A Sub-Quadratic Exact Medoid Algorithm

TL;DR

This paper introduces trimed, a novel sub-quadratic exact medoid algorithm that efficiently computes medoids in high-dimensional data, significantly reducing distance calculations compared to existing methods.

Contribution

The paper presents trimed, the first sub-quadratic exact medoid algorithm for high-dimensional data, and demonstrates its effectiveness in spatial network analysis and clustering acceleration.

Findings

Expected run time of O(N^{3/2}) in R^d under certain assumptions

Requires two orders of magnitude fewer distance calculations than approximate algorithms

Enables faster K-medoids clustering with minimal quality loss

Abstract

We present a new algorithm, trimed, for obtaining the medoid of a set, that is the element of the set which minimises the mean distance to all other elements. The algorithm is shown to have, under certain assumptions, expected run time O(N^(3/2)) in R^d where N is the set size, making it the first sub-quadratic exact medoid algorithm for d>1. Experiments show that it performs very well on spatial network data, frequently requiring two orders of magnitude fewer distance calculations than state-of-the-art approximate algorithms. As an application, we show how trimed can be used as a component in an accelerated K-medoids algorithm, and then how it can be relaxed to obtain further computational gains with only a minor loss in cluster quality.