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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 144–152Cite as

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Approximate Axial Symmetries from Continuous Time Quantum Walks

Approximate Axial Symmetries from Continuous Time Quantum Walks

  • Luca Rossi24,
  • Andrea Torsello24 &
  • Edwin R. Hancock25 
  • Conference paper
  • 2401 Accesses

  • 8 Citations

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

Abstract

The analysis of complex networks is usually based on key properties such as small-worldness and vertex degree distribution. The presence of symmetric motifs on the other hand has been related to redundancy and thus robustness of the networks. In this paper we propose a method for detecting approximate axial symmetries in networks. For each pair of nodes, we define a continuous-time quantum walk which is evolved through time. By measuring the probability that the quantum walker to visits each node of the network in this time frame, we are able to determine whether the two vertices are symmetrical with respect to any axis of the graph. Moreover, we show that we are able to successfully detect approximate axial symmetries too. We show the efficacy of our approach by analysing both synthetic and real-world data.

Keywords

  • Complex Network
  • Symmetry
  • Quantum Walk

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Author information

Authors and Affiliations

  1. Department of Environmental Science, Informatics and Statistics, Ca’ Foscari University of Venice, Italy

    Luca Rossi & Andrea Torsello

  2. Department of Computer Science, University of York, UK

    Edwin R. Hancock

Authors
  1. Luca Rossi
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  2. Andrea Torsello
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  3. Edwin R. Hancock
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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

Rossi, L., Torsello, A., Hancock, E.R. (2012). Approximate Axial Symmetries from Continuous Time Quantum Walks. 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_16

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  • DOI: https://doi.org/10.1007/978-3-642-34166-3_16

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  • Print ISBN: 978-3-642-34165-6

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