Skip to main content
Erschienen in: Advances in Data Analysis and Classification 3/2017

25.05.2016 | Regular Article

A new approach for determining the prior probabilities in the classification problem by Bayesian method

verfasst von: Thao Nguyen-Trang, Tai Vo-Van

Erschienen in: Advances in Data Analysis and Classification | Ausgabe 3/2017

Einloggen

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

search-config
loading …

Abstract

In this article, we suggest a new algorithm to identify the prior probabilities for classification problem by Bayesian method. The prior probabilities are determined by combining the information of populations in training set and the new observations through fuzzy clustering method (FCM) instead of using uniform distribution or the ratio of sample or Laplace method as the existing ones. We next combine the determined prior probabilities and the estimated likelihood functions to classify the new object. In practice, calculations are performed by Matlab procedures. The proposed algorithm is tested by the three numerical examples including bench mark and real data sets. The results show that the new approach is reasonable and gives more efficient than existing ones.

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
Zurück zum Zitat Bora DJ, Gupta AK (2014) Impact of exponent parameter value for the partition matrix on the performance of fuzzy C means Algorithm. arXiv:1406.4007 (arXiv preprint) Bora DJ, Gupta AK (2014) Impact of exponent parameter value for the partition matrix on the performance of fuzzy C means Algorithm. arXiv:​1406.​4007 (arXiv preprint)
Zurück zum Zitat Cannon RL, Dave JV, Bezdek JC (1986) Efficient implementation of the fuzzy c-means clustering algorithms. IEEE Trans Pattern Anal Mach Intell 2:248–255CrossRefMATH Cannon RL, Dave JV, Bezdek JC (1986) Efficient implementation of the fuzzy c-means clustering algorithms. IEEE Trans Pattern Anal Mach Intell 2:248–255CrossRefMATH
Zurück zum Zitat Fadili MJ et al (2001) On the number of clusters and the fuzziness index for unsupervised FCA application to BOLD fMRI time series. Med Image Anal 5(1):55–67CrossRef Fadili MJ et al (2001) On the number of clusters and the fuzziness index for unsupervised FCA application to BOLD fMRI time series. Med Image Anal 5(1):55–67CrossRef
Zurück zum Zitat Ghosh AK, Chaudhuri P, Sengupta D (2006) Classification using Kernel density estimates. Technometrics 48(1):120–132MathSciNetCrossRef Ghosh AK, Chaudhuri P, Sengupta D (2006) Classification using Kernel density estimates. Technometrics 48(1):120–132MathSciNetCrossRef
Zurück zum Zitat Hall LO et al (1992) A comparison of neural network and fuzzy clustering techniques in segmenting magnetic resonance images of the brain. IEEE Trans Neural Netw 3(5):672–682CrossRef Hall LO et al (1992) A comparison of neural network and fuzzy clustering techniques in segmenting magnetic resonance images of the brain. IEEE Trans Neural Netw 3(5):672–682CrossRef
Zurück zum Zitat Inman HF, Bradley EL Jr (1989) The overlapping coefficient as a measure of agreement between probability distributions and point estimation of the overlap of two normal densities. Commun Stat Theory Methods 18(10):3851–3874MathSciNetCrossRefMATH Inman HF, Bradley EL Jr (1989) The overlapping coefficient as a measure of agreement between probability distributions and point estimation of the overlap of two normal densities. Commun Stat Theory Methods 18(10):3851–3874MathSciNetCrossRefMATH
Zurück zum Zitat Mardia KV, Kent JT, Bibby JM (1979) Multivariate analysis. Academic Press, CambridgeMATH Mardia KV, Kent JT, Bibby JM (1979) Multivariate analysis. Academic Press, CambridgeMATH
Zurück zum Zitat Martinez WL, Martinez AR (2007) Computational statistics handbook with MATLAB. CRC Press, Boca RatonMATH Martinez WL, Martinez AR (2007) Computational statistics handbook with MATLAB. CRC Press, Boca RatonMATH
Zurück zum Zitat McLachlan GJ, Basford KE (1988) Mixture models: inference and applications to clustering. Statistics: textbooks and monographs. Dekker, New York McLachlan GJ, Basford KE (1988) Mixture models: inference and applications to clustering. Statistics: textbooks and monographs. Dekker, New York
Zurück zum Zitat Miller G et al (2001) Bayesian prior probability distributions for internal dosimetry. Radiat Prot Dosim 94(4):347–352CrossRef Miller G et al (2001) Bayesian prior probability distributions for internal dosimetry. Radiat Prot Dosim 94(4):347–352CrossRef
Zurück zum Zitat Pal NR, Bezdek JC (1995) On cluster validity for the fuzzy c-means model. IEEE Trans Fuzzy Syst 3(3):370–379CrossRef Pal NR, Bezdek JC (1995) On cluster validity for the fuzzy c-means model. IEEE Trans Fuzzy Syst 3(3):370–379CrossRef
Zurück zum Zitat Pham-Gia T, Turkkan N, Vovan T (2008) Statistical discrimination analysis using the maximum function. Commun Stat Simul Comput 37(2):320–336MathSciNetCrossRefMATH Pham-Gia T, Turkkan N, Vovan T (2008) Statistical discrimination analysis using the maximum function. Commun Stat Simul Comput 37(2):320–336MathSciNetCrossRefMATH
Zurück zum Zitat Scott DW (1992) Multivariate density estimation: theory, practice, and visualization. Wiley Scott DW (1992) Multivariate density estimation: theory, practice, and visualization. Wiley
Zurück zum Zitat Silverman BW (1986) Density estimation for statistics and data analysis, vol 26. CRC Press, Boca RatonCrossRefMATH Silverman BW (1986) Density estimation for statistics and data analysis, vol 26. CRC Press, Boca RatonCrossRefMATH
Zurück zum Zitat Webb AR (2003) Statistical pattern recognition. Wiley, New YorkMATH Webb AR (2003) Statistical pattern recognition. Wiley, New YorkMATH
Zurück zum Zitat Yu J, Cheng Q, Huang H (2004) Analysis of the weighting exponent in the FCM. IEEE Trans Syst Man Cybern Part B Cybern 34(1):634–639CrossRef Yu J, Cheng Q, Huang H (2004) Analysis of the weighting exponent in the FCM. IEEE Trans Syst Man Cybern Part B Cybern 34(1):634–639CrossRef
Metadaten
Titel
A new approach for determining the prior probabilities in the classification problem by Bayesian method
verfasst von
Thao Nguyen-Trang
Tai Vo-Van
Publikationsdatum
25.05.2016
Verlag
Springer Berlin Heidelberg
Erschienen in
Advances in Data Analysis and Classification / Ausgabe 3/2017
Print ISSN: 1862-5347
Elektronische ISSN: 1862-5355
DOI
https://doi.org/10.1007/s11634-016-0253-y

Weitere Artikel der Ausgabe 3/2017

Advances in Data Analysis and Classification 3/2017 Zur Ausgabe

Premium Partner