Logical analysis of numerical data

Mathematical Programming, Series B

Volumn 79, Issue 1-3, 1997, Pages 163-190

  Boros, Endre ^a   Hammer, Peter L ^a   Ibaraki, Toshihide ^b   Kogan, Alexander ^a,c  

^a RUTGERS UNIVERSITY   (United States)

^b KYOTO UNIVERSITY   (Japan)

^c RUTGERS UNIVERSITY   (United States)

Author keywords

Binarization; Boolean functions; Computational complexity; Data analysis; Machine learning; Monotonicity; Set covering; Thresholdness

Indexed keywords

EID: 0001405180     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02614316     Document Type: Article

References (24)

1. D. Angluin, Queries and concept learning, Machine Learning 2 (1988) 319-342.
2. E. Balas and A. Ho, Set covering algorithms using cutting planes, heuristics and subgradient optimization: A computational study, Mathematical Programming 12 (1980) 37-60.
3. R. Bellman, Introduction to Matrix Analysis (McGraw-Hill, New York, 1960).
4. J.C. Bioch and T. Ibaraki, Complexity of identification and dualization of positive Boolean functions, Information and Computation 123 (1995) 50-63.
5. E. Boros, V. Gurvich, P.L. Hammer, T. Ibaraki and A. Kogan, Decompositions of partially defined Boolean functions, Discrete Applied Mathematics 62 (1995) 51-75.
6. E. Boros, P.L. Hammer, T. Ibaraki, A. Kogan, Logical analysis of numerical data, RUTCOR Research Report RRR 04-97, RUTCOR, Rutgers University, 1997.
7. E. Boros, P.L. Hammer, T. Ibaraki, A. Kogan, E. Mayoraz and I. Muchnik, An implementation of logical analysis of data, RUTCOR Research Report RRR 22-96, RUTCOR, Rutgers University, 1996.
8. E. Boros, T. Ibaraki and K. Makino, Error-free and best-fit extensions of partially defined Boolean functions, RUTCOR Research Report RRR 14-95, RUTCOR, Rutgers University, 1995.
9. E. Boros, T. Ibaraki and K. Makino, Extensions of partially defined Boolean functions with missing data, RUTCOR Research Report RRR 06-96, RUTCOR, Rutgers University, 1996.
10. P. Clark and T. Niblett, The CN2 induction algorithm, Machine Learning 3 (1989) 261-283.
11. Y. Crama, P.L. Hammer and T. Ibaraki, Cause-effect relationships and partially defined Boolean functions, Annals of Operations Research 16 (1988) 299-326.
12. R. Dechter and J. Pearl, Structure identification in relational data, Artificial Intelligence 58 (1992) 237-270.
13. O. Ekin, P.L. Hammer and A. Kogan, On connected Boolean functions, RUTCOR Research Report RRR 36-96, RUTCOR, Rutgers University, 1996.
14. M.R. Garey and D.S. Johnson, Computers and Intractability (Freeman, New York, 1979).
15. P.L. Hammer, Partially defined Boolean functions and cause-effect relationships, in: Proceedings of the International Conference on Multi-Attribute Decision Making Via OR-Based Expert Systems, University of Passau, Passau, Germany, 1986.
16. A.B. Hammer, P.L. Hammer and I. Muchnik, Logical analysis of Chinese productivity patterns, RUTCOR Report RR 1-96, RUTCOR, Rutgers University, 1996.
17. S.J. Hong, R-MINI: An iterative approach for generating minimal rules from examples, IEEE Transactions on Knowledge and Data Engineering, to appear.
18. O.L. Mangasarian, Mathematical programming in machine learning, in: G. Di Pillo and F. Giannessi, eds., Nonlinear Optimization and Applications (Plenum Publishing, New York, 1996) 283-295.
19. I. Muchnik and L. Yampolsky, A pilot study of the concurrent validity of logical analysis of data, as applied to two Beck inventories, RUTCOR Technical Report RTR 02-95, RUTCOR, Rutgers University, 1995.
20. S. Muroga, Threshold Logic and Its Applications (Wiley-Interscience, New York, 1971).
21. P.M. Murphy and D.W. Aha, UCI repository of machine learning databases: Machine readable data repository, Department of Computer Science, University of California, Irvine, 1994.
22. J.R. Quinlan, Induction of decision trees, Machine Learning 1 (1986) 81-106.
23. J.R. Quinlan and R. Rivest, Inferring decision trees using minimum description length principle, Information and Computation 80 (1989) 227-248.
24. L.G. Valiant, A theory of the learnable, Communications of the ACM 27 (1984) 1134-1142.