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A Generalization of the k-NN Rule

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1 Author(s)
Tomek, Ivan ; Department of Computer Science, Acadia University, Wolfville, N.S., Canada.

A modification of the k-nearest neighbors (k-NN) rule is presented in which classification is made not according to the ``majority vote'' but rather an integer threshold k1 (k1-NN rule). It is shown that while k-NN approximates the minimum expected error rule, k1-NN approximates the minimum expected risk rule with a threshold t. The relationship between t and values of k and k1 is derived. Several practical methods of using k1-NN for minimum expected risk classification and for classification with a reject option are described and illustrated with examples.

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Systems, Man and Cybernetics, IEEE Transactions on  (Volume:SMC-6 ,  Issue: 2 )