A Branch and Bound Algorithm for Computing k-Nearest Neighbors
Computation of the k-nearest neighbors generally requires a large number of expensive distance computations. The method of branch and bound is implemented in the present algorithm to facilitate rapid calculation of the k-nearest neighbors, by eliminating the necesssity of calculating many distances. Experimental results demonstrate the efficiency of the algorithm. Typically, an average of only 61 distance computations were made to find the nearest neighbor of a test sample among 1000 design samples.
An improved branch and bound algorithm for computing k-nearest neighbors
In 1975 Fukunaga and Narendra proposed an efficient branch and bound algorithm for computing k-nearest neighbors. Their algorithm, after a hierarchical decomposition of the design set into disjoint subsets, employs two rules in order to eliminate the necessity of calculating many distances. This correspondence discusses the applicability of two additional rules for a further reduction of the number of distance computations. Experimental results using samples from bivariate Gaussian and uniform distributions suggest that the number of distance computations required by the modified is typicaly one fourth of that of the Fukunaga-Narendra algorithm.
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