Tangles: a structural approach to artificial intelligence in the empirical sciences (Part I)

TL;DR

This paper introduces tangles as a novel structural method for identifying groups of qualities that co-occur, offering a new approach to clustering and understanding complex data in empirical sciences.

Contribution

It presents tangles as a new, quantitative paradigm for clustering that does not require object assignment, extending graph tangles to broader scientific applications.

Findings

Tangles can identify co-occurring qualities without assigning objects to clusters.

They are particularly suited for fuzzy clusters.

Tangles provide a new structural perspective for data analysis.

Abstract

Traditional clustering identifies groups of objects that share certain qualities. Tangles do the converse: they identify groups of qualities that often occur together. They can thereby discover, relate, and structure types: of behaviour, political views, texts, or viruses. If desired, tangles can also be used as a new method for traditional clustering. They offer a precise, quantitative paradigm suited particularly to fuzzy clusters, since they do not require any assignment of objects to the clusters which these collectively form. This is the first of four parts of a book with the above title. The book explores applications outside mathematics of the notion and theory of tangles generalised from the graph tangles know from graph minor theory.