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Tangles: a new paradigm for clusters and types

06/03/2020
by   Reinhard Diestel, et al.
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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 for direct clustering of objects. They offer a precise, quantitative paradigm suited particularly to fuzzy clusters, since they do not require any `hard' assignments of objects to the clusters they collectively form. This is a draft of the introductory chapter of a book I am preparing on the application of tangles in the empirical sciences. The purpose of posting this draft early is to give authors of tangle application papers a generic reference for the basic guiding principles underlying tangle applications outside mathematics, so that in their own papers they can concentrate on the ideas specific to their particular application rather than having to repeat the generic story each time. The text starts with three separate generic introductions to tangles in the natural sciences, in the social sciences, and in data science including machine learning. It then gives a short informal description of the abstract notion of tangles that encompasses all these potential applications.

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