  The k Nearest Neighbors (kNN) method has received much attention in the past
decades, where some theoretical bounds on its performance were identified and
where practical optimizations were proposed for making it work fairly well in
high dimensional spaces and on large datasets. From countless experiments of
the past it became widely accepted that the value of k has a significant impact
on the performance of this method. However, the efficient optimization of this
parameter has not received so much attention in literature. Today, the most
common approach is to cross-validate or bootstrap this value for all values in
question. This approach forces distances to be recomputed many times, even if
efficient methods are used. Hence, estimating the optimal k can become
expensive even on modern systems. Frequently, this circumstance leads to a
sparse manual search of k. In this paper we want to point out that a systematic
and thorough estimation of the parameter k can be performed efficiently. The
discussed approach relies on large matrices, but we want to argue, that in
practice a higher space complexity is often much less of a problem than
repetitive distance computations.
