Similarity Search for Adaptive Ellipsoid Queries Using Spatial Transformation

Similarity retrieval mechanisms should utilize generalized quadratic form distance functions as well as the Euclidean distance function since ellipsoid queries parameters may vary with the user and situation. In this paper, we present the spatial transformation technique that yields a new search method for adaptive ellipsoid queries with quadratic form distance functions. The basic idea is to transform the bounding rectangles in the original space, wherein distance from a query point is measured by quadratic form distance functions, into spatial objects in a new space wherein distance is measured by Euclidean distance functions. Our method significantly reduces CPU cost due to the distance approximation by the spatial transformation; exact distance evaluations are avoided for most of the accessed bounding rectangles in the index structures. We also present the multiple spatial transformation technique as an extension of the spatial transformation technique. The multiple spatial transformation technique adjusts the tree structures to suit typical ellipsoid queries; the search algorithm utilizes the adjusted structure. This technique reduces both page accesses and CPU time for ellipsoid queries. Experiments using various matrices and index structures demonstrate the superiority of the proposed methods.