A Hypergraph-Based Model for Graph Clustering: Application to Image Indexing

In this paper, we introduce a prototype-based clustering algorithm dealing with graphs. We propose a hypergraph-based model for graph data sets by allowing clusters overlapping. More precisely, in this representation one graph can be assigned to more than one cluster. Using the concept of the graph median and a given threshold, the proposed algorithm detects automatically the number of classes in the graph database. We consider clusters as hyperedges in our hypergraph model and we define a retrieval technique indexing the database with hyperedge centroids. This model is interesting to travel the data set and efficient to cluster and retrieve graphs.

[1]  Sameer A. Nene,et al.  Columbia Object Image Library (COIL100) , 1996 .

[2]  Horst Bunke,et al.  Matching of Hypergraphs - Algorithms, Applications, and Experiments , 2008, Applied Pattern Recognition.

[3]  Joachim Hornegger,et al.  Applied Pattern Recognition , 1999 .

[4]  Edwin R. Hancock,et al.  Spectral Feature Vectors for Graph Clustering , 2002, SSPR/SPR.

[5]  Ali Shokoufandeh,et al.  A Unified Framework for Indexing and Matching Hierarchical Shape Structures , 2001, IWVF.

[6]  Mads Nielsen,et al.  Computer Vision — ECCV 2002 , 2002, Lecture Notes in Computer Science.

[7]  Salvatore Tabbone,et al.  Graph Matching Based on Node Signatures , 2009, GbRPR.

[8]  Philip N. Klein,et al.  Shock-Based Indexing into Large Shape Databases , 2002, ECCV.

[9]  Robert F. Ling,et al.  Cluster analysis algorithms for data reduction and classification of objects , 1981 .

[10]  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.

[11]  J. H. Ward.  Hierarchical Grouping to Optimize an Objective Function , 1963 .

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

[13]  Ernest Valveny,et al.  Report on the Second Symbol Recognition Contest , 2005, GREC.

[14]  Robert M. Haralick,et al.  Organization of Relational Models for Scene Analysis , 1982, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[15]  Shengrui Wang,et al.  A graph clustering algorithm with applications to content-based image retrieval , 2003, Proceedings of the 2003 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.03EX693).

[16]  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.

[17]  T. Ravindra Babu,et al.  Comparison of genetic algorithm based prototype selection schemes , 2001, Pattern Recognit..

[18]  Edwin R. Hancock,et al.  Spectral Embedding of Feature Hypergraphs , 2008, SSPR/SPR.

[19]  James M. Keller,et al.  Fuzzy Models and Algorithms for Pattern Recognition and Image Processing , 1999 .

[20]  Horst Bunke,et al.  Graph Clustering Using the Weighted Minimum Common Supergraph , 2003, GbRPR.

[21]  Gabriella Sanniti di Baja,et al.  Visual Form 2001 , 2001, Lecture Notes in Computer Science.

[22]  Daniel P. Huttenlocher,et al.  Efficient Graph-Based Image Segmentation , 2004, International Journal of Computer Vision.

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

[24]  K. Boyer,et al.  Organizing Large Structural Modelbases , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[25]  C. Berge.  Graphes et hypergraphes , 1970 .

[26]  Christopher G. Harris,et al.  A Combined Corner and Edge Detector , 1988, Alvey Vision Conference.

[27]  Pietro Perona,et al.  Beyond pairwise clustering , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

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

[29]  Andrea Torsello,et al.  Beyond partitions: Allowing overlapping groups in pairwise clustering , 2008, 2008 19th International Conference on Pattern Recognition.