Nonparametric Estimation of the Bayes Error of Feature Extractors Using Ordered Nearest Neighbor Sets

James M. Garnett, Stephen S. Yau

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Since the Bayes classifier is the optimum classifier in the sense of having minimum probability of misclassification among all the classifiers using the same set of pattern features, the error rate of the Bayes classifier using the set of features provided by a feature extractor, called the Bayes error of the feature extractor, is the smallest possible for the feature extractor. Consequently, the Bayes error can be used to evaluate the effectiveness of the feature extractors in a pattern recognition system. In this paper, a nonparametric technique for estimating the Bayes error for any two-category feature extractor is presented. This technique uses the nearest neighbor sample sets and is based on an infinite series expansion of the general form of the Bayes error. It is shown that this technique is better than the existing methods, and the estimates obtained by this technique are more meaningful in evaluating the quality of feature extractors. Computer simulation as well as application to electrocardiogram analysis are used to demonstrate this technique.

Original languageEnglish (US)
Pages (from-to)46-54
Number of pages9
JournalIEEE Transactions on Computers
Issue number1
StatePublished - Jan 1977
Externally publishedYes


  • Bayes error
  • comparison
  • feature extractors
  • nearest neighbor sets
  • nonparametric estimation
  • pattern recognition systems
  • series expansion

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture
  • Computational Theory and Mathematics


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