On the Comparison of Structured Data

  • Jyrko Correa-Morris
  • Noslen Hernández
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7441)

Abstract

This paper introduces a theoretical framework to characterize measures on structured data. We firstly describe the lattice of structured data. Then, four basic and intuitive properties which any measure on structure data must fulfill are formally introduced. Metrics and kernel functions are studied as particular cases of (dis)similarity measures. In the case of metrics we prove that the well-known edit distances meet all the desirable properties. We also give sufficient conditions for a kernel function to satisfy those properties. Some examples are given for particular kinds of structured data.

Keywords

structured data kernel functions metrics 

References

  1. 1.
    Chen, H., Jain, A.K.: Dental biometrics: Alignment and matching of dental radiographs. IEEE Trans. Pattern Anal. Mach. Intell. 27(8), 1319–1326 (2005)CrossRefGoogle Scholar
  2. 2.
    Dinu, L.P., Sgarro, A.: A low-complexity distance for dna strings. Fundam. Inform. 73(3), 361–372 (2006)MathSciNetMATHGoogle Scholar
  3. 3.
    Zhu, E., Hancock, E.R., Ren, P., Yin, J., Zhang, J.: Associating Minutiae between Distorted Fingerprints Using Minimal Spanning Tree. In: Campilho, A., Kamel, M. (eds.) ICIAR 2010, 235–245. LNCS, vol. 6112, Springer, Heidelberg (2010)Google Scholar
  4. 4.
    Dinu, L.P., Ionescu, R.: A genetic approximation of closest string via rank distance. In: SYNASC, pp. 207–214 (2011)Google Scholar
  5. 5.
    González-Díaz, R., Ion, A., Ham, M.I., Kropatsch, W.G.: Invariant representative cocycles of cohomology generators using irregular graph pyramids. Computer Vision and Image Understanding 115(7), 1011–1022 (2011)CrossRefGoogle Scholar
  6. 6.
    Correa-Morris, J., Espinosa-Isidrón, D.L., Álvarez-Nadiozhin, D.R.: An incremental nested partition method for data clustering. Pattern Recognition 43(7), 2439–2455 (2010)MATHCrossRefGoogle Scholar
  7. 7.
    Bunke, H., Riesen, K.: Recent advances in graph-based pattern recognition with applications in document analysis. Pattern Recognition 44(5), 1057–1067 (2011)MATHCrossRefGoogle Scholar
  8. 8.
    Bunke, H., Shearer, K.: A graph distance metric based on the maximal common subgraph. Pattern Recognition Letters 19(3-4), 255–259 (1998)MATHCrossRefGoogle Scholar
  9. 9.
    Kashima, H., Tsuda, K., Inokuchi, A.: Marginalized kernels between labeled graphs. In: Proceedings of the Twentieth International Conference on Machine Learning, pp. 321–328. AAAI Press (2003)Google Scholar
  10. 10.
    Bunke, H., Riesen, K.: A Family of Novel Graph Kernels for Structural Pattern Recognition. In: Rueda, L., Mery, D., Kittler, J. (eds.) CIARP 2007. LNCS, vol. 4756, pp. 20–31. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Riesen, K., Bunke, H.: Approximate graph edit distance computation by means of bipartite graph matching. Image Vision Comput. 27(7), 950–959 (2009)CrossRefGoogle Scholar
  12. 12.
    Vega-Pons, S., Correa-Morris, J., Ruiz-Shulcloper, J.: Weighted partition consensus via kernels. Pattern Recognition 43(8), 2712–2724 (2010)MATHCrossRefGoogle Scholar
  13. 13.
    Thor, A.: Toward an adaptive string similarity measure for matching product offers. In: GI Jahrestagung (1), 702–710 (2010)Google Scholar
  14. 14.
    Meila, M.: Comparing clusterings: an axiomatic view. In: ICML, pp. 577–584 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jyrko Correa-Morris
    • 1
  • Noslen Hernández
    • 2
  1. 1.Institute for Pure and Applied Mathematics (IMPA)Brazil
  2. 2.Advanced Technologies Application Center (CENATAV)Cuba

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