Antipole Tree Indexing to Support Range Search and

Abstract

Range and k-nearest neighbor searching are core problems in pattern recognition, where one is given a database D of objects in a metric space M and a query object q in M , and one wants to nd those objects in D that are similar to q. In range searching one looks for the objects of D within some threshold distance to q. In k-nearest neighbor searching, the k elements of D closest to q must be produced. These problems can obviously be solved with a linear number of distance calculations by comparing the query object against every object in the database. The goal however is to solve the problem much faster. We combine and extend ideas from the M-Tree, the Multi-Vantage Point structure, and the FQ- tree to create a new structure of the isector tree" class called the Antipole Tree. Bisection is based on the proximitytoan"antipole" pair of elements generated by a suitable linear randomized tournament. The nal winners a; b of this tournament are far enough apart to approximate the diameter of the splitting set. If dist(a; b) is larger than the chosen cluster diameter threshold, then the cluster is split. The proposed data structure is an indexing scheme suitable for (exact and approximate) best match searching on generic metric spaces allowing also dynamic insertions. Comparing Antipole Tree with existing structures suchas M-trees and others shows an improvementinmany cases including on secondary memory.