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Joint IAPR International Workshops on Statistical Techniques in Pattern Recognition (SPR) and Structural and Syntactic Pattern Recognition (SSPR)

SSPR /SPR 2012: Structural, Syntactic, and Statistical Pattern Recognition pp 135–143Cite as

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On the Correlation of Graph Edit Distance and L 1 Distance in the Attribute Statistics Embedding Space

On the Correlation of Graph Edit Distance and L 1 Distance in the Attribute Statistics Embedding Space

  • Jaume Gibert24,
  • Ernest Valveny24,
  • Horst Bunke25 &
  • …
  • Alicia Fornés24 
  • Conference paper
  • 2387 Accesses

  • 1 Citations

Part of the Lecture Notes in Computer Science book series (LNIP,volume 7626)

Abstract

Graph embeddings in vector spaces aim at assigning a pattern vector to every graph so that the problems of graph classification and clustering can be solved by using data processing algorithms originally developed for statistical feature vectors. An important requirement graph features should fulfil is that they reproduce as much as possible the properties among objects in the graph domain. In particular, it is usually desired that distances between pairs of graphs in the graph domain closely resemble those between their corresponding vectorial representations. In this work, we analyse relations between the edit distance in the graph domain and the L 1 distance of the attribute statistics based embedding, for which good classification performance has been reported on various datasets. We show that there is actually a high correlation between the two kinds of distances provided that the corresponding parameter values that account for balancing the weight between node and edge based features are properly selected.

Keywords

  • Edit Distance
  • Graph Match
  • Node Label
  • Edit Operation
  • Node Information

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.

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References

  1. Bunke, H.: On a relation between graph edit distance and maximum common subgraph. Pattern Recognition Letters 18(8), 689–694 (1997)

    CrossRef  MathSciNet  Google Scholar 

  2. Bunke, H., Allermann, G.: Inexact graph matching for structural pattern recognition. Pattern Recognition Letters 1, 245–253 (1983)

    CrossRef  MATH  Google Scholar 

  3. Conte, D., Foggia, P., Sansone, C., Vento, M.: Thirty years of graph matching in pattern recognition. International Journal of Pattern Recognition and Artificial Intelligence 18(3), 265–298 (2004)

    CrossRef  Google Scholar 

  4. Geusebroek, J.M., Burghouts, G.J., Smeulders, A.W.M.: The Amsterdam library of object images. International Journal of Computer Vision 61(1), 103–112 (2005)

    CrossRef  Google Scholar 

  5. Gibert, J., Valveny, E., Bunke, H.: Graph embedding in vector spaces by node attribute statistics. Pattern Recognition 45(9), 3072–3083 (2012)

    CrossRef  Google Scholar 

  6. Ren, P., Wilson, R., Hancock, E.: Graph characterization via Ihara coefficients. IEEE Transactions on Neural Networks 22(2), 233–245 (2011)

    CrossRef  Google Scholar 

  7. Riesen, K., Bunke, H.: IAM Graph Database Repository for Graph Based Pattern Recognition and Machine Learning. In: da Vitoria Lobo, N., et al. (eds.) S+SSPR 2008. LNCS, vol. 5342, pp. 287–297. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  8. Riesen, K., Bunke, H.: Approximate graph edit distance computation by means of bipartite graph matching. Image and Vision Computing 27, 950–959 (2009)

    CrossRef  Google Scholar 

  9. Riesen, K., Bunke, H.: Graph Classification and Clustering Based on Vector Space Embedding. World Scientific (2010)

    Google Scholar 

  10. Sanfeliu, A., Fu, K.S.: A distance measure between attributed relational graphs for pattern recognition. IEEE Transactions on Systems, Man, and Cybernetics - Part B 13(3), 353–363 (1983)

    CrossRef  MATH  Google Scholar 

  11. Tarr, M.J.: The object databank, http://www.cnbc.cmu.edu/tarrlab/stimuli/objects/index.html

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Author information

Authors and Affiliations

  1. Computer Vision Center, Universitat Autònoma de Barcelona, Edifici O Campus UAB, 08193, Bellaterra, Spain

    Jaume Gibert, Ernest Valveny & Alicia Fornés

  2. Institute for Computer Science and Applied Mathematics, University of Bern, Neubrückstrasse 10, CH-3012, Bern, Switzerland

    Horst Bunke

Authors
  1. Jaume Gibert
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  2. Ernest Valveny
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  3. Horst Bunke
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  4. Alicia Fornés
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Auckland, Private Bag 92019, 1142, Auckland, New Zealand

    Georgy Gimel’farb

  2. Department of Computer Science, University of York, Deramore Lane, YO10 5GH, York, UK

    Edwin Hancock

  3. Institute of Media and Information Technology, Chiba University, Yayoi-cho 1-33, 263-8522, Inage-ku, Chiba, Japan

    Atsushi Imiya

  4. Technische Universität/Fraunhofer IGD, Fraunhoferstraße 5, 64283, Darmstadt, Germany

    Arjan Kuijper

  5. Graduate School of Information Science and Technology, Hokkaido University, 060-0814, Sapporo, Japan

    Mineichi Kudo

  6. Graduate School of Engineering, Tohoku University, 6-6-05 Aoba, Aramaki, Aoba-ku, 980-8579, Sendai, Miyagi, Japan

    Shinichiro Omachi

  7. Centre for Vision, Speech and Signal Processing, University of Surrey, GU2 7XH, Guildford, Surrey, UK

    Terry Windeatt

  8. C&C Innovation Research Laboratories, NEC Corporation, 8916-47 Takayama-cho, Ikoma-Shi, Nara, Japan

    Keiji Yamada

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© 2012 Springer-Verlag Berlin Heidelberg

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Cite this paper

Gibert, J., Valveny, E., Bunke, H., Fornés, A. (2012). On the Correlation of Graph Edit Distance and L 1 Distance in the Attribute Statistics Embedding Space. In: Gimel’farb, G., et al. Structural, Syntactic, and Statistical Pattern Recognition. SSPR /SPR 2012. Lecture Notes in Computer Science, vol 7626. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34166-3_15

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  • DOI: https://doi.org/10.1007/978-3-642-34166-3_15

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  • Print ISBN: 978-3-642-34165-6

  • Online ISBN: 978-3-642-34166-3

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