Abstract
A number of two-class classification methods first discretize each attribute of two given training sets and then construct a propositional DNF formula that evaluates to True for one of the two discretized training sets and to False for the other one. The formula is not just a classification tool but constitutes a useful explanation for the differences between the two underlying populations if it can be comprehended by humans and is reliable. This paper shows that comprehensibility as well as reliability of the formulas can sometimes be improved using a discretization scheme where linear combinations of a small number of attributes are discretized.
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References
Abidi, S., Hoe, K.: Symbolic exposition of medical data-sets: A data mining workbench to inductively derive data-defining symbolic rules. In: Proceedings of the 15th IEEE Symposium on Computer-based Medical Systems (CBMS 2002) (2002)
Agrawal, R., Imielinski, T., Swami, A.N.: Mining association rules between sets of items in large databases. In: Proceedings of the 1993 ACM SIGMOD International Conference on Management of Data (1993)
An, A.: Learning classification rules from data. Computers and Mathematics with Applications 45, 737–748 (2003)
An, A., Cercone, N.: Discretization of continuous attributes for learning classification rules. In: Zhong, N., Zhou, L. (eds.) PAKDD 1999. LNCS, vol. 1574, pp. 509–514. Springer, Heidelberg (1999)
Atzmueller, M., Puppe, F., Buscher, H.-P.: Subgroup mining for interactive knowledge refinement. In: Miksch, S., Hunter, J., Keravnou, E.T. (eds.) AIME 2005. LNCS, vol. 3581, pp. 453–462. Springer, Heidelberg (2005)
Au, W.-H., Chan, K.C.C., Wong, A.K.C.: A fuzzy approach to partitioning continuous attributes for classification. IEEE Transactions on Knowledge and Data Engineering 18, 715–719 (2006)
Bartnikowski, S., Granberry, M., Mugan, J., Truemper, K.: Transformation of rational and set data to logic data. In: Data Mining and Knowledge Discovery Approaches Based on Rule Induction Techniques. Springer, Heidelberg (2006)
Bay, S., Pazzani, M.: Detecting group differences: Mining contrast sets. Data Mining and Knowledge Discovery 5, 213–246 (2001)
Bay, S.D.: Multivariate discretization of continuous variables for set mining. In: Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data mining (2000)
Boros, E., Hammer, P., Ibaraki, T., Kogan, A.: A logical analysis of numerical data. Mathematical Programming 79, 163–190 (1997)
Boros, E., Hammer, P., Ibaraki, T., Kogan, A., Mayoraz, E., Muchnik, I.: An implementation of logical analysis of data. IEEE Transactions on Knowledge and Data Engineering 12, 292–306 (2000)
Boullé, M.: Khiops: A statistical discretization method of continuous attributes. Machine Learning 55, 53–69 (2004)
Boullé, M.: MODL: A Bayes optimal discretization method for continuous attributes. Machine Learning 65, 131–165 (2006)
Chao, S., Li, Y.: Multivariate interdependent discretization for continuous attribute. In: Proceedings of the Third International Conference on Information Technology and Applications (ICITA 2005)(2005)
Chmielewski, M.R., Grzymala-Busse, J.W.: Global discretization of continuous attributes as preprocessing for machine learning. International Journal of Approximate Reasoning 15, 319–331 (1996)
Clark, D., Schreter, Z., Adams, A.: A quantitative comparison of dystal and backpropagation. In: Proceedings of Seventh Australian Conference on Neural Networks (ACNN 1996) (1996)
Clark, P., Boswell, R.: Rule induction with CN2: Some recent improvements. In: Proceedings Fifth European Working Session on Learning (1991)
Cohen, W.W.: Fast effective rule induction. In: Machine Learning: Proceedings of the Twelfth International Conference (1995)
Cohen, W.W., Singer, Y.: A simple, fast, and effective rule learner. In: Proceedings of the Sixteenth National Conference on Artificial Intelligence (1999)
Cowan, N.: The magical number 4 in short-term memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences 24, 87–185 (2001)
Dougherty, J., Kohavi, R., Sahami, M.: Supervised and unsupervised discretization of continuous features. In: Machine Learning: Proceedings of the Twelfth International Conference (1995)
Fayyad, U., Irani, K.: On the handling of continuous-valued attributes in decision tree generation. Machine Learning 8, 87–102 (1992)
Fayyad, U., Irani, K.: Multi-interval discretization of continuous-valued attributes for classification learning. In: Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence (1993)
Felici, G., Sun, F., Truemper, K.: Learning logic formulas and related error distributions. In: Data Mining and Knowledge Discovery Approaches Based on Rule Induction Techniques. Springer, Heidelberg (2006)
Felici, G., Truemper, K.: A MINSAT approach for learning in logic domain. INFORMS Journal of Computing 14, 20–36 (2002)
Friedman, N., Goldszmidt, M.: Discretizing continuous attributes while learning Bayesian networks. In: International Conference on Machine Learning (1996)
Gamberger, D., Lavrač, N.: Expert-guided subgroup discovery: Methodology and application. Journal of Artificial Intelligence Research 17, 501–527 (2002)
Gamberger, D., Lavrač, N., Krstačic, G.: Active subgroup mining: a case study in coronary heart disease risk group detection. Artificial Intelligence in Medicine 28 (2003)
Gamberger, D., Lavrač, N., Železný, F., Tolar, J.: Induction of comprehensible models for gene expression datasets by subgroup discovery methodology. Journal of Biomedical Informatics 37 (2004)
Guyon, I., Elisseef, A.: An introduction to variable and feature selection. Journal of Machine Learning Research 3, 1157–1182 (2003)
Halford, G.S., Baker, R., McCredden, J.E., Bain, J.D.: How many variables can humans process? Psychological Science 16, 70–76 (2005)
Halford, G.S., Cowan, N., Andrews, G.: Separating cognitive capacity from knowledge: a new hypothesis. Trends in Cognitive Sciences 11, 236–242 (2007)
Jin, R., Breitbart, Y., Muoh, C.: Data discretization unification. In: Proceedings of the IEEE International Conference on Data Mining (ICDM 2007) (2007)
Klösgen, W.: EXPLORA: A multipattern and multistrategy discovery assistant. In: Advances in Knowledge Discovery and Data Mining. AAAI Press, Menlo Park (1996)
Kohavi, R., Sahami, M.: Error-based and entropy-based discretization of continuous features. In: Proceedings of the Second International Conference on Knowledge Discovery and Data Mining (1996)
Koller, D., Sahami, M.: Toward optimal feature selection. In: International Conference on Machine Learning (1996)
Kurgan, L.A., Cios, K.J.: CAIM discretization algorithm. IEEE Transactions on Knowledge and Data Engineering 16, 145–153 (2004)
Lavrač, N., Cestnik, B., Gamberger, D., Flach, P.: Decision support through subgroup discovery: Three case studies and the lessons learned. Machine Learning 57, 115–143 (2004)
Liu, H., Yu, L.: Toward integrating feature selection algorithms for classification and clustering. IEEE Transactions on Knowledge and Data Engineering 17, 491–502 (2005)
Miller, G.A.: The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological Review 63, 81–97 (1956)
Monti, S., Cooper, G.F.: A multivariate discretization method for learning Bayesian networks from mixed data. In: Proceedings of the Fourteenth Conference of Uncertainty in AI (1998)
Mugan, J., Truemper, K.: Discretization of rational data. In: Proceedings of MML 2004 (Mathematical Methods for Learning). IGI Publishing Group (2007)
Muhlenbach, F., Rakotomalala, R.: Multivariate supervised discretization, a neighborhood graph approach. In: Proceedings of the IEEE International Conference on Data Mining (ICDM 2002) (2002)
Perner, P., Trautzsch, S.: Multi-interval discretization for decision tree learning. In: Advances in Pattern Recognition. Springer, Heidelberg (2004)
Quinlan, J.: Induction of decision trees. Machine Learning 1, 81–106 (1986)
Riehl, K.: Data Mining Logic Explanations from Numerical Data. PhD thesis, Department of Computer Science, University of Texas at Dallas (2006)
Triantaphyllou, E.: Data Mining and Knowledge Discovery via a Novel Logic-based Approach. Springer, Heidelberg (2008)
Vapnik, V., Levin, E., Cun, Y.L.: Measuring the VC-dimension of a learning machine. International Journal of Human Computer Systems 6, 851–876 (2008)
Wrobel, S.: An algorithm for multi-relational discovery of subgroups. In: Proceedings of First European Conference on Principles of Data Mining and Knowledge Discovery (1997)
Yang, Y., Webb, G.I.: Weighted proportional k-interval discretization for Naive-Bayes classifiers. In: Whang, K.-Y., Jeon, J., Shim, K., Srivastava, J. (eds.) PAKDD 2003. LNCS, vol. 2637. Springer, Heidelberg (2003)
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Truemper, K. (2009). Improved Comprehensibility and Reliability of Explanations via Restricted Halfspace Discretization. In: Perner, P. (eds) Machine Learning and Data Mining in Pattern Recognition. MLDM 2009. Lecture Notes in Computer Science(), vol 5632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03070-3_1
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DOI: https://doi.org/10.1007/978-3-642-03070-3_1
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