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2014 | OriginalPaper | Chapter

12. Applications to Databases and Data Mining

Authors : Dan A. Simovici, Chabane Djeraba

Published in: Mathematical Tools for Data Mining

Publisher: Springer London

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Abstract

This chapter presents an introduction to the relational model, which is of paramount importance for data mining. We continue with certain equivalence relations (and partitions) that can be associated to sets of attributes of tables.

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Literature
1.
go back to reference E.F. Codd, A relational model of data for large shared data banks. Commun. ACM 13, 377–387 (1970)CrossRefMATH E.F. Codd, A relational model of data for large shared data banks. Commun. ACM 13, 377–387 (1970)CrossRefMATH
2.
go back to reference E.F. Codd, The Relational Model for Database Management, Version 2 (Addison-Wesley, Reading, 1990)MATH E.F. Codd, The Relational Model for Database Management, Version 2 (Addison-Wesley, Reading, 1990)MATH
3.
go back to reference C.J. Date, An Introduction to Database Systems, 8th edn. (Addison-Wesley, Boston, 2003)MATH C.J. Date, An Introduction to Database Systems, 8th edn. (Addison-Wesley, Boston, 2003)MATH
4.
go back to reference J.H. Havrda, F. Charvat, Quantification methods of classification processes: concepts of structural \(\alpha \)-entropy. Kybernetica 3, 30–35 (1967)MATHMathSciNet J.H. Havrda, F. Charvat, Quantification methods of classification processes: concepts of structural \(\alpha \)-entropy. Kybernetica 3, 30–35 (1967)MATHMathSciNet
5.
go back to reference B. Sayrafi, A Measure-Theoretic Framework for Constraints and Bounds on Measurements of Data. Ph.D. thesis, Indiana University, 2005 B. Sayrafi, A Measure-Theoretic Framework for Constraints and Bounds on Measurements of Data. Ph.D. thesis, Indiana University, 2005
6.
go back to reference E.H. Lieb, M. Ruskai, Proof of the strong subadditivity of quantum-mechanical entropy. J. Math. Phys. 14, 1938–1941 (1973)CrossRefMathSciNet E.H. Lieb, M. Ruskai, Proof of the strong subadditivity of quantum-mechanical entropy. J. Math. Phys. 14, 1938–1941 (1973)CrossRefMathSciNet
7.
go back to reference B. Sayrafi, D. van Gucht, in Principles of Database Systems, ed. by C. Li. Differential Constraints, Baltimore, MD, (ACM, New York, 2005), pp. 348–357 B. Sayrafi, D. van Gucht, in Principles of Database Systems, ed. by C. Li. Differential Constraints, Baltimore, MD, (ACM, New York, 2005), pp. 348–357
8.
go back to reference B. Sayrafi, D. van Gucht, M. Gyssens, Measures in databases and datamining. Technical Report TR602, Indiana University, 2004 B. Sayrafi, D. van Gucht, M. Gyssens, Measures in databases and datamining. Technical Report TR602, Indiana University, 2004
9.
go back to reference F.M. Malvestuto, Statistical treatment of the information content of a database. Inf. Syst. 11, 211–223 (1986)CrossRefMATH F.M. Malvestuto, Statistical treatment of the information content of a database. Inf. Syst. 11, 211–223 (1986)CrossRefMATH
10.
go back to reference T.T. Lee, An information-theoretic analysis of relational databases. IEEE Trans. Softw. Eng. 13, 1049–1061 (1997) T.T. Lee, An information-theoretic analysis of relational databases. IEEE Trans. Softw. Eng. 13, 1049–1061 (1997)
11.
go back to reference M.M. Dalkilic, E.L. Robertson, Information dependencies. Technical Report TR531, Indiana University, 1999 M.M. Dalkilic, E.L. Robertson, Information dependencies. Technical Report TR531, Indiana University, 1999
12.
go back to reference T.M. Mitchell, Machine Learning (McGraw-Hill, New York, 1997)MATH T.M. Mitchell, Machine Learning (McGraw-Hill, New York, 1997)MATH
13.
go back to reference J.R. Quinlan, C4.5: Programs for Machine Learning (Morgan Kaufmann, San Mateo, 1993) J.R. Quinlan, C4.5: Programs for Machine Learning (Morgan Kaufmann, San Mateo, 1993)
14.
go back to reference E. Boros, P.L. Hammer, T. Ibaraki, A. Kogan, E. Mayoraz, I. Muchnik, An implementation of logical analysis of data. IEEE Trans. Knowl. Data Eng. 12, 292–306 (2000)CrossRef E. Boros, P.L. Hammer, T. Ibaraki, A. Kogan, E. Mayoraz, I. Muchnik, An implementation of logical analysis of data. IEEE Trans. Knowl. Data Eng. 12, 292–306 (2000)CrossRef
15.
go back to reference F. Rosenblatt, The perceptron: a probabilistic model for information storage and organization in the brain. Psychol. Rev. 65, 386–407 (1958)CrossRefMathSciNet F. Rosenblatt, The perceptron: a probabilistic model for information storage and organization in the brain. Psychol. Rev. 65, 386–407 (1958)CrossRefMathSciNet
16.
go back to reference A.B.J. Novikoff, On convergence proofs on perceptrons, in Proceedings of the Symposium on Mathematical Theory of Automata A.B.J. Novikoff, On convergence proofs on perceptrons, in Proceedings of the Symposium on Mathematical Theory of Automata
17.
go back to reference Y. Freund, R.E. Shapire, Large margin classification using the perceptron algorithm. Mach. Learn. 37, 277–296 (1999)CrossRefMATH Y. Freund, R.E. Shapire, Large margin classification using the perceptron algorithm. Mach. Learn. 37, 277–296 (1999)CrossRefMATH
18.
go back to reference N. Cristianini, J. Shawe-Taylor, Support Vector Machines (Cambridge University, Cambridge, 2000) N. Cristianini, J. Shawe-Taylor, Support Vector Machines (Cambridge University, Cambridge, 2000)
19.
go back to reference D. Maier, The Theory of Relational Databases (Computer Science Press, Rockville, 1983)MATH D. Maier, The Theory of Relational Databases (Computer Science Press, Rockville, 1983)MATH
20.
go back to reference J.D. Ullman, Database and Knowledge-Base Systems (2 vols.) (Computer Science Press, Rockville, 1988) J.D. Ullman, Database and Knowledge-Base Systems (2 vols.) (Computer Science Press, Rockville, 1988)
21.
go back to reference D.A. Simovici, R.L. Tenney, Relational Database Systems (Academic Press, New York, 1995) D.A. Simovici, R.L. Tenney, Relational Database Systems (Academic Press, New York, 1995)
22.
go back to reference Y. Huhtala, J. Kärkkäinen, P. Porkka, H. Toivonen, Efficient discovery of functional and approximate dependencies using partitions (extended version). TR C-79, University of Helsinki, Department of Computer Science, Helsinki, Finland, 1997 Y. Huhtala, J. Kärkkäinen, P. Porkka, H. Toivonen, Efficient discovery of functional and approximate dependencies using partitions (extended version). TR C-79, University of Helsinki, Department of Computer Science, Helsinki, Finland, 1997
25.
26.
go back to reference S. Jaroszewicz, D.A. Simovici, On axiomatization of conditional entropy, Proceedings of the 29th International Symposium for Multiple-Valued Logic, Freiburg, Germany (IEEE Computer Society, Los Alamitos, 1999), pp. 24–31 S. Jaroszewicz, D.A. Simovici, On axiomatization of conditional entropy, Proceedings of the 29th International Symposium for Multiple-Valued Logic, Freiburg, Germany (IEEE Computer Society, Los Alamitos, 1999), pp. 24–31
27.
go back to reference D. Simovici, S. Jaroszewicz, Generalized conditional entropy and decision trees, in Proceedings of Extraction et Gestion des connaissances—EGC 2003 (Lavoisier, Paris, 2003), pp. 363–380 D. Simovici, S. Jaroszewicz, Generalized conditional entropy and decision trees, in Proceedings of Extraction et Gestion des connaissances—EGC 2003 (Lavoisier, Paris, 2003), pp. 363–380
28.
go back to reference D.A. Simovici, S. Jaroszewicz, in Finite Versus Infinite, ed. by C. Calude, G. Paun. On Information-Theoretical Aspects of Relational Databases (Springer, London, 2000), pp. 301–321 D.A. Simovici, S. Jaroszewicz, in Finite Versus Infinite, ed. by C. Calude, G. Paun. On Information-Theoretical Aspects of Relational Databases (Springer, London, 2000), pp. 301–321
29.
go back to reference E. Boros, P.L. Hammer, T. Ibaraki, A. Kogan, A logical analysis of numerical data. Math. Prog. 79, 163–190 (1997)MATHMathSciNet E. Boros, P.L. Hammer, T. Ibaraki, A. Kogan, A logical analysis of numerical data. Math. Prog. 79, 163–190 (1997)MATHMathSciNet
Metadata
Title
Applications to Databases and Data Mining
Authors
Dan A. Simovici
Chabane Djeraba
Copyright Year
2014
Publisher
Springer London
DOI
https://doi.org/10.1007/978-1-4471-6407-4_12

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