Subspace Tree

Abstract

We are interested in designing a data structure for n objects of dimension d, with the following objectives: Space requirements should be  O(d * n) and the query time should be O(d * log(n)). Such a structure corresponds to subspace trees. A subspace tree divides the distances between the subspaces. It is realized by  the hierarchical linear subspace method. By doing so, the data is divided into disjoint entities. The asymptotic upper bound estimation of the maximum applicable number of subspaces is logarithmically constrained by the number of represented elements and their dimension.The search in such a tree starts at the subspace with the lowest dimension.  In this subspace, the set of all possible similar objects is determined. In the next subspace, additional metric information corresponding to a higher dimension is used to reduce this set.