A Statistical Confidence-Based Adaptive Nearest Neighbor Algorithm for Pattern Classification

  • Jigang Wang
  • Predrag Neskovic
  • Leon N. Cooper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3930)


The k-nearest neighbor rule is one of the simplest and most attractive pattern classification algorithms. It can be interpreted as an empirical Bayes classifier based on the estimated a posteriori probabilities from the k nearest neighbors. The performance of the k-nearest neighbor rule relies on the locally constant a posteriori probability assumption. This assumption, however, becomes problematic in high dimensional spaces due to the curse of dimensionality. In this paper we introduce a locally adaptive nearest neighbor rule. Instead of using the Euclidean distance to locate the nearest neighbors, the proposed method takes into account the effective influence size of each training example and the statistical confidence with which the label of each training example can be trusted. We test the new method on real-world benchmark datasets and compare it with the standard k-nearest neighbor rule and the support vector machines. The experimental results confirm the effectiveness of the proposed method.


Support Vector Machine Class Label Majority Rule Near Neighbor Query Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Fix, E., Hodges, J.: Discriminatory analysis, nonparametric discrimination: consistency properties. Tech. Report 4, USAF School of Aviation Medicine, Randolph Field, Texas (1951)Google Scholar
  2. 2.
    Cover, T.M., Hart, P.E.: Nearest Neighbor Pattern Classification. IEEE Transactions on Information Theory IT-13(1), 21–27 (1967)MATHCrossRefGoogle Scholar
  3. 3.
    Devroye, L.: On the inequality of Cover and Hart. IEEE Transactions on Pattern Analysis and Machine Intelligence 3, 75–78 (1981)MATHCrossRefGoogle Scholar
  4. 4.
    Stone, C.J.: Consistent nonparametric regression. Annals of Statistics 5, 595–645 (1977)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Devroye, L., Györfi, L., Krzyżak, A., Lugosi, G.: On the strong universal consistency of nearest neighbor regression function estimates. Annals of Statistics 22, 1371–1385 (1994)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Geman, S., Bienenstock, E., Doursat, R.: Neural networks and the bias/variance dilemma. Neural Computation 4(1), 1–58 (1992)CrossRefGoogle Scholar
  7. 7.
    Friedman, J.: Flexible metric nearest neighbor classification. Technical Report 113, Stanford University Statistics Department (1994)Google Scholar
  8. 8.
    Hastie, T., Tibshirani, R.: Discriminant adaptive nearest neighbor classification. IEEE Transactions on Pattern Analysis and Machine Intelligence 18, 607–615 (1996)CrossRefGoogle Scholar
  9. 9.
    Domeniconi, C., Peng, J., Gunopulos, D.: Locally adaptive metric nearest-neighbor classification. IEEE Transactions on Pattern Analysis and Machine Intelligence 24, 1281–1285 (2002)CrossRefGoogle Scholar
  10. 10.
    Hoeffding, W.: Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association 58, 13–30 (1963)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Blake, C.L., Merz, C.J.: UCI Repository of machine learning databases, Dept. of Information and Computer Sciences, University of California, Irvine (1998),

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jigang Wang
    • 1
  • Predrag Neskovic
    • 1
  • Leon N. Cooper
    • 1
  1. 1.Institute for Brain and Neural Systems, Department of PhysicsBrown UniversityProvidenceUSA

Personalised recommendations