Representative Selection in Non Metric Datasets

TL;DR

This paper introduces $oldsymbol{ ext{ extdelta}- ext{medoids}}$, a novel algorithm for selecting representative samples from non-metric datasets, validated in music and motion analysis with theoretical performance bounds.

Contribution

Proposes $ extdelta$-medoids, an extension of k-medoids tailored for non-metric data, with empirical validation and theoretical analysis.

Findings

$ extdelta$-medoids effectively selects representatives in non-metric data.

The method outperforms traditional clustering approaches in the tested domains.

Theoretical bounds and complexity results are provided for the approach.

Abstract

This paper considers the problem of representative selection: choosing a subset of data points from a dataset that best represents its overall set of elements. This subset needs to inherently reflect the type of information contained in the entire set, while minimizing redundancy. For such purposes, clustering may seem like a natural approach. However, existing clustering methods are not ideally suited for representative selection, especially when dealing with non-metric data, where only a pairwise similarity measure exists. In this paper we propose $\delta$-medoids, a novel approach that can be viewed as an extension to the $k$-medoids algorithm and is specifically suited for sample representative selection from non-metric data. We empirically validate $\delta$-medoids in two domains, namely music analysis and motion analysis. We also show some theoretical bounds on the performance of $\delta$-medoids and the hardness of representative selection in general.