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A unified weighting framework for evaluating nearest neighbour classification

Oliver Urs Lenz (UGent) , Henri Bollaert (UGent) and Chris Cornelis (UGent)
(2025) FUZZY SETS AND SYSTEMS. 519.
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Abstract
We present the first comprehensive and large-scale evaluation of classical (NN), fuzzy (FNN) and fuzzy rough (FRNN) nearest neighbour classification. We standardise existing proposals for nearest neighbour weighting with kernel functions, applied to the distance values and/or ranks of the nearest neighbours of a test instance. In particular, we show that the theoretically optimal Samworth weights converge to a kernel. Kernel functions are closely related to fuzzy negation operators, and we propose a new kernel based on Yager negation. We also consider various distance and scaling measures, which we show can be related to each other. Through a systematic series of experiments on 85 real-life classification datasets, we find that NN, FNN and FRNN all perform best with Boscovich distance, and that NN and FRNN perform best with a combination of Samworth rank-and distance-weights and scaling by the mean absolute deviation around the median (r1), the standard deviation (r2) or the semi-interquartile range (r & lowast;infinity), while FNN performs best with only Samworth distance-weights and r1-or r2-scaling. However, NN achieves comparable performance with Yager-12 distance-weights, which are simpler to implement than a combination of Samworth distance-and rank-weights. Finally, FRNN generally outperforms NN, which in turn performs systematically better than FNN.
Keywords
FUZZY, ALGORITHMS, Classification, Fuzzy nearest neighbours, Fuzzy negation, Fuzzy rough nearest neighbours, Kernels, Nearest neighbours, Weighting

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MLA
Lenz, Oliver Urs, et al. “A Unified Weighting Framework for Evaluating Nearest Neighbour Classification.” FUZZY SETS AND SYSTEMS, vol. 519, 2025, doi:10.1016/j.fss.2025.109516.
APA
Lenz, O. U., Bollaert, H., & Cornelis, C. (2025). A unified weighting framework for evaluating nearest neighbour classification. FUZZY SETS AND SYSTEMS, 519. https://doi.org/10.1016/j.fss.2025.109516
Chicago author-date
Lenz, Oliver Urs, Henri Bollaert, and Chris Cornelis. 2025. “A Unified Weighting Framework for Evaluating Nearest Neighbour Classification.” FUZZY SETS AND SYSTEMS 519. https://doi.org/10.1016/j.fss.2025.109516.
Chicago author-date (all authors)
Lenz, Oliver Urs, Henri Bollaert, and Chris Cornelis. 2025. “A Unified Weighting Framework for Evaluating Nearest Neighbour Classification.” FUZZY SETS AND SYSTEMS 519. doi:10.1016/j.fss.2025.109516.
Vancouver
1.
Lenz OU, Bollaert H, Cornelis C. A unified weighting framework for evaluating nearest neighbour classification. FUZZY SETS AND SYSTEMS. 2025;519.
IEEE
[1]
O. U. Lenz, H. Bollaert, and C. Cornelis, “A unified weighting framework for evaluating nearest neighbour classification,” FUZZY SETS AND SYSTEMS, vol. 519, 2025.
@article{01KAGPA7SCWTGYDVNDGM09B3YP,
  abstract     = {{We present the first comprehensive and large-scale evaluation of classical (NN), fuzzy (FNN) and fuzzy rough (FRNN) nearest neighbour classification. We standardise existing proposals for nearest neighbour weighting with kernel functions, applied to the distance values and/or ranks of the nearest neighbours of a test instance. In particular, we show that the theoretically optimal Samworth weights converge to a kernel. Kernel functions are closely related to fuzzy negation operators, and we propose a new kernel based on Yager negation. We also consider various distance and scaling measures, which we show can be related to each other. Through a systematic series of experiments on 85 real-life classification datasets, we find that NN, FNN and FRNN all perform best with Boscovich distance, and that NN and FRNN perform best with a combination of Samworth rank-and distance-weights and scaling by the mean absolute deviation around the median (r1), the standard deviation (r2) or the semi-interquartile range (r & lowast;infinity), while FNN performs best with only Samworth distance-weights and r1-or r2-scaling. However, NN achieves comparable performance with Yager-12 distance-weights, which are simpler to implement than a combination of Samworth distance-and rank-weights. Finally, FRNN generally outperforms NN, which in turn performs systematically better than FNN.}},
  articleno    = {{109516}},
  author       = {{Lenz, Oliver Urs and Bollaert, Henri and Cornelis, Chris}},
  issn         = {{0165-0114}},
  journal      = {{FUZZY SETS AND SYSTEMS}},
  keywords     = {{FUZZY,ALGORITHMS,Classification,Fuzzy nearest neighbours,Fuzzy negation,Fuzzy rough nearest neighbours,Kernels,Nearest neighbours,Weighting}},
  language     = {{eng}},
  pages        = {{21}},
  title        = {{A unified weighting framework for evaluating nearest neighbour classification}},
  url          = {{http://doi.org/10.1016/j.fss.2025.109516}},
  volume       = {{519}},
  year         = {{2025}},
}
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