent Systems and Computing, vol 295. Springer, Cham. https://doi.org/10.1007/978-3-319-07695-9_1

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  • DOI: https://doi.org/10.1007/978-3-319-07695-9_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07694-2

  • Online ISBN: 978-3-319-07695-9

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