The 2-NN Rule for More Accurate NN Risk Estimation

By proper design of a nearest-neighbor (NN) rule, it is possible to reduce effects of sample size in NN risk estimation. The 2-NN rule for the two-class problem eliminates the first-order effects of sample size. Since its asymptotic value is exactly half that of the 1-NN rule, it is possible to substitute the 2-NN rule for the 1-NN rule with a resultant increase in accuracy. For further stabilization of the risk estimate with respect to sample size, 2-NN polarization is suggested. Examples are included. The 2-NN approach is extended to M-class and 2k-NN.