Class Representative Computation Using Graph Embedding

  • Fahri Aydos
  • Ahmet Soran
  • M. Fatih Demirci
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8156)

Abstract

Due to representative power of graphs, graph-based object recognition has received a great deal of research attention in literature. Given an object represented as a graph, performing graph matching with each member of the database in order to locate the graph which most resembles the query is inefficient especially when the size of the database is large. In this paper we propose an algorithm which represents the graphs belonging to a particular set as points through graph embedding and operates in the vector space to compute the representative of the set. We use the k-means clustering algorithm to learn centroids forming the representatives. Once the representative of each set is obtained, we embed the query into the vector space and compute the matching in this space. The query is classified into the most similar representative of a set. This way, we are able to overcome the complexity of graph matching and still perform the classification for the query effectively. Experimental evaluation of the proposed work demonstrates the efficiency, effectiveness, and stability of the overall approach.

Keywords

object recognition graph embedding clustering 

References

  1. 1.
    Babilon, R., Matousek, J., Maxová, J., Valtr, P.: Low-distortion embeddings of trees. Journal of Graph Algorithms and Applications 7(4), 399–409 (2003)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Blum, H.: Biological shape and visual science (part i). Journal of Theoretical Biology 38(2), 205–287 (1973), http://www.sciencedirect.com/science/article/B6WMD-4F1Y9M7-D5/2/1b17959a78e759a89f524d9f3eae0938 CrossRefGoogle Scholar
  3. 3.
    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), http://dx.doi.org/10.1016/S0167-86559900094-X Google Scholar
  4. 4.
    Demirci, M.: Retrieving 2D shapes using caterpillar decomposition. Machine Vision and Applications 24(2), 435–445 (2013)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Demirci, M., Osmanlioglu, Y., Shokoufandeh, A., Dickinson, S.: Efficient many-to-many feature matching under the ℓ1 norm. Computer Vision and Image Understanding 115(7), 976–983 (2011), http://dx.doi.org/10.1016/j.cviu.2010.12.012 CrossRefGoogle Scholar
  6. 6.
    Demirci, M., Shokoufandeh, A., Keselman, Y., Bretzner, L., Dickinson, S.: Object recognition as many-to-many feature matching. International Journal of Computer Vision 69(2), 203–222 (2006)CrossRefGoogle Scholar
  7. 7.
    Ferrer, M., Valveny, E., Serratosa, F., Riesen, K., Bunke, H.: An approximate algorithm for median graph computation using graph embedding. In: 19th International Conference on Pattern Recognition, pp. 1–4. IEEE (2008)Google Scholar
  8. 8.
    Giblin, P., Kimia, B.: On the local form and transitions of symmetry sets, medial axes, and shocks. International Journal of Computer Vision 54(1-3), 143–156 (2003)CrossRefMATHGoogle Scholar
  9. 9.
    Huttenlocher, D., Klanderman, D., Rucklige, A.: Comparing images using the Hausdorff distance. IEEE Transactions on Pattern Analysis and Machine Intelligence 15(9), 850–863 (1993), citeseer.ist.psu.edu/huttenlocher93comparing.html CrossRefGoogle Scholar
  10. 10.
    Indyk, P.: Algorithmic aspects of geometric embeddings. In: Proceedings of the 42nd Annual Symposium on Foundations of Computer Science (2001)Google Scholar
  11. 11.
    Jiang, X., Münger, A., Bunke, H.: On median graphs: Properties, algorithms, and applications 23(10), 1144–1151 (2001)Google Scholar
  12. 12.
    Lozano, M., Escolano, F.: Protein classification by matching and clustering surface graphs. Pattern Recognition 39(4), 539–551 (2006)CrossRefMATHGoogle Scholar
  13. 13.
    Matousek, J.: On embedding trees into uniformly convex banach spaces. Israel Journal of Mathematics 237, 221–237 (1999)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Torsello, A., Hancock, E.: Graph embedding using tree edit-union. Pattern recognition 40(5), 1393–1405 (2007)CrossRefMATHGoogle Scholar
  15. 15.
    Torsello, A., Hancock, E.R.: Learning shape-classes using a mixture of tree-unions. IEEE Transactions on Pattern Analysis and Machine Intelligence 28(6), 954–967 (2006)CrossRefGoogle Scholar
  16. 16.
    Torsello, A., Robles-Kelly, A., Hancock, E.: Discovering shape classes using tree edit-distance and pairwise clustering. International Journal of Computer Vision 72(3), 259–285 (2007)CrossRefGoogle Scholar
  17. 17.
    Weiszfeld, E.: Sur le point pour lequel la somme des distances de n points donns est minimum. Thoku Mathematical Journal 43, 355–386 (1937)Google Scholar
  18. 18.
    Xiao, B., Torsello, A., Hancock, E.: Isotree: Tree clustering via metric embedding. Neurocomputing 71(10), 2029–2036 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Fahri Aydos
    • 1
  • Ahmet Soran
    • 1
  • M. Fatih Demirci
    • 1
  1. 1.Computer Engineering DepartmentTOBB University of Economics and TechnologyAnkaraTurkey

Personalised recommendations