Knowledge discovery in data using formal concept analysis and random projections

Cherukuri Kumar

doi:10.2478/v10006-011-0059-1

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Knowledge discovery in data using formal concept analysis and random projections

International Journal of Applied Mathematics and Computer Science

Volume 21 (2011): Issue 4 (December 2011)

By: Cherukuri Kumar

Open Access

|Dec 2011

Abstract

In this paper our objective is to propose a random projections based formal concept analysis for knowledge discovery in data. We demonstrate the implementation of the proposed method on two real world healthcare datasets. Formal Concept Analysis (FCA) is a mathematical framework that offers a conceptual knowledge representation through hierarchical conceptual structures called concept lattices. However, during the design of a concept lattice, complexity plays a major role.

References

Achilioptas, D. (2003). Database friendly random projections: Johnson-Lindenstrauss with binary coins, Journal of Computer and System Sciences 66(4): 671-687.10.1016/S0022-0000(03)00025-4
Search in Google Scholar
Aswani Kumar, Ch. (2009). Analysis of unsupervised dimensionality reductions, Computer Science and Information Systems 6(2): 217-227.10.2298/CSIS0902217K
Search in Google Scholar
Aswani Kumar, Ch. (2010). Random projections for concept lattice reduction, Proceedings of the 4th International Conference on Information Processing, Bengaluru, India, pp. 1-11.
Search in Google Scholar
Aswani Kumar, Ch. (2011). Reducing data dimensionality using random projections and fuzzy k-means clustering, International Journal of Intelligent Computing and Cybernetics 4(3): 353-365.10.1108/17563781111160020
Search in Google Scholar
Aswani Kumar, Ch. and Srinivas, S. (2006). Latent semantic indexing using eigenvalue analysis for efficient information retrieval, International Journal of Applied Mathematics and Computer Science 16(4): 551-558.
Search in Google Scholar
Aswani Kumar, Ch. and Srinivas, S. (2010a). Concept lattice reduction using fuzzy k-means clustering, Expert Systems with Applications 9(1): 2696-2704.10.1016/j.eswa.2009.09.026
Search in Google Scholar
Aswani Kumar, Ch. and Srinivas, S. (2010b). Mining associations in health care data using formal concept analysis and singular value decomposition, Biological Systems 18(4): 787-807.10.1142/S0218339010003512
Search in Google Scholar
Aswani Kumar, Ch. and Srinivas, S. (2010c). A note on weighted fuzzy k-means clustering for concept decomposition, Cybernetics and Systems 41(6): 455-467.10.1080/01969722.2010.500861
Search in Google Scholar
Belohlavek, R. and Vychodil, V. (2009). Formal concept analysis with background knowledge: Attribute priorities, IEEE Transactions on Systems, Man and Cybernetics 39(4): 399-409.10.1109/TSMCC.2008.2012168
Search in Google Scholar
Belohlavek, R. and Vychodil, V. (2010). Discovery of optimal factors in binary data via a novel method of matrix decomposition, Journal of Computer and System Sciences 76(1): 3-20.10.1016/j.jcss.2009.05.002
Search in Google Scholar
Bingham, E. and Mannila, H. (2001). Random projections in dimensionality reduction, Proceedings of the 7th International Conference on Knowledge Discovery and Data Mining, San Franscisco, CA, USA, pp. 245-250.
Search in Google Scholar
Carpineto, C. and Romano, G. (2004). Concept Data Analysis: Theory and Applications, John Wiley, Chichester.10.1002/0470011297
Search in Google Scholar
Divya, R., Aswani Kumar, Ch., Saijanani, S., and Priyadharshini, M. (2011). Deceiving communication links on an organization email corpus, Malaysian Journal of Computer Science 24(1): 17-33.
Search in Google Scholar
Elloumi, S., Jaam, J., Hasnah, A., Jaoua, A., and Nafkha, I. (2004). A multi-level conceptual data reduction approach based on the Lukasiewicz implication, Information Sciences 163(4): 253-262.10.1016/j.ins.2003.06.013
Search in Google Scholar
Ganter, B. and Wille, R. (1999). Formal Concept Analysis: Mathematical Foundations, Springer, Berlin.10.1007/978-3-642-59830-2
Search in Google Scholar
Ghosh, P., Kundu, K. and Sarkar, D. (2010). Fuzzy graph representation of fuzzy concept lattice, Fuzzy Sets and Systems 161(12): 1669-1675.10.1016/j.fss.2009.10.027
Search in Google Scholar
Horner, V. (2007). Developing a consumer health informatics decision support system using formal concept analysis, Masters' thesis, University of Pretoria, Pretoria.
Search in Google Scholar
Jamil, S. and Deogun, J. S. (2001). Concept approximations based on rough sets and similarity measures, International Journal of Applied Mathematics and Computer Science 11(3): 655-674.
Search in Google Scholar
Kazienko, P. (2009). Mining indirect association rules for web recommendation, International Journal of Applied Mathematics and Computer Science 19(1):165-186, DOI: 10.2478/v10006-009-0015-5.10.2478/v10006-009-0015-5
Search in Google Scholar
Liu, M., Shao, M., Zhang, W., and Wu, W. C. (2007). Reduction method for concept lattices based on rough set theory and its application, Computers and Mathematics with Applications 53(9): 1390-1410.10.1016/j.camwa.2006.03.040
Search in Google Scholar
Pattison, P. E. and Breiger, R. L. (2002). Lattices and dimensional representations: Matrix decompositions and ordering structures, Social Networks 24(4): 423-444.10.1016/S0378-8733(02)00015-1
Search in Google Scholar
Poelmans, J., Elzinga, P., Viaene, S., Dedene., G. (2010). Formal concept analysis in knowledge discovery: A Survey in R. Goebel (Ed.) Proceedings of the 18th International Conference on Conceptual Structures, Springer-Verlag, Berlin, pp. 139-153.10.1007/978-3-642-14197-3_15
Search in Google Scholar
Priss, U. (2006). Formal concept analysis in information science, Annual Review of Information Science and Technology 40(1): 521-543.10.1002/aris.1440400120
Search in Google Scholar
Snasel, V., Polovincak, M., Dahwa, H. M. and Horak, Z. (2008). On concept lattices and implication bases from reduced contexts, Proceedings of the ICCS Supplement, Toulouse, France, pp. 83-90.
Search in Google Scholar
Stumme, G. (2009). Formal concept analysis, in S. Staab and R. Studer (Eds.), Handbook on Ontologies, Springer-Verlag, Berlin, pp. 177-199.10.1007/978-3-540-92673-3_8
Search in Google Scholar
Stumme, G., Wille, R. and Wille, U. (1998). Conceptual knowledge discovery in databases using formal concept analysis methods, Proceedings of the 2nd European Symposium on Principles of Data Mining and Knowledge Discovery, Nantes, France, pp. 450-458.
Search in Google Scholar
Valtchev P, Missaoul R, and Godin R. (2004). Formal concept analysis for knowledge discovery and data mining: The new challenges, Proceedings of the 2nd International Conference on Formal Concept Analysis, Sydney, Australia, pp. 352-371.
Search in Google Scholar
Varmuza, K., Filzmoser, P. and Liebmann, B. (2010). Random projection experiments with chemometric data, Journal of Chemometrics 24(3-4): 209-217.10.1002/cem.1295
Search in Google Scholar
Venter, F. J., Oosthuizen, G. D. and Ross, J. D. (1997). Knowledge discovery in databases using concept lattices, Experts Systems with Applications 13(4): 259-264.10.1016/S0957-4174(97)00047-X
Search in Google Scholar
Wille, R. (2002). Why can concept lattices support knowledge discovery in databases?, Journal of Experimental and Theoretical Artificial Intelligence 14(2-3): 81-92.10.1080/09528130210164161
Search in Google Scholar
Wille, R. (2008). Formal concept analysis as an applied lattice theory, Proceedings of the 4th International Conference on Concept Lattices and Applications, Tunis, Tunisia, pp. 42-67.
Search in Google Scholar
Wu, W. Z., Leung, Y., and Mi, J. S. (2009). Granular computing and knowledge reduction in formal contexts, IEEE Transactions on Knowledge and Data Engineering 21(10): 1461-1474.10.1109/TKDE.2008.223
Search in Google Scholar