Optimal distance bounds for the Mahalanobis distance

Abstract

The Mahalanobis distance, or quadratic form distance, is a distance measure commonly used for feature-based similarity search in scenarios where features are correlated. For efficient query processing on such data effective distance-based spatial pruning techniques are required. In this work we investigate such pruning techniques by means of distance bounds of the Mahalanobis distance in the presence of rectangular spatial approximations. Specifically we discuss how to transform the problem of computing minimum and maximum distance approximations between two minimum bounding rectangles (MBRs) into a quadratic optimization problem. Furthermore, we show how the recently developed concept of spatial domination can be solved under the Mahalanobis distance by a quadratic programming approach. © 2013 Springer-Verlag.