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Semantics-Preserving Dimensionality Reduction: Rough and Fuzzy-Rough-Based Approaches
December 2004 (vol. 16 no. 12)
pp. 1457-1471
Semantics-preserving dimensionality reduction refers to the problem of selecting those input features that are most predictive of a given outcome; a problem encountered in many areas such as machine learning, pattern recognition, and signal processing. This has found successful application in tasks that involve data sets containing huge numbers of features (in the order of tens of thousands), which would be impossible to process further. Recent examples include text processing and Web content classification. One of the many successful applications of rough set theory has been to this feature selection area. This paper reviews those techniques that preserve the underlying semantics of the data, using crisp and fuzzy rough set-based methodologies. Several approaches to feature selection based on rough set theory are experimentally compared. Additionally, a new area in feature selection, feature grouping, is highlighted and a rough set-based feature grouping technique is detailed.

[1] H. Almuallim and T.G. Dietterich, “Learning with Many Irrelevant Features,” Proc. Ninth Nat'l Conf. Artificial Intelligence, pp. 547-552, 1991.
[2] “Rough Sets and Current Trends in Computing,” Proc. Third Int'l Conf., J.J. Alpigini, J.F. Peters, J. Skowronek, and N. Zhong, eds., 2002.
[3] J. Bazan, A. Skowron, and P. Synak, “Dynamic Reducts as a Tool for Extracting Laws from Decision Tables,” Proc. Eighth Symp. Methodologies for Intelligent Systems, Z.W. Ras and M. Zemankova, eds., pp. 346-355, 1994.
[4] J. Bazan, “A Comparison of Dynamic and Non-Dynamic Rough Set Methods for Extracting Laws from Decision Tables,” Rough Sets in Knowledge Discovery, L. Polkowski and A. Skowron, eds., pp. 321-365, Physica - Verlag, 1998.
[5] T. Beaubouef, F.E. Petry, and G. Arora, “Information Measures for Rough and Fuzzy Sets and Application to Uncertainty in Relational Databases,” Rough-Fuzzy Hybridization: A New Trend in Decision Making, 1999.
[6] M.J. Beynon, “An Investigation of $\beta{\hbox{-}}{\rm{Reduct}}$ Selection within the Variable Precision Rough Sets Model,” Proc. Second Int'l Conf. Rough Sets and Current Trends in Computing (RSCTC 2000), pp. 114-122, 2000.
[7] M.J. Beynon, “Reducts within the Variable Precision Rough Sets Model: A Further Investigation,” European J. Operational Research, vol. 134, no. 3, pp. 592-605, 2001.
[8] C.L. Blake and C.J. Merz UCI Repository of Machine Learning Databases, University of California at Irvine, 1998,
[9] A.T., Bjorvand and J. Komorowski, “Practical Applications of Genetic Algorithms for Efficient Reduct Computation,” Proc. 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics, A. Sydow, ed., vol. 4, pp. 601-606, 1997.
[10] A. Chouchoulas and Q. Shen, “Rough Set-Aided Keyword Reduction for Text Categorisation,” Applied Artificial Intelligence, vol. 15, no. 9, pp. 843-873, 2001.
[11] A. Chouchoulas, J. Halliwell, and Q. Shen, “On the Implementation of Rough Set Attribute Reduction,” Proc. 2002 UK Workshop Computational Intelligence, pp. 18-23, 2002.
[12] M. Dash and H. Liu, “Feature Selection for Classification,” Intelligent Data Analysis, vol. 1, no. 3, 1997.
[13] P. Devijver and J. Kittler, Pattern Recognition: A Statistical Approach. Prentice Hall, 1982.
[14] J. Dong, N. Zhong, and S. Ohsuga, “Using Rough Sets with Heuristics for Feature Selection,” New Directions in Rough Sets, Data Mining, and Granular-Soft Computing, Proc. Seventh Int'l Workshop (RSFDGrC '99), pp. 178-187, 1999.
[15] G. Drwal and A. Mrókek, “System RClass— Software Implementation of the Rough Classifier,” Proc. Seventh Int'l Symp. Intelligent Information Systems, pp. 392-395, 1998.
[16] G. Drwal, “Rough and Fuzzy-Rough Classification Methods Implemented in RClass System,” Proc. Second Int'l Conf. Rough Sets and Current Trends in Computing (RSCTC 2000), pp. 152-159, 2000.
[17] D. Dubois and H. Prade, “Putting Rough Sets and Fuzzy Sets Together,” Intelligent Decision Support, pp. 203-232, 1992.
[18] “Rough Set Data Analysis,” I. Düntsch and G. Gediga, eds., Encyclopedia of Computer Science and Technology, A. Kent and J.G. Williams, eds., pp. 281-301, 2000.
[19] I. Düntsch and G. Gediga, Rough Set Data Analysis: A Road to Non-Invasive Knowledge Discovery. Bangor: Methodos, 2000.
[20] A Brief Introduction to Rough Sets, EBRSC, Copyright 1993, information available at tro.txt .
[21] U. Höhle, “Quotients with Respect to Similarity Relations,” Fuzzy Sets and Systems, vol. 27, pp. 31-44, 1988.
[22] J. Jelonek, K. Krawiec, and R. Slowinski, “Rough Set Reduction of Attributes and Their Domains for Neural Networks,” Computational Intelligence 11, pp. 339-347, 1995.
[23] R. Jensen and Q. Shen, “Using Fuzzy Dependency-Guided Attribute Grouping in Feature Selection,” Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, Proc. Ninth Int'l Conf. (RSFDGrC 2003), pp. 250-255, 2003.
[24] R. Jensen and Q. Shen, “Finding Rough Set Reducts with Ant Colony Optimization,” Proc. 2003 UK Workshop Computational Intelligence, pp. 15-22, 2003.
[25] R. Jensen and Q. Shen, “Fuzzy-Rough Attribute Reduction with Application to Web Categorization,” Fuzzy Sets and Systems, vol. 141, no. 3, pp. 469-485, 2004.
[26] K. Kira and L.A. Rendell, “The Feature Selection Problem: Traditional Methods and a New Algorithm,” Proc. Ninth Nat'l Conf. Artificial Intelligence, pp. 129-134, 1992.
[27] J. Komorowski, Z. Pawlak, L. Polkowski, and A. Skowron, “Rough Sets: A Tutorial,” Rough-Fuzzy Hybridization: A New Trend in Decision Making, pp. 3-98, 1999.
[28] M. Kryszkiewicz, “Maintenance of Reducts in the Variable Precision Rough Sets Model,” ICS Research Report 31/94, Warsaw Univ. of Tech nology, 1994.
[29] P. Langley, “Selection of Relevant Features in Machine Learning,” Proc. AAAI Fall Symp. Relevance, pp. 1-5, 1994.
[30] Feature Extraction, Construction and Selection: A Data Mining Perspective (Kluwer International Series in Engineering & Computer Science), H. Liu and H. Motoda, eds. Kluwer Academic Publishers, 1998.
[31] A.J. Miller, Subset Selection in Regression. Chapman and Hall, 1990.
[32] T. Mitchell, Machine Learning. McGraw-Hill, 1997.
[33] M. Modrzejewski, “Feature Selection Using Rough Sets Theory,” Proc. 11th Int'l Conf. Machine Learning, pp. 213-226, 1993.
[34] S.H. Nguyen and H.S. Nguyen, “Some Efficient Algorithms for Rough Set Methods,” Proc. Conf. Information Processing and Management of Uncertainty in Knowledge-Based Systems, pp. 1451-1456, 1996.
[35] H.S. Nguyen and A. Skowron, “Boolean Reasoning for Feature Extraction Problems,” Proc. Int'l Symp. Methodologies for Intelligent Systems (ISMIS), pp. 117-126, 1997.
[36] Rough-Fuzzy Hybridization: A New Trend in Decision Making, S.K. Pal and A. Skowron, eds. Springer Verlag, 1999.
[37] Z. Pawlak, “Rough Sets,” Int'l J. Computer and Information Sciences, vol. 11, no. 5, pp. 341-356, 1982.
[38] Z. Pawlak, Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishing, 1991.
[39] Z. Pawlak and A. Skowron, “Rough Membership Functions,” Advances in the Dempster-Shafer Theory of Evidence, R. Yager, M. Fedrizzi, and J. Kacprzyk, eds., pp. 251-271, 1994.
[40] “Rough Set Methods and Applications: New Developments in Knowledge Discovery in Information Systems,” Studies in Fuzziness and Soft Computing, L. Polkowski, T.Y. Lin, and S. Tsumoto, eds., vol. 56, Physica-Verlag, 2000.
[41] L. Polkowski, “Rough Sets: Mathematical Foundations,” Advances in Soft Computing, Physica Verlag, 2002.
[42] J.R. Quinlan, “C4.5: Programs for Machine Learning,” The Morgan Kaufmann Series in Machine Learning, Morgan Kaufmann Publishers, 1993.
[43] B. Raman and T.R. Ioerger, “Instance-Based Filter for Feature Selection,” J. Machine Learning Research 1, pp. 1-23, 2002.
[44] The ROSETTA homepage, http://rosetta.lcb.uu.segeneral/, 2004.
[45] RSES: Rough Set Exploration System, http://logic.mimuw., 2004.
[46] J.C. Schlimmer, “Efficiently Inducing Determinations— A Complete and Systematic Search Algorithm that Uses Optimal Pruning,” Proc. Int'l Conf. Machine Learning, pp. 284-290, 1993.
[47] R. Setiono and H. Liu, “Neural Network Feature Selector,” IEEE Trans. Neural Networks, vol. 8, no. 3, pp. 645-662, 1997.
[48] H. Sever, V.V. Raghavan, and T.D. Johnsten, “The Status of Research on Rough Sets for Knowledge Discovery in Databases,” Proc. ICNPAA-98: Second Int'l Conf. Nonlinear Problems in Aviation and Aerospace, 1998.
[49] G. Shafer, A Mathematical Theory of Evidence. Princeton Univ. Press, 1976.
[50] C. Shang and Q. Shen, “Rough Feature Selection for Neural Network Based Image Classification,” Int'l J. Image Graphics, vol. 2, no. 4, pp. 541-556, 2002.
[51] Q. Shen and A. Chouchoulas, “A Fuzzy-Rough Approach for Generating Classification Rules,” Pattern Recognition, vol. 35, no. 11, pp. 341-354, 2002.
[52] Q. Shen and R. Jensen, “Selecting Informative Features with Fuzzy-Rough Sets and Its Application for Complex Systems Monitoring,” Pattern Recognition, vol. 37, no. 7, pp. 1351-1363, 2004.
[53] A. Skowron and C. Rauszer, “The Discernibility Matrices and Functions in Information Systems,” Intelligent Decision Support, pp. 331-362, 1992.
[54] A. Skowron and J.W. Grzymala-Busse, “From Rough Set Theory to Evidence Theory,” Advances in the Dempster-Shafer Theory of Evidence, R. Yager, M. Fedrizzi, and J. Kasprzyk, eds. John Wiley & Sons, Inc., 1994.
[55] A. Skowron and J. Stepaniuk, “Tolerance Approximation Spaces,” Fundamenta Informaticae, vol. 27, no. 2, pp. 245-253, 1996.
[56] A. Skowron, J. Komorowski, Z. Pawlak, and L. Polkowski, “Rough Sets Perspective on Data and Knowledge,” Handbook of Data Mining and Knowledge Discovery, pp. 134-149, Oxford Univ. Press, 2002.
[57] A. Skowron and S.K. Pal, “Rough Sets, Pattern Recognition, and Data Mining,” Pattern Recognition Letters, vol. 24, no. 6, pp. 829-933, 2003.
[58] D. Slezak, “Approximate Reducts in Decision Tables,” Proc. Sixth Int'l Conf., Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU '96), pp. 1159-1164, 1996.
[59] D. Slezak, “Normalized Decision Functions and Measures for Inconsistent Decision Tables Analysis,” Fundamenta Informaticae, vol. 44, no. 3, pp. 291-319, 2000.
[60] Intelligent Decision Support, R. Slowinski, ed. Kluwer Academic Publishers, 1992.
[61] R. Slowinski and D. Vanderpooten, “Similarity Relation as a Basis for Rough Approximations,” Advances in Machine Intelligence and Soft Computing, pp. 17-33, P. Wang, ed., vol. IV, , Duke Univ. Press, 1997.
[62] J. Stefanowski and A. Tsoukiàs, “Valued Tolerance and Decision Rules,” Rough Sets and Current Trends in Computing, pp. 212-219, 2000.
[63] R.W. Swiniarski and A. Skowron, “Rough Set Methods in Feature Selection and Recognition,” Pattern Recognition Letters, vol. 24, no. 6, pp. 833-849, 2003.
[64] H. Thiele, “Fuzzy Rough Sets versus Rough Fuzzy Sets— An Interpretation and a Comparative Study Using Concepts of Modal Logics,” Technical Report no. CI-30/98, Univ. of Dortmund, 1998.
[65] C.J. van Rijsbergen, Information Retrieval. London: Butterworths, 1979.
[66] J. Wang and J. Wang, “Reduction Algorithms Based on Discernibility Matrix: The Ordered Attributes Method,” J. Computer Science and Technology, vol. 16, no. 6, pp. 489-504, 2001.
[67] J. Wróblewski, “Finding Minimal Reducts Using Genetic Algorithms,” Proc. Second Ann. Joint Conf. Information Sciences, pp. 186-189, 1995.
[68] M. Wygralak, “Rough Sets and Fuzzy Sets— Some Remarks on Interrelations,” Fuzzy Sets and Systems, vol. 29, pp. 241-243, 1989.
[69] Y.Y. Yao, “A Comparative Study of Fuzzy Sets and Rough Sets,” Information Sciences, vol. 109, pp. 21-47, 1998.
[70] L.A. Zadeh, “Fuzzy Sets,” Information and Control, vol. 8, pp. 338-353, 1965.
[71] N. Zhong, J. Dong, and S. Ohsuga, “Using Rough Sets with Heuristics for Feature Selection,” J. Intelligent Information Systems, vol. 16, no. 3, pp. 199-214, 2001.
[72] W. Ziarko, “Variable Precision Rough Set Model,” J. Computer and System Sciences, vol. 46, no. 1, pp. 39-59, 1993.

Index Terms:
Dimensionality reduction, feature selection, feature transformation, rough selection, fuzzy-rough selection.
Richard Jensen, Qiang Shen, "Semantics-Preserving Dimensionality Reduction: Rough and Fuzzy-Rough-Based Approaches," IEEE Transactions on Knowledge and Data Engineering, vol. 16, no. 12, pp. 1457-1471, Dec. 2004, doi:10.1109/TKDE.2004.96
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