Skip to main content

2017 | OriginalPaper | Buchkapitel

Fuzzy Clustering with \(\varepsilon \)-Hyperballs and Its Application to Data Classification

verfasst von : Michal Jezewski, Robert Czabanski, Jacek Leski

Erschienen in: Artificial Intelligence and Soft Computing

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In the presented paper the Fuzzy Clustering with \(\varepsilon \)-Hyperballs being the prototypes is proposed. It is based on the idea of regions of insensitivity – described by the hyperballs of radius \(\varepsilon \), in which the distances of objects from the centers of the hyperballs are considered as equal to zero. The proposed clustering was applied to determine the parameters of fuzzy sets in antecedents of the classifier based on fuzzy if-then rules. The classification quality obtained for six benchmark datasets was compared with the reference classifiers. The results show the improvement of the classification accuracy using the proposed method.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Aggarwal, C.C., Reddy, C.K.: Data Clustering. Algorithms and Applications. CRC Press, Boca Raton (2014)MATH Aggarwal, C.C., Reddy, C.K.: Data Clustering. Algorithms and Applications. CRC Press, Boca Raton (2014)MATH
2.
Zurück zum Zitat Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)CrossRefMATH Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)CrossRefMATH
3.
Zurück zum Zitat Cortes, C., Vapnik, V.: Support-vector networks. Mach. Learn. 20(3), 273–297 (1995)MATH Cortes, C., Vapnik, V.: Support-vector networks. Mach. Learn. 20(3), 273–297 (1995)MATH
4.
Zurück zum Zitat Doring, C., Lesot, M.-J., Kruse, R.: Data analysis with fuzzy clustering methods. Comput. Stat. Data Anal. 51, 192–214 (2006)MathSciNetCrossRefMATH Doring, C., Lesot, M.-J., Kruse, R.: Data analysis with fuzzy clustering methods. Comput. Stat. Data Anal. 51, 192–214 (2006)MathSciNetCrossRefMATH
5.
Zurück zum Zitat Gorzalczany, M.B., Rudzinski, F.: Interpretable and accurate medical data classification - a multi-objective genetic-fuzzy optimization approach. Expert Syst. Appl. 71, 26–39 (2017)CrossRef Gorzalczany, M.B., Rudzinski, F.: Interpretable and accurate medical data classification - a multi-objective genetic-fuzzy optimization approach. Expert Syst. Appl. 71, 26–39 (2017)CrossRef
6.
Zurück zum Zitat Ho, Y.-C., Kashyap, R.L.: An algorithm for linear inequalities and its applications. IEEE Trans. Electron. Comput. 14(5), 683–688 (1965)CrossRefMATH Ho, Y.-C., Kashyap, R.L.: An algorithm for linear inequalities and its applications. IEEE Trans. Electron. Comput. 14(5), 683–688 (1965)CrossRefMATH
7.
Zurück zum Zitat Jezewski, M., Czabanski, R., Horoba, K., Leski, J.M.: Clustering with pairs of prototypes to support automated assessment of the fetal state. Appl. Artif. Intell. 30(6), 572–589 (2016)CrossRef Jezewski, M., Czabanski, R., Horoba, K., Leski, J.M.: Clustering with pairs of prototypes to support automated assessment of the fetal state. Appl. Artif. Intell. 30(6), 572–589 (2016)CrossRef
8.
Zurück zum Zitat Jezewski, M., Leski, J.M., Czabanski, R.: Classification based on incremental fuzzy \((1+p)\)-means clustering. In: Gruca, A., Brachman, A., Kozielski, S., Czachórski, T. (eds.) Man–Machine Interactions 4. AISC, vol. 391, pp. 563–572. Springer, Cham (2016). doi:10.1007/978-3-319-23437-3_48 Jezewski, M., Leski, J.M., Czabanski, R.: Classification based on incremental fuzzy \((1+p)\)-means clustering. In: Gruca, A., Brachman, A., Kozielski, S., Czachórski, T. (eds.) Man–Machine Interactions 4. AISC, vol. 391, pp. 563–572. Springer, Cham (2016). doi:10.​1007/​978-3-319-23437-3_​48
9.
Zurück zum Zitat Kruse, R., Doring, C., Lesot, M.-J.: Fundamentals of fuzzy clustering. In: de Oliveira, J.V., Pedrycz, W. (eds.) Advances in Fuzzy Clustering and Its Applications, pp. 3–30. Wiley Ltd., Chichester (2007) Kruse, R., Doring, C., Lesot, M.-J.: Fundamentals of fuzzy clustering. In: de Oliveira, J.V., Pedrycz, W. (eds.) Advances in Fuzzy Clustering and Its Applications, pp. 3–30. Wiley Ltd., Chichester (2007)
10.
Zurück zum Zitat Leski, J.M.: An \(\varepsilon \)-insensitive approach to fuzzy clustering. Int. J. Appl. Math. Comput. Sci. 11(4), 993–1007 (2001)MathSciNetMATH Leski, J.M.: An \(\varepsilon \)-insensitive approach to fuzzy clustering. Int. J. Appl. Math. Comput. Sci. 11(4), 993–1007 (2001)MathSciNetMATH
11.
Zurück zum Zitat Leski, J.M.: Fuzzy \((c+p)\)-means clustering and its application to a fuzzy rule-based classifier: toward good generalization and good interpretability. IEEE Trans. Fuzzy Syst. 23(4), 802–812 (2015)CrossRef Leski, J.M.: Fuzzy \((c+p)\)-means clustering and its application to a fuzzy rule-based classifier: toward good generalization and good interpretability. IEEE Trans. Fuzzy Syst. 23(4), 802–812 (2015)CrossRef
12.
Zurück zum Zitat Leski, J.M.: Ho-Kashyap classifier with generalization control. Pattern Recogn. Lett. 24(14), 2281–2290 (2003)CrossRefMATH Leski, J.M.: Ho-Kashyap classifier with generalization control. Pattern Recogn. Lett. 24(14), 2281–2290 (2003)CrossRefMATH
13.
Zurück zum Zitat Leski, J.M.: Iteratively reweighted least squares classifier and its \(\ell _2\)- and \(\ell _1\)-regularized kernel versions. Bull. Polish Acad. Sci. Tech. Sci. 58(1), 171–182 (2010)MathSciNet Leski, J.M.: Iteratively reweighted least squares classifier and its \(\ell _2\)- and \(\ell _1\)-regularized kernel versions. Bull. Polish Acad. Sci. Tech. Sci. 58(1), 171–182 (2010)MathSciNet
14.
Zurück zum Zitat Mangasarian, O.L., Musicant, D.R.: Lagrangian support vector machines. J. Mach. Learn. Res. 1, 161–177 (2001)MathSciNetMATH Mangasarian, O.L., Musicant, D.R.: Lagrangian support vector machines. J. Mach. Learn. Res. 1, 161–177 (2001)MathSciNetMATH
15.
Zurück zum Zitat Mika, S., Ratsch, G., Weston, J., Scholkopf, B., Muller, K.-R.: Fisher discriminant analysis with kernels. In: Proceedings of Neural Networks for Signal Processing IX, pp. 41–48 (1999) Mika, S., Ratsch, G., Weston, J., Scholkopf, B., Muller, K.-R.: Fisher discriminant analysis with kernels. In: Proceedings of Neural Networks for Signal Processing IX, pp. 41–48 (1999)
16.
Zurück zum Zitat Ratsch, G., Onoda, T., Muller, K.-R.: Soft margins for AdaBoost. Mach. Learn. 42, 287–320 (2001)CrossRefMATH Ratsch, G., Onoda, T., Muller, K.-R.: Soft margins for AdaBoost. Mach. Learn. 42, 287–320 (2001)CrossRefMATH
17.
Zurück zum Zitat Xu, R., Wunsch, II, D.C.: Clustering. Wiley Inc., Hoboken (2009) Xu, R., Wunsch, II, D.C.: Clustering. Wiley Inc., Hoboken (2009)
Metadaten
Titel
Fuzzy Clustering with -Hyperballs and Its Application to Data Classification
verfasst von
Michal Jezewski
Robert Czabanski
Jacek Leski
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-59060-8_9

Premium Partner