Combining methods for searches in nested metric spaces

Abstract

Most search methods in metric spaces assume that the topology of the object collection is reasonably regular. However, there exist nested metric spaces, where objects in the collection can be grouped into clusters or subspaces, in such a way that different dimensions or variables explain the differences between objects inside each subspace. This paper proposes a two levels index to solve search problems in spaces with this topology. The idea is to have a first level with a list of clusters, which are identified and sorted using Sparse Spatial Selection (SSS) and Lists of Clusters techniques, and a second level having an index for each dense cluster, based on pivot selection, using SSS. It is also proposed for future work to adjust the second level indexes through dynamic pivots selection to adapt the pivots according to the searches performed in the database.