Forward supervised discretization for multivariate with categorical responses

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July 2016, 1(2&3): 217-225. doi: 10.3934/bdia.2016005

Forward supervised discretization for multivariate with categorical responses

Wenxue Huang ^1, and Qitian Qiu ^1,

1.	School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong 510006, China, China

Received April 2016 Revised September 2016 Published September 2016

Abstract
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Given a data set with one categorical response variable and multiple categorical or continuous explanatory variables, it is required in some applications to discretize the continuous explanatory ones. A proper supervised discretization usually achieves a better result than the unsupervised ones. Rather than individually doing so as recently proposed by Huang, Pan and Wu in [12,13], we suggest a forward supervised discretization algorithm to capture a higher association from the multiple explanatory variables to the response variable. Experiments with the GK-tau and the GK-lambda are presented to support the statement.

Keywords: independent supervised discretization., the $GK-\lambda$, the $GK-\tau$, Categorical data, forward supervise discretization.

Mathematics Subject Classification: Primary: 62H20; Secondary: 62F07, 68T3.

Citation: Wenxue Huang, Qitian Qiu. Forward supervised discretization for multivariate with categorical responses. Big Data & Information Analytics, 2016, 1 (2&3) : 217-225. doi: 10.3934/bdia.2016005

References:

[1]	M. Boulle, Khiops: A statistical discretization method of continuous attributes, Machine Learning, 55 (2004), 53-69. doi: 10.1023/B:MACH.0000019804.29836.05.
[2]	J. Catlett, On changing continuous attributes into ordered discrete attributes, In: Machine LearningEWSL-91, 482 (1991), 164-178. doi: 10.1007/BFb0017012.
[3]	D. Chiu, B. Cheung and A. Wong, Information synthesis based on hierarchical maximum entropy discretization, Journal of Experimental and Theoretical Artificial Intelligence, 2 (1989), 117-129. doi: 10.1080/09528139008953718.
[4]	M. Chmielewski and J. Grzymala-Busse, Global discretization of continuous attributes as preprocessing for machine learning, International Journal of Approximate Reasoning, 15 (1996), 319-331. doi: 10.1016/S0888-613X(96)00074-6.
[5]	J. Dougherty, R. Kohavi and M. Sahami, Supervised and unsupervised discretization of continuous features, In Machine learning-International Workshop. Morgan Kaufmann Publishers, 2 (1995), 194-202. doi: 10.1016/B978-1-55860-377-6.50032-3.
[6]	U. Fayyad and K. Irani, Multi-interval discretization of continuous-valued attributes for classification learning, Proceedings of the International Joint Conference on Uncertainty in AI, 2 (1993), 1022-1027.
[7]	G. Gan, C. Ma and J. Wu, Data clustering: Theory, algorithms, and applications(ASA-SIAM series on statistics and applied probability), Society for Industrial and Applied Mathematics, 20 (2007), xxii+466 pp. doi: 10.1137/1.9780898718348.
[8]	L. Goodman and W. Kruskal, Measures of association for cross classifications, Journal of the American Statistical Association, 49 (1954), 732-764.
[9]	I. Guyon and A. Elisseeff, An Introduction to Variable and Feature Selection, Applied Physics Letters, 3 (2002), 1157-1182.
[10]	R. Holte, Very sim1ple classification rules perform well on most commonly used datasets, Machine Learning, 11 (1993), 63-90.
[11]	W. Huang and Y. Pan, On balalncing between optimal and proportional predictions, Big Data and Information Analytics, 1 (2016), 129-137.
[12]	W. Huang, Y. Pan and J. Wu, Supervised discretization with $GK-\tau$, In Procedia Computer Science, 17 (2013), 114-120.
[13]	W. Huang, Y. Pan and J. Wu, Supervised discretization with $GK-\lambda$, Procedia Computer Science, 30 (2014), 75-80.
[14]	W. Huang, Y. Shi and X. Wang, A nomminal association matrix with feature selection for categorical data, Communications in Statistics - Theory and Methods, to appear.
[15]	R. Kerber, Chimerge: Discretization of numeric attributes, In Proceedings of the tenth national conference on Artificial intelligence.AAAI Press, 1994, 123-128.
[16]	S. Kotsiantis and D. Kanellopoulos, Discretization techniques: A recent survey, GESTS International Transactions on Computer Science and Engineering, 32 (2006), 47-58.
[17]	H. Liu and R. Setiono, Chi2: Feature selection and discretization of numeric attributes, In: Proceedings of the Seventh International Conference on Tools with Artificial Intelligence, 55 (1995), 388-391.
[18]	C. Lloyd, Statistical Analysis with Missing Data, John Wiley & Sons, Inc. 1987, New York, NY, USA.
[19]	J. MacQueen, Some methods for classification and analysis of multivariate observations, Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, 1 (1967), 281-297.
[20]	D. Olson and Y. Shi, Introduction to business data mining, Knowledge and information systems, 2007, McGraw-Hill/Irwin.
[21]	I. Rish, An empirical study of the naive bayes classifier, IJCAI 2001 workshop on empirical methods in artificial intelligence, 2001, 41-46.
[22]	S. Safavian and D. Landgrebe, A survey of decision tree classifier methodology, IEEE Transactions on Systems, Man and Cybernetics, 21 (1991), 660-674. doi: 10.1109/21.97458.
[23]	STATCAN, Survey of Family Expenditures - 1996.
[24]	K. Ting, Discretization of Continuous-Valued Attributes and Instance-Based Learning, Basser Department of Computer Science,University of Sydney, 1994.

show all references

References:

[1]	M. Boulle, Khiops: A statistical discretization method of continuous attributes, Machine Learning, 55 (2004), 53-69. doi: 10.1023/B:MACH.0000019804.29836.05.
[2]	J. Catlett, On changing continuous attributes into ordered discrete attributes, In: Machine LearningEWSL-91, 482 (1991), 164-178. doi: 10.1007/BFb0017012.
[3]	D. Chiu, B. Cheung and A. Wong, Information synthesis based on hierarchical maximum entropy discretization, Journal of Experimental and Theoretical Artificial Intelligence, 2 (1989), 117-129. doi: 10.1080/09528139008953718.
[4]	M. Chmielewski and J. Grzymala-Busse, Global discretization of continuous attributes as preprocessing for machine learning, International Journal of Approximate Reasoning, 15 (1996), 319-331. doi: 10.1016/S0888-613X(96)00074-6.
[5]	J. Dougherty, R. Kohavi and M. Sahami, Supervised and unsupervised discretization of continuous features, In Machine learning-International Workshop. Morgan Kaufmann Publishers, 2 (1995), 194-202. doi: 10.1016/B978-1-55860-377-6.50032-3.
[6]	U. Fayyad and K. Irani, Multi-interval discretization of continuous-valued attributes for classification learning, Proceedings of the International Joint Conference on Uncertainty in AI, 2 (1993), 1022-1027.
[7]	G. Gan, C. Ma and J. Wu, Data clustering: Theory, algorithms, and applications(ASA-SIAM series on statistics and applied probability), Society for Industrial and Applied Mathematics, 20 (2007), xxii+466 pp. doi: 10.1137/1.9780898718348.
[8]	L. Goodman and W. Kruskal, Measures of association for cross classifications, Journal of the American Statistical Association, 49 (1954), 732-764.
[9]	I. Guyon and A. Elisseeff, An Introduction to Variable and Feature Selection, Applied Physics Letters, 3 (2002), 1157-1182.
[10]	R. Holte, Very sim1ple classification rules perform well on most commonly used datasets, Machine Learning, 11 (1993), 63-90.
[11]	W. Huang and Y. Pan, On balalncing between optimal and proportional predictions, Big Data and Information Analytics, 1 (2016), 129-137.
[12]	W. Huang, Y. Pan and J. Wu, Supervised discretization with $GK-\tau$, In Procedia Computer Science, 17 (2013), 114-120.
[13]	W. Huang, Y. Pan and J. Wu, Supervised discretization with $GK-\lambda$, Procedia Computer Science, 30 (2014), 75-80.
[14]	W. Huang, Y. Shi and X. Wang, A nomminal association matrix with feature selection for categorical data, Communications in Statistics - Theory and Methods, to appear.
[15]	R. Kerber, Chimerge: Discretization of numeric attributes, In Proceedings of the tenth national conference on Artificial intelligence.AAAI Press, 1994, 123-128.
[16]	S. Kotsiantis and D. Kanellopoulos, Discretization techniques: A recent survey, GESTS International Transactions on Computer Science and Engineering, 32 (2006), 47-58.
[17]	H. Liu and R. Setiono, Chi2: Feature selection and discretization of numeric attributes, In: Proceedings of the Seventh International Conference on Tools with Artificial Intelligence, 55 (1995), 388-391.
[18]	C. Lloyd, Statistical Analysis with Missing Data, John Wiley & Sons, Inc. 1987, New York, NY, USA.
[19]	J. MacQueen, Some methods for classification and analysis of multivariate observations, Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, 1 (1967), 281-297.
[20]	D. Olson and Y. Shi, Introduction to business data mining, Knowledge and information systems, 2007, McGraw-Hill/Irwin.
[21]	I. Rish, An empirical study of the naive bayes classifier, IJCAI 2001 workshop on empirical methods in artificial intelligence, 2001, 41-46.
[22]	S. Safavian and D. Landgrebe, A survey of decision tree classifier methodology, IEEE Transactions on Systems, Man and Cybernetics, 21 (1991), 660-674. doi: 10.1109/21.97458.
[23]	STATCAN, Survey of Family Expenditures - 1996.
[24]	K. Ting, Discretization of Continuous-Valued Attributes and Instance-Based Learning, Basser Department of Computer Science,University of Sydney, 1994.

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