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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).

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