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Graph-Based k-Means Clustering: A Comparison of the Set Median versus the Generalized Median Graph

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Computer Analysis of Images and Patterns (CAIP 2009)

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Abstract

In this paper we propose the application of the generalized median graph in a graph-based k-means clustering algorithm. In the graph-based k-means algorithm, the centers of the clusters have been traditionally represented using the set median graph. We propose an approximate method for the generalized median graph computation that allows to use it to represent the centers of the clusters. Experiments on three databases show that using the generalized median graph as the clusters representative yields better results than the set median graph.

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References

  1. Jain, A.K., Murty, M.N., Flynn, P.J.: Data clustering: A review. ACM Comput. Surv. 31(3), 264–323 (1999)

    Article  Google Scholar 

  2. Günter, S., Bunke, H.: Self-organizing map for clustering in the graph domain. Pattern Recognition Letters 23(4), 405–417 (2002)

    Article  MATH  Google Scholar 

  3. Serratosa, F., Alquézar, R., Sanfeliu, A.: Synthesis of function-described graphs and clustering of attributed graphs. International Journal of Pattern Recognition and Artificial Intelligence 16(6), 621–656 (2002)

    Article  Google Scholar 

  4. Luo, B., Robles-Kelly, A., Torsello, A., Wilson, R.C., Hancock, E.: Clustering shock trees. In: Proc. 3rd IAPR Workshop Graph-Based Representations in Pattern Recognition, pp. 217–228 (2001)

    Google Scholar 

  5. Schenker, A., Bunke, H., Last, M., Kandel, A.: Graph-Theoretic Techniques for Web Content Mining. World Scientific Publishing, USA (2005)

    MATH  Google Scholar 

  6. Jiang, X., Münger, A., Bunke, H.: On median graphs: Properties, algorithms, and applications. IEEE Trans. Pattern Anal. Mach. Intell. 23(10), 1144–1151 (2001)

    Article  Google Scholar 

  7. Bunke, H., Münger, A., Jiang, X.: Combinatorial search versus genetic algorithms: A case study based on the generalized median graph problem. Pattern Recognition Letters 20(11-13), 1271–1277 (1999)

    Article  Google Scholar 

  8. Hlaoui, A., Wang, S.: Median graph computation for graph clustering. Soft Comput. 10(1), 47–53 (2006)

    Article  Google Scholar 

  9. Ferrer, M., Serratosa, F., Sanfeliu, A.: Synthesis of median spectral graph. In: Marques, J.S., Pérez de la Blanca, N., Pina, P. (eds.) IbPRIA 2005. LNCS, vol. 3523, pp. 139–146. Springer, Heidelberg (2005)

    Google Scholar 

  10. Riesen, K., Neuhaus, M., Bunke, H.: Graph embedding in vector spaces by means of prototype selection. In: Escolano, F., Vento, M. (eds.) GbRPR 2007. LNCS, vol. 4538, pp. 383–393. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  11. Bunke, H., Günter, S.: Weighted mean of a pair of graphs. Computing 67(3), 209–224 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. Mitchell, T.M.: Machine Learning. McGraw-Hill, New York (1997)

    MATH  Google Scholar 

  13. Bunke, H., Allerman, G.: Inexact graph matching for structural pattern recognition. Pattern Recognition Letters 1(4), 245–253 (1983)

    Article  MATH  Google Scholar 

  14. Sanfeliu, A., Fu, K.: A distance measure between attributed relational graphs for pattern recognition. IEEE Transactions on Systems, Man and Cybernetics 13(3), 353–362 (1983)

    MATH  Google Scholar 

  15. Indyk, P.: Algorithmic applications of low-distortion geometric embeddings. In: IEEE Symposium on Foundations of Computer Science, pp. 10–33 (2001)

    Google Scholar 

  16. Luo, B., Wilson, R.C., Hancock, E.R.: Spectral embedding of graphs. Pattern Recognition 36(10), 2213–2230 (2003)

    Article  MATH  Google Scholar 

  17. Wilson, R.C., Hancock, E.R., Luo, B.: Pattern vectors from algebraic graph theory. IEEE Trans. Pattern Anal. Mach. Intell. 27(7), 1112–1124 (2005)

    Article  Google Scholar 

  18. Robles-Kelly, A., Hancock, E.R.: A Riemannian approach to graph embedding. Pattern Recognition 40(3), 1042–1056 (2007)

    Article  MATH  Google Scholar 

  19. Pekalska, E., Duin, R.P.W., Paclík, P.: Prototype selection for dissimilarity-based classifiers. Pattern Recognition 39(2), 189–208 (2006)

    Article  MATH  Google Scholar 

  20. Ferrer, M., Valveny, E., Serratosa, F., Riesen, K., Bunke, H.: An approximate algorithm for median graph computation using graph embedding. In: Proceedings of 19th ICPR, pp. 287–297 (2008)

    Google Scholar 

  21. Neuhaus, M., Riesen, K., Bunke, H.: Fast suboptimal algorithms for the computation of graph edit distance. In: Yeung, D.-Y., Kwok, J.T., Fred, A., Roli, F., de Ridder, D. (eds.) SSPR 2006 and SPR 2006. LNCS, vol. 4109, pp. 163–172. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  22. Riesen, K., Neuhaus, M., Bunke, H.: Bipartite graph matching for computing the edit distance of graphs. In: Escolano, F., Vento, M. (eds.) GbRPR 2007. LNCS, vol. 4538, pp. 1–12. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  23. Weiszfeld, E.: Sur le point pour lequel la somme des distances de n points donnés est minimum. Tohoku Math. Journal (43), 355–386 (1937)

    Google Scholar 

  24. Riesen, K., Bunke, H.: IAM graph database repository for graph based pattern recognition and machine learning. In: da Vitoria Lobo, N., Kasparis, T., Roli, F., Kwok, J.T., Georgiopoulos, M., Anagnostopoulos, G.C., Loog, M. (eds.) S+SSPR 2008. LNCS, vol. 5342, pp. 287–297. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  25. Rand, W.M.: Objective criteria for the evaluation of clustering methods. Journal of the American Statistival Association 66, 846–850 (1971)

    Article  Google Scholar 

  26. Dunn, J.: Well separated clusters and optimal fuzzy partitions. Journal of Cibernetics 4, 95–104 (1974)

    Article  MathSciNet  Google Scholar 

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Ferrer, M., Valveny, E., Serratosa, F., Bardají, I., Bunke, H. (2009). Graph-Based k-Means Clustering: A Comparison of the Set Median versus the Generalized Median Graph. In: Jiang, X., Petkov, N. (eds) Computer Analysis of Images and Patterns. CAIP 2009. Lecture Notes in Computer Science, vol 5702. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03767-2_42

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  • DOI: https://doi.org/10.1007/978-3-642-03767-2_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03766-5

  • Online ISBN: 978-3-642-03767-2

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