Geometric decision tree

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

Volumn 42, Issue 1, 2012, Pages 181-192

  Manwani, Naresh ^a   Sastry, P S ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

Decision trees; generalized eigenvalue problem; multiclass classification; oblique decision tree

Indexed keywords

DECISION-TREE ALGORITHM; EMPIRICAL STUDIES; GENERALIZED EIGENVALUE PROBLEM; GEOMETRIC STRUCTURE; METHOD OF LEARNING; MULTICLASS CLASSIFICATION; OBLIQUE DECISION TREE; OPTIMIZATION PROBLEMS; SHOW THROUGH; TOPDOWN;

DECISION TREES; EIGENVALUES AND EIGENFUNCTIONS; FORESTRY; GEOMETRY; LEARNING ALGORITHMS;

TREES (MATHEMATICS);

ALGORITHMS; FORESTRY; GEOMETRY; PROBLEM SOLVING; TREES;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; COMPUTER SIMULATION; DECISION SUPPORT SYSTEM; METHODOLOGY; THEORETICAL MODEL;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; COMPUTER SIMULATION; DECISION SUPPORT TECHNIQUES; MODELS, THEORETICAL; PATTERN RECOGNITION, AUTOMATED;

EID: 84856295338     PISSN: 10834419     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSMCB.2011.2163392     Document Type: Article

References (35)

1. L. Breiman, J. Friedman, R. Olshen, C. Stone Classification Regression Trees. Belmont CA: Wadsworth and Brooks, 1984, ser. Statistics/Probability Series.
2. J. Quinlan, "Induction of decision trees," Mach. Learn., vol. 1, no. 1, pp. 81-106, 1986.
3. R. O. Duda and H. Fossum, "Pattern classification by iteratively determined linear and piecewise linear discriminant functions," IEEE Trans. Electron. Comput., vol. EC-15, no. 2, pp. 220-232, Apr. 1966.
4. M. I. Jordan, "A statistical approach to decision tree modeling," in Proc. 7th Annu. Conf. COLT, New Brunswick, NJ, Jul. 1994, pp. 13-20.
5. K. P. Bennett, "Global tree optimization: A non-greedy decision tree algorithm," Comput. Sci. Statist., vol. 26, pp. 156-160, 1994.
6. K. P. Bennett and J. A. Blue, "Optimal decision trees," Dept. Math. Sci., Rensselaer Polytech. Inst., Troy, NY, Tech. Rep. R.P.I. Math Report No. 214, 1996.
7. K. P. Bennett and J. A. Blue, "A support vector machine approach to decision trees," in Proc. IEEE World Congr. Comput. Intell., Anchorage, AK, May 1998, vol. 3, pp. 2396-2401.
8. A. Suarez and J. F. Lutsko, "Globally optimal fuzzy decision trees for classification and regression," IEEE Trans. Pattern Anal. Mach. Intell., vol. 21, no. 12, pp. 1297-1311, Dec. 1999. (Pubitemid 30568930)
9. L. Rokach and O. Maimon, "Top-down induction of decision trees classifiers-A survey," IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 35, no. 4, pp. 476-487, Nov. 2005. (Pubitemid 41638167)
10. O. L. Mangasarian, "Multisurface method of pattern separation," IEEE Trans. Inf. Theory, vol. IT-14, no. 6, pp. 801-807, Nov. 1968.
11. T. Lee and J. A. Richards, "Piecewise linear classification using seniority logic committee methods, with application to remote sensing," Pattern Recognit., vol. 17, no. 4, pp. 453-464, 1984. (Pubitemid 14646539)
12. P. E. Utgoff and C. E. Brodley, "Linear machine decision trees," Dept. Comput. Sci., Univ. Massachusettes, Amhersts, MA, Tech. Rep. 91-10, Jan. 1991.
13. M. Lu, C. L. P. Chen, J. Huo, and X. Wang, "Multi-stage decision tree based on inter-class and inner-class margin of SVM," in Proc. IEEE Int. Conf. Syst., Man, Cybern., San Antonio, TX, 2009, pp. 1875-1880.
14. R. Tibshirani and T. Hastie, "Margin trees for high dimensional classification," J. Mach. Learn. Res., vol. 8, pp. 637-652, Mar. 2007. (Pubitemid 46473522)
15. M. F. Amasyali and O. Ersoy, "Cline: A new decision-tree family," IEEE Trans. Neural Netw., vol. 19, no. 2, pp. 356-363, Feb. 2008. (Pubitemid 351359300)
16. A. Kołakowska and W. Malina, "Fisher sequential classifiers," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 35, no. 5, pp. 988-998, Oct. 2005. (Pubitemid 41444582)
17. D. Dancey, Z. A. Bandar, and D. McLean, "Logistic model tree extraction from artificial neural networks," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 37, no. 4, pp. 794-802, Aug. 2007. (Pubitemid 47103934)
18. W. Pedrycz and Z. A. Sosnowski, "Genetically optimized fuzzy decision trees," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 35, no. 3, pp. 633-641, Jun. 2005. (Pubitemid 40794874)
19. B. Chandra and P. P. Varghese, "Fuzzy SLIQ decision tree algorithm," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 38, no. 5, pp. 1294-1301, Oct. 2008.
20. C. Ferri, P. Flach, and J. Hernández-Orallo, "Learning decision trees using the area under the ROC curve," in Proc. 19th ICML, San Francisco, CA, Jul. 2002, pp. 139-146.
21. S. K. Murthy, S. Kasif, and S. Salzberg, "A system for induction of oblique decision trees," J. Artif. Intell. Res., vol. 2, no. 1, pp. 1-32, Aug. 1994.
22. S.-H. Cha and C. Tappert, "A genetic algorithm for constructing compact binary decision trees," J. Pattern Recognit. Res., vol. 4, no. 1, pp. 1-13, Feb. 2009.
23. Z. Fu, B. L. Golden, S. Lele, S. Raghavan, and E. A. Wasil, "A genetic algorithm-based approach for building accurate decision trees," INFORMS J. Comput., vol. 15, no. 1, pp. 3-22, Jan. 2003. (Pubitemid 39042730)
24. E. Cantú-Paz and C. Kamath, "Inducing oblique decision trees with evolutionary algorithms," IEEE Trans. Evol. Comput., vol. 7, no. 1, pp. 54-68, Feb. 2003.
25. J. M. Pangilinan and G. K. Janssens, "Pareto-optimality of oblique decision trees from evolutionary algorithms," J. Global Optim., pp. 1-11, Oct. 2010.
26. S. Shah and P. S. Sastry, "New algorithms for learning and pruning oblique decision trees," IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 29, no. 4, pp. 494-505, Nov. 1999. (Pubitemid 32081624)
27. P. S. Sastry, M. Magesh, and K. P. Unnikrishnan, "Two timescale analysis of the alopex algorithm for optimization," Neural Comput., vol. 14, no. 11, pp. 2729-2750, Nov. 2002.
28. O. L. Mangasarian and E. W. Wild, "Multisurface proximal support vector machine classification via generalized eigenvalues," IEEE Trans. Pattern Anal. Mach. Intell., vol. 28, no. 1, pp. 69-74, Jan. 2006. (Pubitemid 46395305)
29. N. Manwani and P. S. Sastry, "A geometric algorithm for learning oblique decision trees," in Proc. 3rd Int. Conf. PReMI, New Delhi, India, Dec. 2009, pp. 25-31.
30. G. H. Gulub and C. F. V. Loan, Matrix Computations, 3rd ed. Baltimore, MD: Johns Hopkins Univ. Press, 1996.
31. L. F. Chen, H. Y. M. Liao, M. T. Ko, J. C. Lin, and G. J. Yu, "A new LDA-based face recognition system which can solve the small sample size problem," Pattern Recognit., vol. 33, no. 10, pp. 1713-1726, Oct. 2000.
32. N. Manwani and P. S. Sastry, "Geometric decision tree," CoRR, vol. abs/1009.3604, 2010. [Online]. Available: http://arxiv.org/abs/1009.3604
33. D. N. A. Asuncion,UCI Machine Learning Repository, School Inf. Com-put. Sci., Univ. California, Irvine, Irvine, CA, 2007. [Online]. Available: http://www.ics.uci.edu/~mlearn/MLRepository.html
34. S. K. Murthy, S. Kasif, and S. Salzberg, The OC1 Decision Tree Software System, 1993. [Online]. Available: http://www.cbcb.umd.edu/salzberg/announce- oc1.html
35. C.-C. Chang and C.-J. Lin, LIBSVM: A Library for Support Vector Machines, 2001. [Online]. Available: http://www.csie.ntu.edu.tw/~cjlin/libsvm