Towards Ordinal Data Science

TL;DR

This paper advocates for the development of Ordinal Data Science, emphasizing the importance of order-based methods in data analysis and proposing new computational approaches for ordinal structures like directed graphs.

Contribution

It introduces the concept of Ordinal Data Science, discusses methods for measuring and computing with ordinal structures, and aims to establish it as a new research field.

Findings

Proposes new methods for ordinal computations

Shows how to infer knowledge from ordinal structures

Highlights interdisciplinary applications of ordinal data analysis

Abstract

Order is one of the main instruments to measure the relationship between objects in (empirical) data. However, compared to methods that use numerical properties of objects, the amount of ordinal methods developed is rather small. One reason for this is the limited availability of computational resources in the last century that would have been required for ordinal computations. Another reason -- particularly important for this line of research -- is that order-based methods are often seen as too mathematically rigorous for applying them to real-world data. In this paper, we will therefore discuss different means for measuring and 'calculating' with ordinal structures -- a specific class of directed graphs -- and show how to infer knowledge from them. Our aim is to establish Ordinal Data Science as a fundamentally new research agenda. Besides cross-fertilization with other cornerstone machine learning and knowledge representation methods, a broad range of disciplines will benefit from this endeavor, including, psychology, sociology, economics, web science, knowledge engineering, scientometrics.