Abstract
The problem considered in this article stems from the observation that practical applications of near set theory requires 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 contribution of this article is a parallelized algorithm for finding tolerance classes using NVIDIA’s Compute Unified Device Architecture (CUDA). The parallelized algorithm is illustrated in terms of a content-based image retrieval application.
This research has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) grant 194376 and the University of Winnipeg Research Start-Up Grant.
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References
Carpenter: A cuda implementation of support vector classification and regression. Tech. Rep. 2009 (2009), http://www.scribd.com/doc/1562222
Duda, R., Hart, P., Stork, D.: Pattern Classification, 2nd edn. Wiley, Chichester (2001)
Garcia, V., Debreuva, E., Barland, M.: Fast k nearest neighbor search using gpu. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshop, pp. 1–6
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)
Henry, C.: Near set Evaluation And Recognition (NEAR) System, pp. 7–1–7–22. CRC Press, Taylor & Francis Group (2010) ISBN 13: 9781439803295
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
Henry, C.J.: Near Sets: Theory and Applications. Ph.D. thesis (2010)
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); Database, http://wang.ist.psu.edu/docs/related/ (permission recived May 2010)
Liu, Y., Liao, W., Choudhary, A., Li, J.: Parallel data mining algorithms for association rules and clustering, pp. 32–1–32–20. Chapman and Hall, Boca Raton (2008) ISBN: 978-1-58488-623-5
NVIDIA: Nvidia cuda programming guide v3.0 (2010), http://developer.download.nvidia.com/compute/cuda/3_0/toolkit/docs/NVIDIA_CUDA_ProgrammingGuide.pdf
Patel, S.J.: Applied parallel programming (2010), http://courses.engr.illinois.edu/ece498/al/
Pavel, M.: Fundamentals of Pattern Recognition. Marcel Dekker, Inc., NY (1993)
Peters, J.F.: Near sets. General theory about nearness of objects. Applied Mathematical Sciences 1(53), 2609–2629 (2007)
Peters, J.F.: Near sets. Special theory about nearness of objects. Fundamenta Informaticae 75(1-4), 407–433 (2007)
Peters, J.F.: Tolerance near sets and image correspondence. International Journal of Bio-Inspired Computation 1(4), 239–245 (2009)
Peters, J.F.: Corrigenda and addenda: Tolerance near sets and image correspondence. International Journal of Bio-Inspired Computation 2(5) (2010) (in press)
Peters, J.F., Wasilewski, P.: Foundations of near sets. Information Sciences 179(18), 3091–3109 (2009)
Poincaré, H.: L’espace et la géomètrie. Revue de Métaphysique et de Morale 3, 631–646 (1895)
Ramanna, S., Meghdadi, A.H., Peters, J.F.: Nature-inspired framework for measuring image resemblance: A near rough set approach. Theoretical Computer Science (2011), doi:10.1016/j.tcs.2011.05.044
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)
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)
Wolski, M.: Perception and classification. A Note on near sets and rough sets. Fundamenta Informaticae 101, 143–155 (2010)
Zeeman, E.C.: The topology of the brain and the visual perception, pp. 240–256. Prentice Hall, New Jersey (1965)
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Henry, C.J., Ramanna, S. (2011). Parallel Computation in Finding Near Neighbourhoods. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds) Rough Sets and Knowledge Technology. RSKT 2011. Lecture Notes in Computer Science(), vol 6954. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24425-4_67
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DOI: https://doi.org/10.1007/978-3-642-24425-4_67
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