Minkowski-type distances in approximate query searches

In approximate query searching (AQS), the given query point ( q ¯ ′ ) can be seen as a noise ( η ¯ ) corrupted version of one of the points ( q ¯ ) in the existing database X , i.e., q ¯ ′ = q ¯ + η ¯ . Thus deciding on an appropriate distance d that would return the correct match ( q ¯ ) entails that the chosen distance should be aware of the type of distribution of the noise. In this work, we study the suitability of Minkowski-type distances in AQS when the q ¯ is afflicted by both white and coloured noises to different extent. To this end, we employ a simple similarity search based scoring algorithm proposed in François et al. (ESANN 2005, 13th European Symposium on Artificial Neural Networks, Bruges, Belgium, April 27–29, 2005, Proceedings, pp 339–344, 2005). Our study reveals an interesting interplay of the following 3D’s in the quest for an appropriate distance: D imensionality and D omain geometry of the data and the type of noise D istribution and has led us to explore this problem from a basic geometric perspective. Our main contribution herein is the proposal of a novel index called the Relative Contained Volume (RCV) that helps explain the performance of the considered distances.