Skip to main content
SpringerLink
Log in

Maximal Clique Enumeration in Finding Near Neighbourhoods

  • Chapter
Transactions on Rough Sets XVI

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 7736))

Abstract

The problem considered in this article stems from the observation that practical applications of near set theory require efficient determination of all the tolerance classes containing objects from the union of two disjoints sets. Near set theory consists in extracting perceptually relevant information from groups of objects based on their descriptions. Tolerance classes are sets where all the pairs of objects within a set must satisfy the tolerance relation and the set is maximal with respect to inclusion. Finding such classes is a computationally complex problem, especially in the case of large data sets or sets of objects with similar features. The contributions of this article are the observation that the problem of finding tolerance classes is equivalent to the MCE problem, empirical evidence verifying the conjecture from [15] that the extra perceptual information obtained by finding all tolerance classes on a set of objects obtained from a pair of images improves the CBIR results when using the tolerance nearness measure, and a new application of MCE to CBIR.

This research has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) grants 194376 and 418413. Also, special thanks to Tariq Alusaifeer for recognizing the problem of finding tolerance classes is equivalent to maximal clique enumeration.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akkoyunlu, E.A.: The enumeration of maximal cliques of large graphs. SIAM Journal on Computing 2(1), 1–6 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bomze, I., Budinich, M., Pardalos, P., Pelillo, M.: The maximum clique problem. In: Du, D.Z., Pardalos, P.M. (eds.) Handbook of Combinatorial Optimization, vol. 4. Kluwer (1999)

    Google Scholar 

  3. Bron, C., Kerbosch, J.: Algorithm 457: finding all cliques of an undirected graph. Communications of the ACM 16(9), 575–577 (1973)

    Article  MATH  Google Scholar 

  4. Cazals, F., Karande, C.: A note on the problem of reporting maximal cliques. Theoretical Computer Science 407(1), 564–568 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Duda, R., Hart, P., Stork, D.: Pattern Classification, 2nd edn. Wiley (2001)

    Google Scholar 

  6. Harary, F., Ross, I.C.: A procedure for clique detection using the group matrix. Sociometry 20(3), 205–215 (1957)

    Article  MathSciNet  Google Scholar 

  7. Hassanien, A.E., Abraham, A., Peters, J.F., Schaefer, G., Henry, C.: Rough sets and near sets in medical imaging: A review. IEEE Transactions on Information Technology in Biomedicine 13(6), 955–968 (2009)

    Article  Google Scholar 

  8. Henry, C.: Near set Evaluation And Recognition (NEAR) system. In: Pal, S.K., Peters, J.F. (eds.) Rough Fuzzy Analysis Foundations and Applications, pp. 7-1–7-22. CRC Press, Taylor & Francis Group (2010), http://wren.ee.umanitoba.ca

  9. Henry, C., Peters, J.F.: Perception-based image classification. International Journal of Intelligent Computing and Cybernetics 3(3), 410–430 (2010), Emerald Literati Network 2011 Award for Excellence

    Google Scholar 

  10. Henry, C., Peters, J.F.: Arthritic hand-finger movement similarity measuresments: Tolerance near set approach. Computational and Mathematical Methods in Medicine, article ID 569898, 14 pp (2011)

    Google Scholar 

  11. Henry, C.J.: Near Sets: Theory and Applications. Ph.D. thesis (2010), https://mspace.lib.umanitoba.ca/handle/1993/4267

  12. Henry, C.J.: Neighbourhoods, classes and near sets. Applied Mathematical Sciences 5(35), 1727–1732 (2011)

    MathSciNet  MATH  Google Scholar 

  13. Henry, C.J.: Perceptual Indiscernibility, Rough Sets, Descriptively Near Sets, and Image Analysis. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets XV. LNCS, vol. 7255, pp. 41–121. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  14. Henry, C.J., Peters, J.F.: Neighbourhood-based vision systems. Cybernetics and Systems 42(1), 33–44 (2011)

    Article  Google Scholar 

  15. Henry, C.J., Ramanna, S.: Parallel Computation in Finding Near Neighbourhoods. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 523–532. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  16. Henry, C.J., Ramanna, S.: Signature-based perceptual nearness. Application of near sets to image retrieval. Mathematics in Computer Science p. 21 (submitted, 2012)

    Google Scholar 

  17. Jenkins, J., Arkatkar, I., Owens, J.D., Choudhary, A., Samatova, N.F.: Lessons learned from exploring the backtracking paradigm on the GPU. In: Proceedings of the 17th International Conference on Parallel Processing, vol. II, pp. 425–437 (2011)

    Google Scholar 

  18. Li, J., Wang, J.Z.: Automatic linguistic indexing of pictures by a statistical modeling approach. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(9), 1075–1088 (2003)

    Article  Google Scholar 

  19. Makino, K., Uno, T.: New Algorithms for Enumerating All Maximal Cliques. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 260–272. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  20. Meghdadi, A.H.: Fuzzy Tolerance Neighborhood Approach to Image Similarity in Content-based Image Retrieval. Ph.D. thesis (2012)

    Google Scholar 

  21. NVIDIA: NVIDIA CUDA programming guide v3.0 (2010), http://docs.nvidia.com/cuda/index.html

  22. Patel, S.J.: Applied parallel programming (2010), http://courses.engr.illinois.edu/ece498/al/

  23. Pavel, M.: Fundamentals of Pattern Recognition. Marcel Dekker, Inc., NY (1993)

    MATH  Google Scholar 

  24. Pawlak, Z., Skowron, A.: Rudiments of rough sets. Information Sciences 177, 3–27 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  25. Peters, J.F.: Classification of objects by means of features. In: Proceedings of the IEEE Symposium Series on Foundations of Computational Intelligence (IEEE SCCI 2007), pp. 1–8 (2007)

    Google Scholar 

  26. Peters, J.F.: Near sets. General theory about nearness of objects. Applied Mathematical Sciences 1(53), 2609–2629 (2007)

    MathSciNet  MATH  Google Scholar 

  27. Peters, J.F.: Near sets. Special theory about nearness of objects. Fundamenta Informaticae 75(1-4), 407–433 (2007)

    MathSciNet  MATH  Google Scholar 

  28. Peters, J.F.: Tolerance near sets and image correspondence. International Journal of Bio-Inspired Computation 1(4), 239–245 (2009)

    Article  Google Scholar 

  29. Peters, J.F.: Corrigenda and addenda: Tolerance near sets and image correspondence. International Journal of Bio-Inspired Computation 2(5), 310–318 (2010)

    Article  Google Scholar 

  30. Peters, J.F., Wasilewski, P.: Foundations of near sets. Info. Sci. 179(18), 3091–3109 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  31. Peters, J.F., Wasilewski, P.: Tolerance spaces: Origins, theoretical aspects and applications. Information Sciences 195, 211–225 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  32. Poincaré, H.: L’espace et la géomètrie. Revue de métaphysique et de morale 3, 631–646 (1895)

    Google Scholar 

  33. Ramanna, S., Meghdadi, A.H., Peters, J.F.: Nature-inspired framework for measuring image resemblance: A near rough set approach. Theoretical Computer Science 412(42), 5926–5938 (2011), doi:10.1016/j.tcs.2011.05.044

    Article  MathSciNet  MATH  Google Scholar 

  34. Schmidt, M.C., Samatova, N.F., Thomas, K., Byung-Hoon, P.: A scalable, parallel algorithm for maximal clique enumeration. Journal of Parallel and Distributed Computing 69, 417–428 (2009)

    Article  Google Scholar 

  35. Shahfar, S.: Near Images: A Tolerance Based Approach to Image Similarity and Its Robustness to Noise and Lightening. M.Sc. thesis (2011)

    Google Scholar 

  36. Smeulders, A.W.M., Worring, M., Santini, S., Gupta, A., Jain, R.: Content-based image retrieval at the end of the early years. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(12), 1349–1380 (2000)

    Article  Google Scholar 

  37. Sossinsky, A.B.: Tolerance space theory and some applications. Acta Applicandae Mathematicae: An International Survey Journal on Applying Mathematics and Mathematical Applications 5(2), 137–167 (1986)

    Article  MathSciNet  Google Scholar 

  38. Tsukiyama, S., Ide, M., Ariyoshi, H., Shirakawa, I.: A new algorithm for generating all the maximal independent sets. SIAM Journal on Computing 6, 505–517 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  39. Wolski, M.: Perception and classification. A Note on near sets and rough sets. Fundamenta Informaticae 101, 143–155 (2010)

    MathSciNet  MATH  Google Scholar 

  40. Zeeman, E.C.: The topology of the brain and the visual perception. In: Fort, K.M. (ed.) Topoloy of 3-manifolds and Selected Topices, pp. 240–256. Prentice Hall, New Jersey (1965)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Winnipeg, Winnipeg, Manitoba, R3B 2E9, Canada

    Christopher J. Henry & Sheela Ramanna

Authors
  1. Christopher J. Henry
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sheela Ramanna
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Manitoba, Winnipeg, MB, Canada

    James F. Peters

  2. University of Warsaw, Poland

    Andrzej Skowron

  3. University of Winnipeg, MB, Canada

    Sheela Ramanna

  4. University of Rzeszów, Poland

    Zbigniew Suraj

  5. University of Calgary, AB, Canada

    Xin Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Henry, C.J., Ramanna, S. (2013). Maximal Clique Enumeration in Finding Near Neighbourhoods. In: Peters, J.F., Skowron, A., Ramanna, S., Suraj, Z., Wang, X. (eds) Transactions on Rough Sets XVI. Lecture Notes in Computer Science, vol 7736. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36505-8_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-36505-8_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36504-1

  • Online ISBN: 978-3-642-36505-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation