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Erschienen in: Soft Computing 1/2018

05.01.2017 | Methodologies and Application

MEMOD: a novel multivariate evolutionary multi-objective discretization

verfasst von: Marzieh Hajizadeh Tahan, Shahrokh Asadi

Erschienen in: Soft Computing | Ausgabe 1/2018

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Abstract

Discretization is an important preprocessing technique, especially in classification problems. It reduces and simplifies data, accelerates the learning process, and improves learner performance. The most challenging aspect of the discretization process is to maintain the accuracy of the classification algorithm and to prevent information loss while reducing the number of discretized values. In this paper, using evolutionary multi-objective optimization, classification error (the first objective function) and number of cut points (the second objective function) are simultaneously reduced. The third objective function involves selecting low-frequency cut points so that a smaller degree of information is lost during this conversion (from continuous to discrete). To the best of our knowledge, this is the first paper to consider the discretization process as a multi-objective optimization problem. Previous discretization methods result in only one solution. However, in real-world problems, decision makers often need several alternatives to make better decisions—a requirement which cannot be fulfilled using these techniques. The multi-objective nature of the proposed algorithm enables the generation of numerous solutions (i.e., the Pareto front) allowing the user to select the most appropriate solution according to the nuances of the problem. A total of 20 benchmark data sets were used to test the performance of the proposed algorithm. Our results show that the proposed algorithm offers superior performance compared to other methods in the literature. Thus, it presents better discretization in classification problems.

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Literatur
Zurück zum Zitat Acosta-Mesa H-G, Rechy-Ramírez F, Mezura-Montes E, Cruz-Ramírez N, Jiménez RH (2014) Application of time series discretization using evolutionary programming for classification of precancerous cervical lesions. J. Biomed. Inf. 49:73–83CrossRef Acosta-Mesa H-G, Rechy-Ramírez F, Mezura-Montes E, Cruz-Ramírez N, Jiménez RH (2014) Application of time series discretization using evolutionary programming for classification of precancerous cervical lesions. J. Biomed. Inf. 49:73–83CrossRef
Zurück zum Zitat Agrawal R, Srikant R (1994) Fast algorithms for mining association rules. In: Proceedings of 20th international conference on very large data bases, VLDB, pp 487–499 Agrawal R, Srikant R (1994) Fast algorithms for mining association rules. In: Proceedings of 20th international conference on very large data bases, VLDB, pp 487–499
Zurück zum Zitat Alcala-Fdez J et al (2009) KEEL: a software tool to assess evolutionary algorithms for data mining problems. Soft Comput 13:307–318 Alcala-Fdez J et al (2009) KEEL: a software tool to assess evolutionary algorithms for data mining problems. Soft Comput 13:307–318
Zurück zum Zitat Ali R, Siddiqi MH, Lee S (2015) Rough set-based approaches for discretization: a compact review. Artif Intell Rev 44:235–263 Ali R, Siddiqi MH, Lee S (2015) Rough set-based approaches for discretization: a compact review. Artif Intell Rev 44:235–263
Zurück zum Zitat Asadi S, Shahrabi J (2016a) ACORI: a novel ACO algorithm for rule induction. Knowl-Based Syst 97:175–187 Asadi S, Shahrabi J (2016a) ACORI: a novel ACO algorithm for rule induction. Knowl-Based Syst 97:175–187
Zurück zum Zitat Asadi S, Shahrabi J (2016b) RipMC: RIPPER for multiclass classification. Neurocomputing 191:19–33 Asadi S, Shahrabi J (2016b) RipMC: RIPPER for multiclass classification. Neurocomputing 191:19–33
Zurück zum Zitat Asadi S, Hadavandi E, Mehmanpazir F, Nakhostin MM (2012a) Hybridization of evolutionary Levenberg–Marquardt neural networks and data pre-processing for stock market prediction. Knowl-Based Syst 35:245–258CrossRef Asadi S, Hadavandi E, Mehmanpazir F, Nakhostin MM (2012a) Hybridization of evolutionary Levenberg–Marquardt neural networks and data pre-processing for stock market prediction. Knowl-Based Syst 35:245–258CrossRef
Zurück zum Zitat Asadi S, Tavakoli A, Hejazi SR (2012b) A new hybrid for improvement of auto-regressive integrated moving average models applying particle swarm optimization. Expert Syst Appl 39:5332–5337CrossRef Asadi S, Tavakoli A, Hejazi SR (2012b) A new hybrid for improvement of auto-regressive integrated moving average models applying particle swarm optimization. Expert Syst Appl 39:5332–5337CrossRef
Zurück zum Zitat Asadi S, Shahrabi J, Abbaszadeh P, Tabanmehr S (2013) A new hybrid artificial neural networks for rainfall-runoff process modeling. Neurocomputing 121:470–480CrossRef Asadi S, Shahrabi J, Abbaszadeh P, Tabanmehr S (2013) A new hybrid artificial neural networks for rainfall-runoff process modeling. Neurocomputing 121:470–480CrossRef
Zurück zum Zitat Augasta MG, Kathirvalavakumar T (2012) A new discretization algorithm based on range coefficient of dispersion and skewness for neural networks classifier. Appl Soft Comput 12:619–625CrossRef Augasta MG, Kathirvalavakumar T (2012) A new discretization algorithm based on range coefficient of dispersion and skewness for neural networks classifier. Appl Soft Comput 12:619–625CrossRef
Zurück zum Zitat Baka A, Wettayaprasit W, Vanichayobon S (2014) A novel discretization technique using Class Attribute Interval Average. In: Fourth International Conference on Digital Information and Communication Technology and it’s Applications (DICTAP), Bangkok. IEEE, pp 95–100 Baka A, Wettayaprasit W, Vanichayobon S (2014) A novel discretization technique using Class Attribute Interval Average. In: Fourth International Conference on Digital Information and Communication Technology and it’s Applications (DICTAP), Bangkok. IEEE, pp 95–100
Zurück zum Zitat Breiman L, Friedman J, Stone CJ, Olshen RA (1984) Classification and regression trees. CRC Press, LondonMATH Breiman L, Friedman J, Stone CJ, Olshen RA (1984) Classification and regression trees. CRC Press, LondonMATH
Zurück zum Zitat Cano A, Nguyen DT, Ventura S, Cios KJ (2016) ur-CAIM: improved CAIM discretization for unbalanced and balanced data. Soft Comput 20:173–188 Cano A, Nguyen DT, Ventura S, Cios KJ (2016) ur-CAIM: improved CAIM discretization for unbalanced and balanced data. Soft Comput 20:173–188
Zurück zum Zitat Cococcioni M, Ducange P, Lazzerini B, Marcelloni F (2007) A Pareto-based multi-objective evolutionary approach to the identification of Mamdani fuzzy systems. Soft Comput 11:1013–1031CrossRef Cococcioni M, Ducange P, Lazzerini B, Marcelloni F (2007) A Pareto-based multi-objective evolutionary approach to the identification of Mamdani fuzzy systems. Soft Comput 11:1013–1031CrossRef
Zurück zum Zitat Coello CAC, Van Veldhuizen DA, Lamont GB (2002) Evolutionary algorithms for solving multi-objective problems, vol 242. Springer, BerlinCrossRefMATH Coello CAC, Van Veldhuizen DA, Lamont GB (2002) Evolutionary algorithms for solving multi-objective problems, vol 242. Springer, BerlinCrossRefMATH
Zurück zum Zitat de Sá CR, Soares C, Knobbe A, Azevedo P (2013) Jorge AM multi-interval discretization of continuous attributes for label ranking. In: Discovery science. Springer, Berlin, pp 155–169 de Sá CR, Soares C, Knobbe A, Azevedo P (2013) Jorge AM multi-interval discretization of continuous attributes for label ranking. In: Discovery science. Springer, Berlin, pp 155–169
Zurück zum Zitat de Sá CR, Soares C, Knobbe A (2016) Entropy-based discretization methods for ranking data. Inf Sci 329:921–936 de Sá CR, Soares C, Knobbe A (2016) Entropy-based discretization methods for ranking data. Inf Sci 329:921–936
Zurück zum Zitat Deb K, Agrawal S, Pratap A, Meyarivan T (2000) A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. Lecture notes in computer science, vol 1917, pp 849–858 Deb K, Agrawal S, Pratap A, Meyarivan T (2000) A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. Lecture notes in computer science, vol 1917, pp 849–858
Zurück zum Zitat del Jesús MJ, Gámez JA, Puerta JM (2009) Evolutionary and metaheuristics based data mining. Soft Comput A Fusion Found Methodol Appl 13:209–212 del Jesús MJ, Gámez JA, Puerta JM (2009) Evolutionary and metaheuristics based data mining. Soft Comput A Fusion Found Methodol Appl 13:209–212
Zurück zum Zitat Demšar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30MathSciNetMATH Demšar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30MathSciNetMATH
Zurück zum Zitat Eshelman LJ (2014) The CHC adaptive search algorithm: how to have safe search when engaging. Found Genetic Algorithms 1991 (FOGA 1) 1:265 Eshelman LJ (2014) The CHC adaptive search algorithm: how to have safe search when engaging. Found Genetic Algorithms 1991 (FOGA 1) 1:265
Zurück zum Zitat Fayyad UM, Irani KB (1993) Multi-interval discretization of continuous-valued attributes for classification learning. In: Proceedings of 13th international joint conference artificial intelligence (IJCAI), pp 1022–1029 Fayyad UM, Irani KB (1993) Multi-interval discretization of continuous-valued attributes for classification learning. In: Proceedings of 13th international joint conference artificial intelligence (IJCAI), pp 1022–1029
Zurück zum Zitat Ferreira AJ, Figueiredo MA (2015) Feature discretization with relevance and mutual information criteria. In: Pattern recognition applications and methods. Springer, pp 101–118 Ferreira AJ, Figueiredo MA (2015) Feature discretization with relevance and mutual information criteria. In: Pattern recognition applications and methods. Springer, pp 101–118
Zurück zum Zitat García S, Fernández A, Luengo J, Herrera F (2009) A study of statistical techniques and performance measures for genetics-based machine learning: accuracy and interpretability. Soft Comput 13:959–977CrossRef García S, Fernández A, Luengo J, Herrera F (2009) A study of statistical techniques and performance measures for genetics-based machine learning: accuracy and interpretability. Soft Comput 13:959–977CrossRef
Zurück zum Zitat Garcia S, Luengo J, Sáez JA, López V, Herrera F (2013) A survey of discretization techniques: taxonomy and empirical analysis in supervised learning. IEEE Trans Knowl Data Eng 25:734–750CrossRef Garcia S, Luengo J, Sáez JA, López V, Herrera F (2013) A survey of discretization techniques: taxonomy and empirical analysis in supervised learning. IEEE Trans Knowl Data Eng 25:734–750CrossRef
Zurück zum Zitat García S, Luengo J, Herrera F (2015) Discretization. In: Data preprocessing in data mining. Springer, pp 245–283 García S, Luengo J, Herrera F (2015) Discretization. In: Data preprocessing in data mining. Springer, pp 245–283
Zurück zum Zitat Gonzalez-Abril L, Cuberos FJ, Velasco F, Ortega JA (2009) Ameva: an autonomous discretization algorithm. Expert Syst Appl 36:5327–5332CrossRef Gonzalez-Abril L, Cuberos FJ, Velasco F, Ortega JA (2009) Ameva: an autonomous discretization algorithm. Expert Syst Appl 36:5327–5332CrossRef
Zurück zum Zitat Holm S (1979) A simple sequentially rejective multiple test procedure. Scand J Stat 6:65–70 Holm S (1979) A simple sequentially rejective multiple test procedure. Scand J Stat 6:65–70
Zurück zum Zitat Hu H-W, Chen Y-L, Tang K (2009) A dynamic discretization approach for constructing decision trees with a continuous label. IEEE Trans Knowl Data Eng 21:1505–1514CrossRef Hu H-W, Chen Y-L, Tang K (2009) A dynamic discretization approach for constructing decision trees with a continuous label. IEEE Trans Knowl Data Eng 21:1505–1514CrossRef
Zurück zum Zitat Huang W, Pan Y, Wu J (2013) Supervised discretization with GK \(\tau \). Proc Comput Sci 17:114–120CrossRef Huang W, Pan Y, Wu J (2013) Supervised discretization with GK \(\tau \). Proc Comput Sci 17:114–120CrossRef
Zurück zum Zitat Huang W, Pan Y, Wu J (2014) Supervised discretization for optimal prediction. Proc Comput Sci 30:75–80CrossRef Huang W, Pan Y, Wu J (2014) Supervised discretization for optimal prediction. Proc Comput Sci 30:75–80CrossRef
Zurück zum Zitat Ishibuchi H, Yamamoto T (2004) Fuzzy rule selection by multi-objective genetic local search algorithms and rule evaluation measures in data mining. Fuzzy Sets Syst 141:59–88CrossRefMATH Ishibuchi H, Yamamoto T (2004) Fuzzy rule selection by multi-objective genetic local search algorithms and rule evaluation measures in data mining. Fuzzy Sets Syst 141:59–88CrossRefMATH
Zurück zum Zitat Ishibuchi H, Yamamoto T (2005) Rule weight specification in fuzzy rule-based classification systems. IEEE Trans Fuzzy Syst 13:428–435CrossRef Ishibuchi H, Yamamoto T (2005) Rule weight specification in fuzzy rule-based classification systems. IEEE Trans Fuzzy Syst 13:428–435CrossRef
Zurück zum Zitat Jung Y-G, Kim KM, Kwon YM (2012) Using weighted hybrid discretization method to analyze climate changes. In: Computer applications for graphics, grid computing, and industrial environment. Springer, pp 189–195 Jung Y-G, Kim KM, Kwon YM (2012) Using weighted hybrid discretization method to analyze climate changes. In: Computer applications for graphics, grid computing, and industrial environment. Springer, pp 189–195
Zurück zum Zitat Kerber R (1991) Chimerge: Discretization of numeric attributes. In: Proceedings of the tenth national conference on artificial intelligence. Aaai Press, pp 123–128 Kerber R (1991) Chimerge: Discretization of numeric attributes. In: Proceedings of the tenth national conference on artificial intelligence. Aaai Press, pp 123–128
Zurück zum Zitat Kurgan L, Cios KJ (2004) CAIM discretization algorithm. IEEE Trans Knowl Data Eng 16:145–153CrossRef Kurgan L, Cios KJ (2004) CAIM discretization algorithm. IEEE Trans Knowl Data Eng 16:145–153CrossRef
Zurück zum Zitat Liu H, Setiono R (1996) Dimensionality reduction via discretization. Knowl-Based Syst 9:67–72CrossRef Liu H, Setiono R (1996) Dimensionality reduction via discretization. Knowl-Based Syst 9:67–72CrossRef
Zurück zum Zitat Liu H, Hussain F, Tan CL, Dash M (2002) Discretization: an enabling technique. Data Min Knowl Discov 6:393–423MathSciNetCrossRef Liu H, Hussain F, Tan CL, Dash M (2002) Discretization: an enabling technique. Data Min Knowl Discov 6:393–423MathSciNetCrossRef
Zurück zum Zitat Madhu G, Rajinikanth T, Govardhan A (2014) Improve the classifier accuracy for continuous attributes in biomedical datasets using a new discretization method. Proc Comput Sci 31:671–679CrossRef Madhu G, Rajinikanth T, Govardhan A (2014) Improve the classifier accuracy for continuous attributes in biomedical datasets using a new discretization method. Proc Comput Sci 31:671–679CrossRef
Zurück zum Zitat Mehmanpazir F, Asadi S (2016) Development of an evolutionary fuzzy expert system for estimating future behavior of stock price. J Ind Eng Int 1–18 Mehmanpazir F, Asadi S (2016) Development of an evolutionary fuzzy expert system for estimating future behavior of stock price. J Ind Eng Int 1–18
Zurück zum Zitat Moskovitch R, Shahar Y (2015) Classification-driven temporal discretization of multivariate time series. Data Min Knowl Disc 29:871–913 Moskovitch R, Shahar Y (2015) Classification-driven temporal discretization of multivariate time series. Data Min Knowl Disc 29:871–913
Zurück zum Zitat Mukhopadhyay A, Maulik U, Bandyopadhyay S, Coello Coello C (2014) A survey of multiobjective evolutionary algorithms for data mining: part I. IEEE Trans Evolut Comput 18:4–19CrossRef Mukhopadhyay A, Maulik U, Bandyopadhyay S, Coello Coello C (2014) A survey of multiobjective evolutionary algorithms for data mining: part I. IEEE Trans Evolut Comput 18:4–19CrossRef
Zurück zum Zitat Ngatchou P, Zarei A, El-Sharkawi, M Pareto (2005) multi objective optimization. In: Proceedings of the 13th international conference on intelligent systems application to power systems. IEEE, pp 84–91 Ngatchou P, Zarei A, El-Sharkawi, M Pareto (2005) multi objective optimization. In: Proceedings of the 13th international conference on intelligent systems application to power systems. IEEE, pp 84–91
Zurück zum Zitat Nguyen H-V, Müller E, Vreeken J, Böhm K (2014) Unsupervised interaction-preserving discretization of multivariate data. Data Min Knowl Discov 28:1366–1397MathSciNetCrossRefMATH Nguyen H-V, Müller E, Vreeken J, Böhm K (2014) Unsupervised interaction-preserving discretization of multivariate data. Data Min Knowl Discov 28:1366–1397MathSciNetCrossRefMATH
Zurück zum Zitat Øhrn A (2000) The Rosetta C++ Library: overview of files and classes department of computer and information science. Norwegian University of Science and Technology (NTNU), Trondheim Øhrn A (2000) The Rosetta C++ Library: overview of files and classes department of computer and information science. Norwegian University of Science and Technology (NTNU), Trondheim
Zurück zum Zitat Quinlan JR (2014) C4. 5: programs for machine learning. Elsevier, Amsterdam Quinlan JR (2014) C4. 5: programs for machine learning. Elsevier, Amsterdam
Zurück zum Zitat Rahman MG, Islam MZ (2016) Discretization of continuous attributes through low frequency numerical values and attribute interdependency. Expert Syst Appl 45:410–423CrossRef Rahman MG, Islam MZ (2016) Discretization of continuous attributes through low frequency numerical values and attribute interdependency. Expert Syst Appl 45:410–423CrossRef
Zurück zum Zitat Ramírez-Gallego S, García S, Benítez JM, Herrera F (2016) Multivariate discretization based on evolutionary cut points selection for classification. IEEE Trans Cybern 46:595–608CrossRef Ramírez-Gallego S, García S, Benítez JM, Herrera F (2016) Multivariate discretization based on evolutionary cut points selection for classification. IEEE Trans Cybern 46:595–608CrossRef
Zurück zum Zitat Razavi SH, Ebadati EOM, Asadi S, Kaur H (2015) An efficient grouping genetic algorithm for data clustering and big data analysis. In: Computational intelligence for big data analysis. Springer, pp 119–142 Razavi SH, Ebadati EOM, Asadi S, Kaur H (2015) An efficient grouping genetic algorithm for data clustering and big data analysis. In: Computational intelligence for big data analysis. Springer, pp 119–142
Zurück zum Zitat Sang Y, Jin Y, Li K, Qi H (2013) UniDis: a universal discretization technique. J Intell Inf Syst 40:327–348CrossRef Sang Y, Jin Y, Li K, Qi H (2013) UniDis: a universal discretization technique. J Intell Inf Syst 40:327–348CrossRef
Zurück zum Zitat Sang Y, Qi H, Li K, Jin Y, Yan D, Gao S (2014) An effective discretization method for disposing high-dimensional data. Inf Sci 270:73–91 Sang Y, Qi H, Li K, Jin Y, Yan D, Gao S (2014) An effective discretization method for disposing high-dimensional data. Inf Sci 270:73–91
Zurück zum Zitat Shehzad K (2012) EDISC: a class-tailored discretization technique for rule-based classification. IEEE Trans Knowl Data Eng 24:1435–1447CrossRef Shehzad K (2012) EDISC: a class-tailored discretization technique for rule-based classification. IEEE Trans Knowl Data Eng 24:1435–1447CrossRef
Zurück zum Zitat Tao G, Yan YG, Zou J, Liu J (2015) The discretization of continuous attributes based on improved SOM clustering. In: Applied mechanics and materials, Trans Tech Publ, pp 88–93 Tao G, Yan YG, Zou J, Liu J (2015) The discretization of continuous attributes based on improved SOM clustering. In: Applied mechanics and materials, Trans Tech Publ, pp 88–93
Zurück zum Zitat Tay FE, Shen L (2002) A modified chi2 algorithm for discretization. IEEE Trans Knowl Data Eng 14:666–670CrossRef Tay FE, Shen L (2002) A modified chi2 algorithm for discretization. IEEE Trans Knowl Data Eng 14:666–670CrossRef
Zurück zum Zitat Wang C, Wang M, She Z, Cao L (2012) CD: a coupled discretization algorithm. In: Advances in knowledge discovery and data mining. Springer, pp 407–418 Wang C, Wang M, She Z, Cao L (2012) CD: a coupled discretization algorithm. In: Advances in knowledge discovery and data mining. Springer, pp 407–418
Zurück zum Zitat Wei Y, Qiu J, Karimi HR, Wang M (2014) Model reduction for continuous-time Markovian jump systems with incomplete statistics of mode information. Int J Syst Sci 45:1496–1507MathSciNetCrossRefMATH Wei Y, Qiu J, Karimi HR, Wang M (2014) Model reduction for continuous-time Markovian jump systems with incomplete statistics of mode information. Int J Syst Sci 45:1496–1507MathSciNetCrossRefMATH
Zurück zum Zitat Wei Y, Qiu J, Karimi HR (2015) Quantized \({\cal{H}}\infty \) filtering for continuous-time Markovian jump systems with deficient mode information. Asian J Control 17:1914–1923MathSciNetCrossRefMATH Wei Y, Qiu J, Karimi HR (2015) Quantized \({\cal{H}}\infty \) filtering for continuous-time Markovian jump systems with deficient mode information. Asian J Control 17:1914–1923MathSciNetCrossRefMATH
Zurück zum Zitat Wei Y, Qiu J, Lam H-K, Wu L (2016a) Approaches to TS fuzzy-affine-model-based reliable output feedback control for nonlinear ITO stochastic systems. IEEE Trans Fuzzy Syst 99:1–14 Wei Y, Qiu J, Lam H-K, Wu L (2016a) Approaches to TS fuzzy-affine-model-based reliable output feedback control for nonlinear ITO stochastic systems. IEEE Trans Fuzzy Syst 99:1–14
Zurück zum Zitat Wei Y, Qiu J, Shi P, Lam H-K (2016b) A new design of H-infinity piecewise filtering for discrete-time nonlinear time-varying delay systems via TS fuzzy affine models. IEEE Trans Syst Man Cybern Syst 99:1–14 Wei Y, Qiu J, Shi P, Lam H-K (2016b) A new design of H-infinity piecewise filtering for discrete-time nonlinear time-varying delay systems via TS fuzzy affine models. IEEE Trans Syst Man Cybern Syst 99:1–14
Zurück zum Zitat Yan D, Liu D, Sang Y (2014) A new approach for discretizing continuous attributes in learning systems. Neurocomputing 133:507–511CrossRef Yan D, Liu D, Sang Y (2014) A new approach for discretizing continuous attributes in learning systems. Neurocomputing 133:507–511CrossRef
Zurück zum Zitat Yang Y, Webb GI (2009) Discretization for naive-Bayes learning: managing discretization bias and variance. Mach Learn 74:39–74CrossRef Yang Y, Webb GI (2009) Discretization for naive-Bayes learning: managing discretization bias and variance. Mach Learn 74:39–74CrossRef
Zurück zum Zitat Yang Y, Webb GI, Wu X (2005) Discretization methods. In: Data mining and knowledge discovery handbook. Springer, pp 113–130 Yang Y, Webb GI, Wu X (2005) Discretization methods. In: Data mining and knowledge discovery handbook. Springer, pp 113–130
Zurück zum Zitat Zhao J, Han C, Wei B, Han D (2012) A novel univariate marginal distribution algorithm based discretization algorithm. Stat Probab Lett 82:2001–2007MathSciNetCrossRefMATH Zhao J, Han C, Wei B, Han D (2012) A novel univariate marginal distribution algorithm based discretization algorithm. Stat Probab Lett 82:2001–2007MathSciNetCrossRefMATH
Zurück zum Zitat Zighed DA, Rabaséda S, Rakotomalala R (1998) FUSINTER: a method for discretization of continuous attributes. Int J Uncertain Fuzziness Knowl-Based Syst 6:307–326CrossRefMATH Zighed DA, Rabaséda S, Rakotomalala R (1998) FUSINTER: a method for discretization of continuous attributes. Int J Uncertain Fuzziness Knowl-Based Syst 6:307–326CrossRefMATH
Metadaten
Titel
MEMOD: a novel multivariate evolutionary multi-objective discretization
verfasst von
Marzieh Hajizadeh Tahan
Shahrokh Asadi
Publikationsdatum
05.01.2017
Verlag
Springer Berlin Heidelberg
Erschienen in
Soft Computing / Ausgabe 1/2018
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-016-2475-5

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