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Vector-based Attribute Reduction Method for Formal Contexts

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Języki publikacji
EN
Abstrakty
EN
Attribute reduction is one basic issue in knowledge discovery of information systems. In this paper, based on the object oriented concept lattice and classical concept lattice, the approach of attribute reduction for formal contexts is investigated. We consider attribute reduction and attribute characteristics from the perspective of linear dependence of vectors. We first introduce the notion of context matrix and the operations of corresponding column vectors, then present some judgment theorems of attribute reduction for formal contexts. Furthermore, we propose a new method to reducing formal context and show corresponding reduction algorithms. Compared with previous reduction approaches which employ discernibility matrix and discernibility function to determine all reducts, the proposed approach is more simpler and easier to implement.
Wydawca
Rocznik
Strony
397--414
Opis fizyczny
Bibliogr. 39 poz., tab., wykr.
Twórcy
autor
  • Computer Engineering Institute, Qingdao Technological University, Qingdao, Shandong, P. R. China, 266520
autor
  • Department of Automation, Tsinghua University, Beijing, P. R. China, 100084
autor
  • College of Information Science and Technology, Shihezi University, Shihezi, Xinjiang, P. R. China, 832000
Bibliografia
  • [1] Belohlavek, R., Vychodil, V: Formal Concept Analysis With Background Knowledge: Attribute Priorities, IEEE Transactions on Systems, Man, and Cybernetics, Cybernetics-Part C: Application and Reviews, 39(4), 2009, 399-409.
  • [2] Belohlavek, R., Bernard, D B., Outrata, J., Vychodil, V: Computing the Lattice of All Fixpoints of a Fuzzy Closure Operator, IEEE Transactions on Fuzzy Systems, 18(3), 2010, 546-557.
  • [3] Belohlavek, R.: Fuzzy closure operators, Journal or Mathematical Analysis and Applications, 262, 2001, 473-489.
  • [4] Beydoun, G.: Formal concept analysis for an e-learning semantic web, Expert Systems with Applications, 36, 2009, 10952-10961.
  • [5] Burusco, A., Fuentes-Gonzalez, R.: Concept lattices defined from implication operators, Fuzzy Sets and systems, 114 (3), 2000, 431-436.
  • [6] Carpineto, C., Romano, G.: A lattice conceptual clustering system and its application to browsing retrieval, Machine Learning 10, (1996) 95-122.
  • [7] Deng, W B., Wang, G Y., Hu, F., Blaszczynski, J., Slowinski, R., and Szelag, M.: A Novel Method for Elimination of Inconsistencies in Ordinal Classification with Monotonicity Constraints, Fundamenta Informaticae, accepted (Special Issue).
  • [8] Dua, Y J., Li, H M.: Strategy for mining association rules for web pages based on formal concept analysis, Applied Soft Computing, 10, 2010, 772-83.
  • [9] Elloumi, S., Jaoua, A.: Automatic classification using fuzzy concepts, Proc. JCIS2000, Atlantic City, USA, vol.1, 2000, 276-279.
  • [10] Elloumi, S., Jaam, J., Hasnah, A., Jaoua, A., Nafkha, I.: A multi-level conceptual data reduction approach based on the Lukasiewicz implication, Information Sciences, 163, 2004, 253-262.
  • [11] Gediga, G., Duntsch, I.: Modal-style operators in qualitative data analysis, Proc. IEEE International Conference on Data Mining, 2002, 155-162.
  • [12] Gediga, B., Wille, R.: Formal Concept Analysis, Mathematic Foundations, Springer, Berlin, 1999.
  • [13] Georgescu, G., Popescu, A.: Non-dual fuzzy connections, Archive for Mathematic Logic, 43(8), 2004,10091039.
  • [14] Harms, S K., Deogum, J S.: Sequential association rule mining with time lags, J. Intell. Inform. Systems, 22(1), 2004, 7-22.
  • [15] Hu, Q., Xie, Z., Yu, D.: Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation, Pattern Recognition, 40, 2007, 3509-3521.
  • [16] Jaoua, A., Elloumi, S.: Galois connection, formal concepts and Galois lattice in real relations: application in a real classifier, The Journal of Systems and Software, 60, 2002, 149-163.
  • [17] Kumar, C A., Srinivas, S.: Concept lattice reduction using fuzzy K-Means clustering, Expert Systems with Applications, 37, 2010, 2696-2704.
  • [18] Kwon, O., Kim, J.: Concept lattices for visualizing and generating user profiles for context-aware service recommendations, Expert Systems with Applications, 36, 2009, 1893-1902.
  • [19] Leung, Y., Fischer, M M., Wu, W Z., Mi, J S.: A rough set approach for the discovery of classification rules in interval- valued information systems, International Journal of Approximate Reasoning, 47(2), 2008, 233-246.
  • [20] Li, H X., Zhou, X C, Zhao,J B, Liu, D.: Non-Monotonic Attribute Reduction in Decision-Theoretic Rough Sets, Fundamenta Informaticae, accepted (Special Issue).
  • [21] Li, L F., Zhang, J K.: Attribute reduction in fuzzy concept lattices based on the T implication, Knowledge- Based Systems, 23, 2010, 497-503.
  • [22] Liu, M., Shao, M W., Zhang, W X., Wu, C.: Reduction Method for Concept Lattices Based on Rough Set Theory and Its Application, Computers and Mathematics with Applications, 53(9), 2007, 1390-1410.
  • [23] Li, Y., Shiu, S C K., Pal, S.K.: Combining feature reduction and case selection in building CBR classifiers,IEEE Transactions on Knowledge and Data Engineer, 18(3), 2006, 415-429.
  • [24] Medina, J., Ojeda-Aciego, M.: Multi-adjoint t-concept lattices, Information Sciences, 180, 2010, 712-725.
  • [25] Mi, J S., Leung, Y., Wu, W Z.: Approaches to attribute reduction in concept lattices induced by axialities, Knowledge-Based Systems, 23, 2010, 504-511.
  • [26] Pawlak, Z.: Rough sets. International Journal of Computer and Information Science, 11, 1982, 341-356.
  • [27] Popescu, A.: A general approach to fuzzy concept, Math.Logic Quaterly, 50(3), 2001,1-17.
  • [28] Saquer, J., Deogun, J S.: Formal rough concept analysis, Proc. New directions in Rough Sets, Data Mining, and Granular-Soft, LNCS 1711, Springer-Verlag, Berlin, 1999, 91-99.
  • [29] Shao, M W., Guo, L., Li, L.: A novel attribute reduction approach based on the object oriented concept lattice, Proc. Rough Sets and Knowledge Technology (RSKT’11), LNCS 6954, Springer-Verlag, Berlin, 2011, 71-80.
  • [30] Wang, G Y.: Rough reduction in algebra view and information view, International Journal of Intelligent Systems, 18, 2003, 679-688.
  • [31] Wang, X., Zhang, W X.: Relations of attribute reduction between object and property oriented concept lattices, Knowledge-Based Systems, 21(5), 2008, 398-403.
  • [32] Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts, in: Ordered Sets (I. Rival, Ed.), Reidel, Dordrecht-Boston, 1982, 445-470.
  • [33] Wu, Q., Liu, Z T.: Real formal concept analysis based on grey-rough set theory, Knowledge-Based Systems, 22, 2009, 38-45.
  • [34] Wu, W Z., Leung, Y., Mi, J S.: Granular Computing and Knowledge Reduction in Formal Contexts, IEEE Transactions Knowledge and Data Engineering, 21(10), 2009, 1461-1474.
  • [35] Yang, X P, Lu, Z J., Li, T J.: Decision-theoretic Rough Set in Incomplete Information System, Fundamenta Informaticae, accepted (Special Issue).
  • [36] Yao, Y Y.: Concept lattices in rough set theory, Proc. Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS 2004), 2004, 796-801.
  • [37] Yao, Y Y.: A Comparative Study of Formal Concept Analysis and Rough Set Theory in Data Analysis, Proc. Rough Sets and Current Trends in Computing (RSCTC 2004), LNCS 3066, Springer, Berlin, 2004,59-68.
  • [38] Zhang, JF., Jiang, YY., Chang, KH., Zhang, S L., Cai, JH., Hu, L H.: A concept lattice based outlier mining method in low-dimensional subspaces, Pattern Recognition Letters, 30, 2009, 1434-1439.
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Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-1147be23-aa4b-4dbd-8c42-b5a842bd3bb8
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