L-nearest-neighbour classifier ($L$-NN)

The L-nearest-neighbour classifier estimates each class probability by its empirical frequency among the $L$ nearest training covariates and predicts a class of greatest estimated probability.

One-nearest-neighbour classification assigns a query the label of its single nearest training observation. Under local regularity, its limiting conditional error is $1-{\sum }_k{p}_k(x{)}^2$.