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
Jain, A.K., Murty, M.N., Flynn, P.J.: Data clustering: A review. ACM Comput. Surv. 31(3), 264–323 (1999)
Günter, S., Bunke, H.: Self-organizing map for clustering in the graph domain. Pattern Recognition Letters 23(4), 405–417 (2002)
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)
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)
Schenker, A., Bunke, H., Last, M., Kandel, A.: Graph-Theoretic Techniques for Web Content Mining. World Scientific Publishing, USA (2005)
Jiang, X., Münger, A., Bunke, H.: On median graphs: Properties, algorithms, and applications. IEEE Trans. Pattern Anal. Mach. Intell. 23(10), 1144–1151 (2001)
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)
Hlaoui, A., Wang, S.: Median graph computation for graph clustering. Soft Comput. 10(1), 47–53 (2006)
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)
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)
Bunke, H., Günter, S.: Weighted mean of a pair of graphs. Computing 67(3), 209–224 (2001)
Mitchell, T.M.: Machine Learning. McGraw-Hill, New York (1997)
Bunke, H., Allerman, G.: Inexact graph matching for structural pattern recognition. Pattern Recognition Letters 1(4), 245–253 (1983)
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)
Indyk, P.: Algorithmic applications of low-distortion geometric embeddings. In: IEEE Symposium on Foundations of Computer Science, pp. 10–33 (2001)
Luo, B., Wilson, R.C., Hancock, E.R.: Spectral embedding of graphs. Pattern Recognition 36(10), 2213–2230 (2003)
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)
Robles-Kelly, A., Hancock, E.R.: A Riemannian approach to graph embedding. Pattern Recognition 40(3), 1042–1056 (2007)
Pekalska, E., Duin, R.P.W., Paclík, P.: Prototype selection for dissimilarity-based classifiers. Pattern Recognition 39(2), 189–208 (2006)
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)
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)
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)
Weiszfeld, E.: Sur le point pour lequel la somme des distances de n points donnés est minimum. Tohoku Math. Journal (43), 355–386 (1937)
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)
Rand, W.M.: Objective criteria for the evaluation of clustering methods. Journal of the American Statistival Association 66, 846–850 (1971)
Dunn, J.: Well separated clusters and optimal fuzzy partitions. Journal of Cibernetics 4, 95–104 (1974)
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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
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