Statistical Analyses of Various Error Functions for Pattern Classifiers

  • Sang-Hoon Oh
Part of the Communications in Computer and Information Science book series (CCIS, volume 206)


There are various error functions for pattern classifiers. This paper analyzes the error functions such as MSE(mean-squared error), CE(crossentropy) error, AN(additive noise) in MSE, MLS(mean log square) error, and nCE(nth order extension of CE) error functions in a statistical perspective. Also, the analyses include CFM(classification figure of merit). The results of analyses provide considerable insights into the properties of different error functions.


Classifier error functions statistical analysis optimal solution 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Park, W.J., Kil, R.M.: Pattern Classification with Class Probability Output Network. IEEE Trans. Neural Network 20, 1659–1673 (2009)CrossRefGoogle Scholar
  2. 2.
    Fukunaga, K., Kessel, D.: Nonparametric Bayes error estimation using unclassified samples. IEEE Trans. Inf. Theory 19, 434–439 (1973)CrossRefzbMATHGoogle Scholar
  3. 3.
    Parzen, E.: On the estimation of a probability density function and mode. Ann. Math. Statist. 33, 1065–1076 (1962)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Rumelhart, D.E., McClelland, J.L.: Parallel Distributed Processing. MIT Press, Cambridge (1986)Google Scholar
  5. 5.
    Wang, C., Principe, J.C.: Training Neural Networks with Additive Noise in the Desired Signal. IEEE Trans. Neural Networks 10, 1511–1517 (1999)CrossRefGoogle Scholar
  6. 6.
    Liano, K.: Robust Error Measure for Supervised Neural Network Learning with Outliers. IEEE Trans. Neural Networks 7, 246–250 (1996)CrossRefGoogle Scholar
  7. 7.
    van Ooyen, A., Nienhuis, B.: Improving the Convergence of the Backpropagation Algorithm. Neural Networks 4, 465–471 (1992)CrossRefGoogle Scholar
  8. 8.
    Oh, S.-H.: Improving the error back-propagation algorithm with a modified error function. IEEE Trans. Neural Networks 8, 799–803 (1997)CrossRefGoogle Scholar
  9. 9.
    Oh, S.-H.: Error Back-Propagation Algorithm for Classification of Imbalanced Data. Neurocomputing 74, 1058–1061 (2011)CrossRefGoogle Scholar
  10. 10.
    Hampshire II, J.B., Waibel, A.H.: A Novel Objective Function for Improved Phoneme Recognition Using Time-Delay Networks. IEEE Trans. Neural Networks 1, 216–218 (1990)CrossRefGoogle Scholar
  11. 11.
    White, H.: Learning in Artificial Neural Networks: A Statistical Perspective. Neural computation 1, 425–464 (1989)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Sang-Hoon Oh
    • 1
  1. 1.Mokwon UniversityDaejonKorea

Personalised recommendations