The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
The Nearest Neighbor Classification Rule with a Reject Option
Abstract
An observation comes from one of two possible classes. If all the statistics of the problem are known, Bayes' classification scheme yields the minimum probability of error. If, instead, the statistics are not known and one is given only a labeled training set, it is known that the nearest neighbor rule has an asymptotic error no greater than twice that of Bayes' rule. Here the (k,k') nearest neighbor rule with a reject option is examined. This rule looks at the k nearest neighbors and rejects if less than k' of these are from the same class; if k' or more are from one class, a decision is made in favor of that class. The error rate of such a rule is bounded in terms of the Bayes' error rate.
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Cites
Nearest neighbor pattern classification
Cover, T., & Hart, P. (1967) · IEEE Transactions on Information Theory · doi:10.1109/tit.1967.1053964 · Cited by 16,936
Cited by
Aleatoric and epistemic uncertainty in machine learning: an introduction to concepts and methods
Hüllermeier, E., & Waegeman, W. (2021) · Machine Learning · doi:10.1007/s10994-021-05946-3 · Cited by 1,834
“Instead, the ultimate decision can often be refused or delayed, like in classification with a reject option (Chow, 1970; Hellman, 1970), or actions can be taken that are specifically directed at reducing uncertainty, like in active learning (Aggarwal et al., 2014).”
BackgroundA k-nearest neighbor classification rule based on Dempster-Shafer theory
Denoeux, T. (1995) · IEEE Transactions on Systems, Man, and Cybernetics · doi:10.1109/21.376493 · Cited by 1,013
A k-Nearest Neighbor Classification Rule Based on Dempster-Shafer Theory
Denœux, T. (2008) · Studies in Fuzziness and Soft Computing · doi:10.1007/978-3-540-44792-4_29 · Cited by 830
Generalized ODIN: Detecting Out-of-Distribution Image Without Learning From Out-of-Distribution Data
Hsu, Y.-C., Shen, Y., Jin, H., & Kira, Z. (2020) · 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr42600.2020.01096 · Cited by 499
Machine learning with a reject option: A survey
Hendrickx, K., Perini, L., Van der Plas, D., Meert, W., & Davis, J. (2024) · Machine Learning · doi:10.1007/s10994-024-06534-x · Cited by 134
Metadata
- Authors
- Hellman, M. E.
- Venue
- IEEE Transactions on Systems Science and Cybernetics
- Published
- 1970-07
- Volume
- 6
- Issue
- 3
- Pages
- 179-185
- ISSN
- 0536-1567 (ISSN-L)
- 2168-2887
- OpenAlex
- W2134177842
- Cited by
- 218
- References
- 1
- FWCI
- 1.79
- Type
- journal article
- Language
- en
- Open access
- closed
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- Hellman, M. E. (1970). The Nearest Neighbor Classification Rule with a Reject Option. IEEE Transactions on Systems Science and Cybernetics. https://doi.org/10.1109/tssc.1970.300339
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