Reaching near neighbors with far and random proxies

Proximity searching is an algorithmic abstraction covering a large number of applications in areas such as machine learning, statistics, multimedia information retrieval, computer vision and pattern recognition, to name a few. The algorithmic problem consist in preprocessing a set of objects to quickly find the objects near a given query. One of the nicest algorithmic constructions in the proximity searching literature is the Spatial Approximation Tree (SAT), built with the primary design goal of approximating to the query spatially instead of using a divide and conquer approach. A key aspect in building the SAT is the order of insertion of nodes in the tree. In the plain version the nodes are inserted in increasing order of distance to the root, and this order is recursively used in the construction. In this paper we introduce the SAT⁺ which generalizes the SAT by using an arbitrary insertion order. We tested two alternative insertion strategies improving the efficiency of the SAT at searching time.