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Effective Proximity Retrieval by Ordering Permutations

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Edgar Chávez, Karina Figueroa, and Gonzalo Navarro

We introduce a new probabilistic proximity search algorithm for range and
*K*-nearest neighbor (*K*-NN) searching in both coordinate and metric
spaces. Although there exist solutions for these problems, they boil down to a
linear scan when the space is intrinsically high-dimensional, as is the case in
many pattern recognition tasks. This, for example, renders the *K*-NN
approach to classification rather slow in large databases.
Our novel idea is to predict closeness between elements according to how they
order their distances towards a distinguished set of anchor objects.
Each element in the space sorts the anchor objects from closest to farthest
to it, and the similarity between orders turns out to be an excellent
predictor of the closeness between the corresponding elements.

We present extensive experiments comparing our method against state-of-the-art
exact and approximate techniques, both in synthetic and real, metric and
non-metric databases, measuring both CPU time and distance computations. The
experiments demonstrate that our technique almost always improves upon the
performance of alternative techniques, in some cases by a wide margin.