Comparison-based centrality measures

Recently, learning only from ordinal information of the type “itemxis closer to itemythan to itemz” has received increasing attention in the machine learning community. Such triplet comparisons are particularly well suited for learning from crowdsourced human intelligence tasks, in which workers make statements about the relative distances in a triplet of items. In this paper, we systematically investigate comparison-based centrality measures on triplets and theoretically analyze their underlying Euclidean notion of centrality. Two such measures already appear in the literature under opposing approaches, and we propose a third measure, which is a natural compromise between these two. We further discuss their relation to statistical depth functions, which comprise desirable properties for centrality measures, and conclude with experiments on real and synthetic datasets for medoid estimation and outlier detection.