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

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.

[1]  Francisco Escolano,et al.  Graph-Based Representations in Pattern Recognition, 6th IAPR-TC-15 International Workshop, GbRPR 2007, Alicante, Spain, June 11-13, 2007, Proceedings , 2007, GbRPR.

[2]  Anil K. Jain,et al.  Data clustering: a review , 1999, CSUR.

[3]  William M. Rand,et al.  Objective Criteria for the Evaluation of Clustering Methods , 1971 .

[4]  Piotr Indyk,et al.  Algorithmic applications of low-distortion geometric embeddings , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[5]  Horst Bunke,et al.  Self-organizing map for clustering in the graph domain , 2002, Pattern Recognit. Lett..

[6]  Edwin R. Hancock,et al.  Structural, Syntactic, and Statistical Pattern Recognition, Joint IAPR International Workshop, SSPR&SPR 2010, Cesme, Izmir, Turkey, August 18-20, 2010. Proceedings , 2010, SSPR/SPR.

[7]  Horst Bunke,et al.  Inexact graph matching for structural pattern recognition , 1983, Pattern Recognit. Lett..

[8]  Alberto Sanfeliu,et al.  Synthesis of Function-Described Graphs and Clustering of Attributed Graphs , 2002, Int. J. Pattern Recognit. Artif. Intell..

[9]  Kaspar Riesen,et al.  Fast Suboptimal Algorithms for the Computation of Graph Edit Distance , 2006, SSPR/SPR.

[10]  J. Dunn.  Well-Separated Clusters and Optimal Fuzzy Partitions , 1974 .

[11]  Horst Bunke,et al.  On Median Graphs: Properties, Algorithms, and Applications , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  Alberto Sanfeliu,et al.  Synthesis of Median Spectral Graph , 2005, IbPRIA.

[13]  M. Shirosaki.  Another proof of the defect relation for moving targets , 1991 .

[14]  Edwin R. Hancock,et al.  Spectral embedding of graphs , 2003, Pattern Recognit..

[15]  Kaspar Riesen,et al.  IAM Graph Database Repository for Graph Based Pattern Recognition and Machine Learning , 2008, SSPR/SPR.

[16]  Kaspar Riesen,et al.  Bipartite Graph Matching for Computing the Edit Distance of Graphs , 2007, GbRPR.

[17]  Edwin R. Hancock,et al.  Pattern Vectors from Algebraic Graph Theory , 2005, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  Edwin R. Hancock,et al.  A Riemannian approach to graph embedding , 2007, Pattern Recognit..

[19]  Robert P. W. Duin,et al.  Prototype selection for dissimilarity-based classifiers , 2006, Pattern Recognit..

[20]  Horst Bunke,et al.  Weighted Mean of a Pair of Graphs , 2001, Computing.

[21]  Thomas G. Dietterich.  What is machine learning? , 2020, Archives of Disease in Childhood.

[22]  Horst Bunke,et al.  Combinatorial search versus genetic algorithms: A case study based on the generalized median graph problem , 1999, Pattern Recognit. Lett..

[23]  Kaspar Riesen,et al.  Graph Embedding in Vector Spaces by Means of Prototype Selection , 2007, GbRPR.

[24]  Andrea Torsello,et al.  Clustering shock trees , 2001 .

[25]  Shengrui Wang,et al.  Median graph computation for graph clustering , 2006, Soft Comput..

[26]  Ernest Valveny,et al.  An approximate algorithm for median graph computation using graph embedding , 2008, 2008 19th International Conference on Pattern Recognition.

[27]  Abraham Kandel,et al.  Graph-Theoretic Techniques for Web Content Mining , 2005, Series in Machine Perception and Artificial Intelligence.

[28]  King-Sun Fu,et al.  A distance measure between attributed relational graphs for pattern recognition , 1983, IEEE Transactions on Systems, Man, and Cybernetics.