Abstract: The concept of uniqueness can play an important role when the assessment of an observation’s distinctiveness is essential. This article introduces a distance-based uniqueness measure that quantifies the relative rarity or commonness of a multi-variate observation within a dataset. Unique observations exhibit rare combinations of values, and not necessarily extreme values. Taking a cognitive psychological perspective, our measure defines uniqueness as the sum of distances between a target observation and all other observations. After presenting the measure u and its corresponding standardised version uz, we propose a method to calculate a p value through a probability density function. We then demonstrate the measure’s behaviour in a case study on the uniqueness of Greater London boroughs, based on real-world socioeconomic variables. This initial investigation indicates that u can support exploratory data analysis.
Associated publications: Ballatore, Andrea and Cavazzi, Stefano (2023) Why is Greenwich so common? Quantifying the uniqueness of multivariate observations. The 12th International Conference on Geographic Information Science (GIScience), Short Papers, Leeds, UK. (see articles folder)
The uniqueness.Rmd notebook contains the development code and analyis of the uniqueness index.
The core uniqueness functions are in file uniq_functions.R, which can be easily imported.