A Comparison of Least Squares and Spectral Methods for Attributed Graph Matching

  • Jianfeng Lu
  • Terry Caelli
  • Jingyu Yang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3138)


In this paper, least squares and spectral methods for attributed graph matching are compared. For the least squares method, complete graphs and decomposed graph models are considered in conjunction with the least squares approximations to optimal permutation matrices. We have used a version of Umeyama’s spectral method for comparison purposes. Results clearly demonstrate how both these methods are affected by additive noise but that, in general, least squares methods are superior.


Spectral Method Input Graph Graph Match Adjacency Matrice Edge Attribute 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    van Wyk, B.J., Van Wyk, M.A.: Kronecker product graph matching. Pattern Recognition 36(9), 2019–2030 (2003)zbMATHCrossRefGoogle Scholar
  2. 2.
    El-Sonbaty, Y., Ismail, M.A.: A new algorithm for subgraph optimal isomorphism. Pattern Recognition 31(2), 205–218 (1998)CrossRefGoogle Scholar
  3. 3.
    Gold, S., Rangarajan, A.: A graduated assignment algorithm for graph matching. IEEE TPAMI 18(4), 377–388 (1996)Google Scholar
  4. 4.
    Umeyama, S.: An Eigen Decomposition Approach to Weighted Graph Matching Problems. IEEE TPAMI 10(5), 695–703 (1988)zbMATHGoogle Scholar
  5. 5.
    Scott, G.L., Longuet-Higgins, H.C.: An algorithm for assoictaing the features for two patterns. Proc. Roy. Soc. Lond. B244, 21–26 (1991)CrossRefGoogle Scholar
  6. 6.
    Shapiro, L., Brady, J.M.: Feature-based Correspondence:an eigenvector approach. Image & Vision Computing 10(5), 283–288 (1992)CrossRefGoogle Scholar
  7. 7.
    Luo, B., Wilson, R.C., Hancock, E.R.: Spectral embedding of graphs. Pattern Recognition 36(9), 2213–2230 (2003)zbMATHCrossRefGoogle Scholar
  8. 8.
    Kosinov, S., Caelli, T.: Inexact Multisubgraph matching using Graph Eigenspace and Clustering Models. In: Caelli, T.M., Amin, A., Duin, R.P.W., Kamel, M.S., de Ridder, D. (eds.) SPR 2002 and SSPR 2002. LNCS, vol. 2396, pp. 133–142. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  9. 9.
    Clark, J., Holton, D.A.: A First Look at Graph Theory. World Scientific Publishing, Singapore (1991)zbMATHGoogle Scholar
  10. 10.
    Yamada, S., Hasai, T.: An efficient algorithm for the linear assignment problem. Elect. Comm. Japan 73(12), 28–36 Part 3 (1990) CrossRefGoogle Scholar
  11. 11.
    Grewe, L., Kak, A.C.: Interactive learning of a multiple-attribute hash table classifier for fast object recognition. CVIU 61(3), 387–416 (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Jianfeng Lu
    • 1
    • 2
  • Terry Caelli
    • 1
  • Jingyu Yang
    • 2
  1. 1.Department of Computing ScienceUniversity of AlbertaEdmontonCanada
  2. 2.Department of Computer ScienceNanjing University of Science & TechnologyNanjingP.R. China

Personalised recommendations