An Adaptive Data Structure for Nearest Neighbors Search in an General Metric Space

We consider the problem of computing nearest neighbors in an arbitrary metric space, particularly a metric space that cannot be easily embedded in R. We present a data structure, the Partition Tree, that can be constructed in O(n logn) time, where n is the size of the set of points to be searched, and has been experimentally shown to have an average query time that is a sublinear function of n (roughly O(log(n)) where 4 ≤ α ≤ 5). Our experiments show that this data structure could have applications in bioinformatics, particularly protein secondary structure prediction, where it can be used for similarity search among short sequences of proteins’ primary structure.