Granulation using Clustering and Rough Set Theory and its Tree Representation

Authors: Girish Kumar Singh, Sonajharia Minz

Abstract:

Granular computing deals with representation of information in the form of some aggregates and related methods for transformation and analysis for problem solving. A granulation scheme based on clustering and Rough Set Theory is presented with focus on structured conceptualization of information has been presented in this paper. Experiments for the proposed method on four labeled data exhibit good result with reference to classification problem. The proposed granulation technique is semi-supervised imbibing global as well as local information granulation. To represent the results of the attribute oriented granulation a tree structure is proposed in this paper.

Keywords: Granular computing, clustering, Rough sets, datamining.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1082317

References:

[1] Ankerst M., M. Breunig, Kriegel H.P., and Sander J., "OPTICS: Ordering Points to Identify the Clustering Structure", In Proceeding ACM SIGMOD, International Conference on Management of Data (SIGMOD'99), Philadelphia, PA, pages 49--60, 1999.
[2] Chiang I-Jen, Lin T. Y., and Liu Y., ''Table Representations of Granulations Revisited'', Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, 10th International Conference, RSFDGrC 2005, Regina, Canada, pp. 728-737, August 31 - September 3, 2005.
[3] Ester M., Kriegel H.-P., Sander J., and Xu X., ''A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise'' In Proceedings of the 2nd International Conference on Knowledge Discovery and Data Mining (KDD?96), Portland: Oregon, pp. 226-231, 1996.
[4] Han, J. & Kamber, M. (2001). Data Mining: Concepts and Techniques. San Francisco: Morgan Kaufmann.
[5] Hinneburg A., and Keim D. A., ''An Efficient Approach to Clustering in Large Multimedia Databases with Noise'', in Proceeding of International Conference on Knowledge Discovery and Data Mining (KDD98), pages 58-65, August 1998.
[6] Hobbs, J.R. ''Granularity'', Proceedings of the 9th International Joint Conference on Artificial Intelligence, 432-435, 1985.
[7] Jain A.K. and Dubes R.C. (1988) ''Algorithms for Clustering Data'' Prentice Hall, Upper Saddle River: New Jersey.
[8] Lin, T. Y., ''Granular computing on binary relations I: data mining and neighborhood systems'', Rough Sets In Knowledge Discovery, Springer-Verlag, pp 107-140, 1998.
[9] Lin, T.Y. ''Granular computing'', LNCS 2639, Springer, Berlin, 16-24, 2003.
[10] Pawlak, Z. "Rough sets." International Journal of Computer and Information Sciences 11 (1982): 341-356.
[11] Pawlak, Z. Granularity of knowledge, indiscernibility and rough sets, Proceedings of 1998 IEEE International Conference on Fuzzy Systems, 106-110, 1998.
[12] Sander J., Ester M., Kriegel H. P., and X. Xu, ''Density-Based Clustering in Spatial Databases: The Algorithm GDBSCAN and its Applications'', Data Mining and Knowledge Discovery, Kluwer Academic Publishers, Vol. 2, No. 2, 1998.
[13] http://www.ics.uci.edu/~mlearn/MLRepository.html.
[14] Yager, R.R. and Filev D., ''Operations for granular computing: mixing words with numbers'', Proceedings of 1998 IEEE International Conference on Fuzzy Systems, 123-128, 1998.
[15] Yao Y. Y., ''Granular computing: basic issues and possible solutions'', Proceedings of the 5th Joint Conference on Information Sciences, ppl86-189, 2000.
[16] Yao Y. Y., ''Granular Computing'', Computer Science, 31(10.A), 1-5, 2004.
[17] Yao Y. Y., ''A partition model of granular computing'', LNCS, Transactions on Rough Sets, 1, 232-253, 2004.
[18] Yao Jing Tao, ''Information Granulation and Granular Relationships'', Proc. Granular Computing, 2005 IEEE International Conference July 2005 Page(s):326 - 329 Vol. 1.
[19] Zadeh L.A., ''Fuzzy sets and information granurity, Advances in Fuzzy Set Theory and Applications'', M. Gupta, R.K. Ragade, R.R. Yager (eds), North-Holland Publishing Company, pp3-18, 1979.
[20] Zadeh, L. A., ''Fuzzy logic = computing with words'', IEEE Transactions on Fuzzy Systems, 4, 103-111, 1996.
[21] Zadeh, L. A., ''The Key Roles of Information Granulation and Fuzzy Logic in Human Reasoning, Concept Formulation and Computing with Words'', FUZZ-IEEE '96, Fifth IEEE International Conference on Fuzzy Systems, New Orleans, USA, September 8--11, 1996.
[22] Zadeh L.A., ''Towards a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic'', Fuzzy Sets and Systems, 90(2), 111-127, 1997.
[23] Zadeh L.A., ''Some reflections on soft computing, granular computing and their roles in the conception, design and utilization of information/intelligent systems'', Soft Computing, 2(1), 23 25, 1998.