Abstract
In this chapter, we describe a new data-driven transformation that facilitates many data mining, interpretation, and analysis tasks. This approach, called MembershipMap, strives to granulate and extract the underlying sub-concepts of each raw attribute. The orthogonal union of these sub-concepts are then used to define a new membership space. The sub-concept soft labels of each point in the original space determine the position of that point in the new space. Since sub-concept labels are prone to uncertainty inherent in the original data and in the initial extraction process, a combination of labeling schemes that are based on different measures of uncertainty will be presented. In particular, we introduce the CrispMap, the FuzzyMap, and the PossibilisticMap. We outline the advantages and disadvantages of each mapping scheme, and we show that the three transformed spaces are complementary. We also show that in addition to improving the performance of clustering by taking advantage of the richer information content, the MembershipMap can be used as a flexible pre-processing tool to support such tasks as: sampling, data cleaning, and outlier detection.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Fayyad, U., Piatetsky-Shapiro, G., Smyth, P., Uthurusamy, R.: Advances in Knowledge Discovery and Data Mining. MIT Press, Cambridge (1996)
Famili, A., Shen, W., Weber, R., Simoudis, E.: Data preprocessing and intelligent data analysis. Intelligent Data Analysis 1(1), 3–23 (1997)
Han, J., Kamber, M.: Data Mining Concepts and Techniques. Morgan Kaufmann, San Francisco (2001)
Pyle, D.: Data Preparation for Data Mining. Morgan Kaufmann, San Francisco (1999)
Jolliffe, I.: Principal Component Analysis. Springer, Heidelberg (1986)
Shepard, R.N.: The analysis of proximities: multidimensional scaling with an unknown distance function I and II. Psychometrika 27, 125–139, 219–246 (1962)
Kohonen, T.: Self-Organization and Associative Memory. Springer, Heidelberg (1989)
Sammon, J.W.: A nonlinear mapping for data analysis. IEEE Transactions on Computers 18, 401–409 (1969)
Jagadish, H.V.: A retrieval technique for similar shape. In: ACM SIGMOD, pp. 208–217 (1991)
Faloutsos, C., Lin, K.-I.: FastMap: A fast algorithm for indexing, data-mining and visualization of traditional and multimedia datasets. In: SIGMOD, pp. 163–174 (1995)
Schafer, J.L.: Analysis of Incomplete Multivariate Data. Chapman and Hall, Boca Raton (1997)
Wang, X., Barbará, S.D.: Modeling and imputation of large incomplete multidimensional data sets. In: Fourth International Conference on Data Warehousing and Knowledge Discovery, pp. 286–295 (2002)
Gray, J., Chaudhuri, S., Bosworth, A., Layman, A., Reichart, D., Venkatrao, M., Pellow, F., Pirahesh, H.: Data cube: A relational aggregation operator generalizing group-by, cross-tab, and sub-totals. J. Data Mining and Knowledge Discovery 1(1), 29–53 (1997)
Chauduri, S., Dayal, U.: An overview of data warehousing and OLAP technology. SIGMOD Record 26(1), 65–74 (1997)
Almuallim, H., Dietterich, T.G.: Learning with many irrelevant features. In: Ninth National Conf. AI, pp. 547–552 (1991)
Dash, M., Liu, H., Yao, J.: Dimensionality reduction for unsupervised data. In: 9th IEEE Int. Conf. on Tools with AI, ICTAI 1997, pp. 532–539 (1997)
Frigui, H., Nasraoui, O.: Unsupervised learning of prototypes and attribute weights. Pattern Recognition 37(3), 567–581 (2004)
Kivinen, J., Mannila, H.: The power of sampling in knowledge discovery. In: Thirteenth ACM SIGACT-SIGMOD-SIGART Symp. Principles of Database Sys., pp. 77–85 (1994)
Dougherty, J., Kohavi, R., Sahami, M.: Supervised and unsupervised discretization of continuous features. In: 12th International Conference on Machine Learning, pp. 194–202 (1995)
Ho, K., Scott, P.: Zeta: a global method for discretization of continuous variables. In: 3rd International Conference on Knowledge Discovery and Data Mining (KDD 1997), pp. 191–194. AAAI Press, Menlo Park (1997)
Liu, H., Hussain, F., Tan, C., Dash, M.: Discretization: an enabling technique. Journal of Data Mining and Knowledge Discovery 6(4), 393–423 (2002)
Barbará, S.D., DuMouchel, W., Faloutsos, C., Haas, P., Hellerstein, J., Ioannidis, Y., Jagadish, H., Johnson, T., Ng, R., Poosala, V., Ross, K., Sevcik, K.: The new jersey data reduction report. Bulletin of the Technical Committee on Data Engineering 20, 3–45 (1997)
Duda, R.O., Hart, P.E.: Pattern Classification and Scene Analysis. John Wiley and Sons, Chichester (1973)
Kaufman, L., Rousseeuw, P.: Finding Groups in Data: An Introduction to Cluster Analysis. John Wiley and Sons, Chichester (1990)
Zimmermann, H.Z.: Fuzzy Set Theory and Its Applications, 4th edn. Kluwer, Dordrecht (2001)
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)
Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society Series B 39(1), 1–38 (1977)
Frigui, H., Krishnapuram, R.: A robust competitive clustering algorithm with applications in computer vision. IEEE Trans. Patt. Analysis Mach. Intell. 21(5), 450–465 (1999)
Krishnapuram, R., Keller, J.: A possibilistic approach to clustering. IEEE Trans. Fuzzy Systems 1(2), 98–110 (1993)
Davé, R.N., Krishnapuram, R.: Robust clustering methods: A unified view. IEEE Trans. Fuzzy Systems 5(2), 270–293 (1997)
Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A.: Robust Statistics the Approach Based on Influence Functions. John Wiley & Sons, New York (1986)
Pedrycz, W.: Granular Computing: An Emerging Paradigm. Springer, Heidelberg (2001)
Yao, Y., Yao, J.: Granular computing as a basis for consistent classification problem. In: Chen, M.-S., Yu, P.S., Liu, B. (eds.) PAKDD 2002. LNCS (LNAI), vol. 2336, pp. 101–106. Springer, Heidelberg (2002)
Runkler, T.A., Roychowdhury, S.: Generating decision trees and membership functions by fuzzy clustering. In: Seventh European Congress on Intelligent Techniques and Soft Computing (1999)
Ishibuchi, H., Nakashima, T., Murata: Performance evaluation of fuzzy classifier systems for multidimensional pattern classification problems. IEEE Trans. on Systems, Man, and Cybernetics - Part B 29, 601–618 (1999)
Klawonn, F., Kruse, R.: Derivation of fuzzy classification rules from multidimensional data. In: Lasker, X.L.G.E. (ed.) Advances in Intelligent Data Analysis, The International Institute for Advanced Studies in Systems Research and Cybernetics, Windsor, Ontario, pp. 90–94 (1995)
Frigui, H., Krishnapuram, R.: Clustering by competitive agglomeration. Pattern Recognition 30(7), 1223–1232 (1997)
Rhouma, M., Frigui, H.: Self-organization of a population of coupled oscillators with application to clustering. IEEE Trans. Patt. Analysis Mach. Intell. 23(2), 180–195 (2001)
Otsu, N.: A threshold selection method from gray level histograms. IEEE Trans. Systems, Man and Cybernetics 9, 62–66 (1979)
Wang, Z., Klir, G.: Fuzzy measure theory. Plenum Press, New York (1992)
Pedrycz, W., Waletzky, J.: Fuzzy clustering with partial supervision. IEEE Trans. Systems, Man and Cybernetics 27(5), 787–795 (1997)
Carson, C., Thomas, M., Belongie, S., Hellerstein, J.M., Malik, J.: Blobworld: A system for region-based image indexing and retrieval. In: Huijsmans, D.P., Smeulders, A.W.M. (eds.) VISUAL 1999. LNCS, vol. 1614, pp. 509–516. Springer, Heidelberg (1999)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Frigui, H. (2008). MembershipMap: A Data Transformation for Knowledge Discovery Based on Granulation and Fuzzy Membership Aggregation. In: Jain, L.C., Sato-Ilic, M., Virvou, M., Tsihrintzis, G.A., Balas, V.E., Abeynayake, C. (eds) Computational Intelligence Paradigms. Studies in Computational Intelligence, vol 137. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79474-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-540-79474-5_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79473-8
Online ISBN: 978-3-540-79474-5
eBook Packages: EngineeringEngineering (R0)