Which Space Partitioning Tree to Use for Search - Summary

Trees like binary-space-partitioning trees, kd-trees, principal axis trees and random projection trees are used to answer the question ”which tree to use for nearest-neighbor search?.” This paper deals with the influence of the vector quantization performance of the trees on the search performance and the margins of the partitions in these trees. Theoretical results show that both factors have an impact on search performance. 1 Nearest-neighbor search The most common techniques for nearest-neighbor search are the search with hierarchical tree indices and search with hash-based indices. Multidimensional binary space-partitioning trees like kd -trees[1] are used very often for nearest neighbor search. The time it takes to find the nearest neighbour in low dimensions is O(log(n)), but with increasing dimensionality the worst case for the search can be every node in every dimension which basically means O(n). Real data has low ”intrinsic” dimensionality. This is why binary spacepartitioning trees in high dimensions are said to perform worse even though there are no scientific results to support this assumption. This paper presents theoretical results which link the search performance of BSP-trees to properties of the data and the tree. In this way individual factors that affect the search performance of the BSP-trees can be dealt with.