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Published in: Journal of Classification 1/2021

18-02-2020

Spherical Classification of Data, a New Rule-Based Learning Method

Authors: Zhengyu Ma, Hong Seo Ryoo

Published in: Journal of Classification | Issue 1/2021

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Abstract

This paper presents a new rule-based classification method that partitions data under analysis into spherical patterns. The forte of the method is twofold. One, it exploits the efficiency of distance metric-based clustering to fast collect similar data into spherical patterns. The other, spherical patterns are each a trait shared among one type of data only, hence are built for classification of new data. Numerical studies with public machine learning datasets from Lichman (2013), in comparison with well-established classification methods from Boros et al. (IEEE Transactions on Knowledge and Data Engineering, 12, 292–306, 2000) and Waikato Environment for Knowledge Analysis (http://​www.​cs.​waikato.​ac.​nz/​ml/​weka/​), demonstrate the aforementioned utilities of the new method well.

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Literature
go back to reference Aha, D., Kibler, D., Albert, M. (1991). Instance-based learning. Machine Learning, 6(1), 37–66. Aha, D., Kibler, D., Albert, M. (1991). Instance-based learning. Machine Learning, 6(1), 37–66.
go back to reference Alexe, S., & Hammer, P.L. (2006b). Accelerated algorithm for pattern detection in logical analysis of data. Discrete Mathematics, 154(7), 1050–1063.MathSciNetMATHCrossRef Alexe, S., & Hammer, P.L. (2006b). Accelerated algorithm for pattern detection in logical analysis of data. Discrete Mathematics, 154(7), 1050–1063.MathSciNetMATHCrossRef
go back to reference Alexe, G., Alexe, S., Bonates, T., Kogan, A. (2007). Logical analysis of data – the vision of Peter L. Hammer. Annals of Mathematics and Artificial Intelligence, 49, 265–312.MathSciNetMATHCrossRef Alexe, G., Alexe, S., Bonates, T., Kogan, A. (2007). Logical analysis of data – the vision of Peter L. Hammer. Annals of Mathematics and Artificial Intelligence, 49, 265–312.MathSciNetMATHCrossRef
go back to reference Balcan, M. -F., Blum, A., Vempala, S. (2008). A discriminative framework for clustering via similarity functions. In Proceedings of the Fortieth ACM Symposium on Theory of Computing (pp. 671– 680). Balcan, M. -F., Blum, A., Vempala, S. (2008). A discriminative framework for clustering via similarity functions. In Proceedings of the Fortieth ACM Symposium on Theory of Computing (pp. 671– 680).
go back to reference Bazaraa, M., Sherali, H., Shetty, C. (2006). Nonlinear programming: theory and algorithms. New York: Wiley.MATHCrossRef Bazaraa, M., Sherali, H., Shetty, C. (2006). Nonlinear programming: theory and algorithms. New York: Wiley.MATHCrossRef
go back to reference Beasley, J., & Chu, P. (1996). A genetic algorithm for the set covering problem. European Journal of Operation Research, 94, 392–404.MATHCrossRef Beasley, J., & Chu, P. (1996). A genetic algorithm for the set covering problem. European Journal of Operation Research, 94, 392–404.MATHCrossRef
go back to reference Bennett, K., & Mangasarian, O. (1992). Robust linear programming discrimination of two linearly inseparable sets. Optimization Methods and Software, 1, 23–34.CrossRef Bennett, K., & Mangasarian, O. (1992). Robust linear programming discrimination of two linearly inseparable sets. Optimization Methods and Software, 1, 23–34.CrossRef
go back to reference Bennett, K., & Mangasarian, O. (1994). Bilinear separation of two sets in n −space. Computational Optimization and Applications, 2, 207–227.MathSciNetMATHCrossRef Bennett, K., & Mangasarian, O. (1994). Bilinear separation of two sets in n −space. Computational Optimization and Applications, 2, 207–227.MathSciNetMATHCrossRef
go back to reference Boros, E., Hammer, P.L., Ibaraki, T., Kogan, A., Mayoraz, E., Muchnik, I. (2000). An implementation of logical analysis of data. IEEE Transactions on Knowledge and Data Engineering, 12, 292–306.CrossRef Boros, E., Hammer, P.L., Ibaraki, T., Kogan, A., Mayoraz, E., Muchnik, I. (2000). An implementation of logical analysis of data. IEEE Transactions on Knowledge and Data Engineering, 12, 292–306.CrossRef
go back to reference Bradley, P., & Mangasarian, O. (2000). Massive data discrimination via linear support vector machines. Optimization Methods and Software, 13(1), 1–20.MathSciNetMATHCrossRef Bradley, P., & Mangasarian, O. (2000). Massive data discrimination via linear support vector machines. Optimization Methods and Software, 13(1), 1–20.MathSciNetMATHCrossRef
go back to reference Cohen, W. W. (1995). Fast effective rule induction. In Proceedings of the Twelfth International Conference on Machine Learning (pp. 115–123). Cohen, W. W. (1995). Fast effective rule induction. In Proceedings of the Twelfth International Conference on Machine Learning (pp. 115–123).
go back to reference Cortes, C., & Vapnik, V. (1995). Support vector networks. Machine Learning, 20, 273–297.MATH Cortes, C., & Vapnik, V. (1995). Support vector networks. Machine Learning, 20, 273–297.MATH
go back to reference Eick, C. F., Zeidat, N., Zhao, Z. (2004). Supervised clustering – algorithms and benefits. In 16Th IEEE international conference on tools with artificial intelligence (pp. 774–776). Eick, C. F., Zeidat, N., Zhao, Z. (2004). Supervised clustering – algorithms and benefits. In 16Th IEEE international conference on tools with artificial intelligence (pp. 774–776).
go back to reference Frank, E., & Witten, I. H. (1998). Generating accurate rule sets without global optimization. In Proceedings of the Fifteenth International Conference on Machine Learning (pp. 144–151). Frank, E., & Witten, I. H. (1998). Generating accurate rule sets without global optimization. In Proceedings of the Fifteenth International Conference on Machine Learning (pp. 144–151).
go back to reference Freund, Y., & Schapire, R. E. (1996). Experiments with a new boosting algorithm. In Thirteenth International Conference on Machine Learning (pp. 148–156). Freund, Y., & Schapire, R. E. (1996). Experiments with a new boosting algorithm. In Thirteenth International Conference on Machine Learning (pp. 148–156).
go back to reference Fung, G., & Mangasarian, O. (2003). Finite Newton method for Lagrangian support vector machine classification. Neurocomputing, 55, 39–55.CrossRef Fung, G., & Mangasarian, O. (2003). Finite Newton method for Lagrangian support vector machine classification. Neurocomputing, 55, 39–55.CrossRef
go back to reference Guo, C., & Ryoo, H.S. (2012). Compact MILP models for optimal and Pareto-optimal LAD patterns. Discrete Applied Mathematics, 160, 2339–2348.MathSciNetMATHCrossRef Guo, C., & Ryoo, H.S. (2012). Compact MILP models for optimal and Pareto-optimal LAD patterns. Discrete Applied Mathematics, 160, 2339–2348.MathSciNetMATHCrossRef
go back to reference Guo, C., & Ryoo, H.S. (2018). On Pareto-optimal Boolean logical patterns for numerical data. Submitted for publication. Guo, C., & Ryoo, H.S. (2018). On Pareto-optimal Boolean logical patterns for numerical data. Submitted for publication.
go back to reference Hammer, P.L., Kogan, A., Simeone, B., Szedmak, S. (2004). Pareto-optimal patterns in logical analysis of data. Discrete Applied Mathematics, 144, 79–102.MathSciNetMATHCrossRef Hammer, P.L., Kogan, A., Simeone, B., Szedmak, S. (2004). Pareto-optimal patterns in logical analysis of data. Discrete Applied Mathematics, 144, 79–102.MathSciNetMATHCrossRef
go back to reference Haykin, S. (1999). Neural networks: a comprehensive foundation. Englewood Cliffs: Prentice Hall.MATH Haykin, S. (1999). Neural networks: a comprehensive foundation. Englewood Cliffs: Prentice Hall.MATH
go back to reference Hoffman, K., & Padberg, M. (1993). Solving airline crew scheduling problems by branch-and-cut. Management Science, 39(6), 657–682.MATHCrossRef Hoffman, K., & Padberg, M. (1993). Solving airline crew scheduling problems by branch-and-cut. Management Science, 39(6), 657–682.MATHCrossRef
go back to reference Jain, A., Murty, M., Flynn, P. (1999). Data clustering: a review. ACM Computing Surveys, 31(3), 264–323.CrossRef Jain, A., Murty, M., Flynn, P. (1999). Data clustering: a review. ACM Computing Surveys, 31(3), 264–323.CrossRef
go back to reference Jain, A. (2010). Data clustering: 50 years beyond k-means. Pattern Recognition Letters, 31, 651–666.CrossRef Jain, A. (2010). Data clustering: 50 years beyond k-means. Pattern Recognition Letters, 31, 651–666.CrossRef
go back to reference John, G., & Langley, P. (1995). Estimating continuous distributions in Bayesian classifiers. In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (pp. 338–345). John, G., & Langley, P. (1995). Estimating continuous distributions in Bayesian classifiers. In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (pp. 338–345).
go back to reference Kim, K., & Ryoo, H.S. (2007a). Data separation via a finite number of discriminant functions: a global optimization approach. Applied Mathematics and Computation, 190 (1), 476–489.MathSciNetMATHCrossRef Kim, K., & Ryoo, H.S. (2007a). Data separation via a finite number of discriminant functions: a global optimization approach. Applied Mathematics and Computation, 190 (1), 476–489.MathSciNetMATHCrossRef
go back to reference Kim, K., & Ryoo, H.S.S. (2007b). Nonlinear separation of data via mixed 0-1 integer and linear programming. Applied Mathematics and Computation, 193(1), 183–196.MathSciNetMATHCrossRef Kim, K., & Ryoo, H.S.S. (2007b). Nonlinear separation of data via mixed 0-1 integer and linear programming. Applied Mathematics and Computation, 193(1), 183–196.MathSciNetMATHCrossRef
go back to reference Kim, K., & Ryoo, H.S. (2008). A LAD-based method for selecting short oligo probes for genotyping applications. OR Spectrum, 30(2), 249–268.MathSciNetMATHCrossRef Kim, K., & Ryoo, H.S. (2008). A LAD-based method for selecting short oligo probes for genotyping applications. OR Spectrum, 30(2), 249–268.MathSciNetMATHCrossRef
go back to reference Kohavi, R. (1995). The power of decision tables. In Proceedings of the Eighth European Conference on Machine Learning (pp. 179–189). Kohavi, R. (1995). The power of decision tables. In Proceedings of the Eighth European Conference on Machine Learning (pp. 179–189).
go back to reference Kolesar, P., & Walker, W. (1974). An algorithm for the dynamic relocation of fire companies. Operations Research, 22, 249–274.CrossRef Kolesar, P., & Walker, W. (1974). An algorithm for the dynamic relocation of fire companies. Operations Research, 22, 249–274.CrossRef
go back to reference Lorena, L., & Lopes, F. (1994). A surrogate heuristic for set covering problems. European Journal of Operational Research, 79, 138–150.MATHCrossRef Lorena, L., & Lopes, F. (1994). A surrogate heuristic for set covering problems. European Journal of Operational Research, 79, 138–150.MATHCrossRef
go back to reference Ma, Z., & Ryoo, H.S. (2012). General set covering for feature selection in data mining. Management Science and Financial Engineering, 18(2), 13–17.CrossRef Ma, Z., & Ryoo, H.S. (2012). General set covering for feature selection in data mining. Management Science and Financial Engineering, 18(2), 13–17.CrossRef
go back to reference Mangasarian, O. (1968). Multisurface method of pattern separation. IEEE Transactions on Information Theory, 14(6), 801–807.MATHCrossRef Mangasarian, O. (1968). Multisurface method of pattern separation. IEEE Transactions on Information Theory, 14(6), 801–807.MATHCrossRef
go back to reference Mangasarian, O. (1993). Mathematical programming in neural network. ORSA Journal on Computing, 5(4), 349–360.MATHCrossRef Mangasarian, O. (1993). Mathematical programming in neural network. ORSA Journal on Computing, 5(4), 349–360.MATHCrossRef
go back to reference Platt, J. (1999). Fast training of support vector machines using sequential minimal optimization, (pp. 185–208). Cambridge: MIT Press. Platt, J. (1999). Fast training of support vector machines using sequential minimal optimization, (pp. 185–208). Cambridge: MIT Press.
go back to reference Quinlan, R. (1993). C4.5: Programs for machine learning. San Mateo: Morgan Kaufmann Publishers. Quinlan, R. (1993). C4.5: Programs for machine learning. San Mateo: Morgan Kaufmann Publishers.
go back to reference Ryoo, H.S., & Jang, I. (2009). MILP approach to pattern generation in logical analysis of data. Discrete Applied Mathematics, 157, 749–761.MathSciNetMATHCrossRef Ryoo, H.S., & Jang, I. (2009). MILP approach to pattern generation in logical analysis of data. Discrete Applied Mathematics, 157, 749–761.MathSciNetMATHCrossRef
go back to reference Ullman, J. (1973). Pattern recognition techniques. London: Crane. Ullman, J. (1973). Pattern recognition techniques. London: Crane.
go back to reference Vapnik, V. (1998). Statistical learning theory. New York: Wiley-Interscience.MATH Vapnik, V. (1998). Statistical learning theory. New York: Wiley-Interscience.MATH
go back to reference Wedelin, D. (1995). An algorithm for large scale 0-1 inter programming with application to airline crew scheduling. Annals of Operations Research, 57, 283–301.MathSciNetMATHCrossRef Wedelin, D. (1995). An algorithm for large scale 0-1 inter programming with application to airline crew scheduling. Annals of Operations Research, 57, 283–301.MathSciNetMATHCrossRef
go back to reference Yan, K., & Ryoo, H.S. (2017a). 0-1 multilinear programming as a unifying theory for LAD pattern generation. Discrete Applied Mathematics, 218, 21–39.MathSciNetMATHCrossRef Yan, K., & Ryoo, H.S. (2017a). 0-1 multilinear programming as a unifying theory for LAD pattern generation. Discrete Applied Mathematics, 218, 21–39.MathSciNetMATHCrossRef
go back to reference Yan, K., & Ryoo, H.S. (2017b). Strong valid inequalities for Boolean logical pattern generation. Journal of Global Optimization, 69(1), 183–230.MathSciNetMATHCrossRef Yan, K., & Ryoo, H.S. (2017b). Strong valid inequalities for Boolean logical pattern generation. Journal of Global Optimization, 69(1), 183–230.MathSciNetMATHCrossRef
go back to reference Yan, K., & Ryoo, H.S. (2020). Cliques for Multi-Term linearization of 0-1 multilinear program for Boolean logical pattern generation. In Optimization of Complex Systems: Theory, Models, Algorithms and Applications, Advances in Intelligent Systems and Computing, 991, 376–386. Yan, K., & Ryoo, H.S. (2020). Cliques for Multi-Term linearization of 0-1 multilinear program for Boolean logical pattern generation. In Optimization of Complex Systems: Theory, Models, Algorithms and Applications, Advances in Intelligent Systems and Computing, 991, 376–386.
Metadata
Title
Spherical Classification of Data, a New Rule-Based Learning Method
Authors
Zhengyu Ma
Hong Seo Ryoo
Publication date
18-02-2020
Publisher
Springer US
Published in
Journal of Classification / Issue 1/2021
Print ISSN: 0176-4268
Electronic ISSN: 1432-1343
DOI
https://doi.org/10.1007/s00357-019-09355-z

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