Geodesic
Modified classification algorithm of $k$-nearest neighbor type
Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 2, pp. 533-548.

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Excessive amount of calculation restricts possibility of using $k$-nearest neighbor classification algorithms. In this paper a new method of estimation of $k$-nearest neighbor type is proposed. It is based on use of blocks of observed data. It is shown that the new estimator converges in probability. Also, the method based on the new estimator provides the same probability of misclassification as the standard algorithm does. But the new method requires much less calculation. 
@article{FPM_2000_6_2_a11,
     author = {D. A. Pavlov and A. P. Serykh},
     title = {Modified classification algorithm of $k$-nearest neighbor type},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {533--548},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2000_6_2_a11/}
}
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D. A. Pavlov; A. P. Serykh. Modified classification algorithm of $k$-nearest neighbor type. Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 2, pp. 533-548. http://geodesic.mathdoc.fr/item/FPM_2000_6_2_a11/