# Orometric Methods in Bounded Metric Data

## TL;DR

This paper introduces a novel method that applies orometric measures, originally used for topographic analysis, to bounded metric data in knowledge graphs, enabling the identification of significant items such as geographic entities.

## Contribution

It transfers orometric valuation functions to metric data in knowledge graphs and demonstrates their effectiveness in item ranking and recommendation tasks.

## Key findings

- Effective identification of relevant geographic entities in Wikidata.
- Oromatic measures improve item ranking accuracy in supervised learning.
- Method generalizes topographic analysis to metric data in knowledge graphs.

## Abstract

A large amount of data accommodated in knowledge graphs (KG) is actually metric. For example, the Wikidata KG contains a plenitude of metric facts about geographic entities like cities, chemical compounds 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 inclosed 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 novel valuations for such processes we use item sets from the Wikidata knowledge graph. We then evaluate the usefulness of 'isolation' and 'prominence' empirically in a supervised machine learning setting. In particular, we find structurally relevant items in the geographic population distributions of Germany and France.