Fast median search in metric spaces

Abstract

Searching for a median of a set of patterns is a well-known technique to model the set or to aid searching for more accurate models such as a generalized median or a k-median. While medians and generalized medians are (relatively) easy to compute in the case of Euclidean representation spaces, this is no longer true when more complex distance measures are to be used. In these cases, a direct method to perform median search is not feasible for large sets of patterns. To cope with this computational problem, we proposed a technique which is significantly faster than the direct approach, both in terms of distance computations and overhead (time not alloted to distance computing). We also proposed another technique which is even faster than its predecessor in terms of distance computations, though it involves significantly more overhead. In this paper we introduce a generalized algorithm for fast median search which includes these two techniques as particular cases. We also develop a new particular case of this generalized algorithm.