Orometric Methods in Bounded Metric Data

Maximilian Stubbemann, Tom Hanika, Gerd Stumme

Abstract: A large amount of data accommodated in knowledge graphs (KG) is metric. For example, the Wikidata KG contains a plenitude of metric facts about geographic entities like cities or celestial objects. In this paper, we propose a novel approach that transfers orometric (topographic) measures to bounded metric spaces. While these methods were originally designed to identify relevant mountain peaks on the surface of the earth, we demonstrate a notion to use them for metric data sets in general. Notably, metric sets of items enclosed in knowledge graphs. Based on this we present a method for identifying outstanding items using the transferred valuations functions isolation and prominence. Building up on this we imagine an item recommendation process. To demonstrate the relevance of the valuations for such processes, we evaluate the usefulness of isolation and prominence empirically in a machine learning setting. In particular, we find structurally relevant items in the geographic population distributions of Germany and France.