Data structures and algorithms for nearest neighbor search in general metric spaces

Abstract

We consider the computational problem of finding nearest neighbors in general metric spaces. Of particular interest are spaces that may not be conveniently embedded or approximated in Euclidian space, or where the dimensionality of a Euclidian representation 1s very high. Also relevant are high-dimensional Euclidian settings in which the distribution of data is in some sense of lower dimension and embedded in the space. The up-tree (vantage point tree) is introduced in several forms, together‘ with &&ciated algorithms, as an improved method for these difficult search nroblems. Tree construcI tion executes in O(nlog(n i ) time, and search is under certain circumstances and in the imit, O(log(n)) expected time. The theoretical basis for this approach is developed and the results of several experiments are reported. In Euclidian cases, kd-tree performance is compared.