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Next: 4.2 Approximate nearest neighbors Up: 4. Nearest Neighbors Searching Previous: 4. Nearest Neighbors Searching

# 4.1 Definition

Definition : A set P of data points in D-dimensional space is given. Then we define the nearest neighbor to some reference point q (also called query point) to be the point of data set P that has the smallest distance to q (we don't issue the problem of ambiguity at this point).The more general task of finding more than one nearest neighbor is called k nearest neighbors problem. In general, the reference point q is an arbitrarily located point, but it is also possible that q is itself a member of data set P (as illustrated in the figure, where five neighbors to q (excluding self match) are found).