"Getting Things in Order: An Introduction to the R Package seriation", Hahsler et al 2008:

Seriation [or "ordination"], i.e., finding a suitable linear order for a set of objects given data and a loss or merit function, is a basic problem in data analysis. Caused by the problem's combinatorial nature, it is hard to solve for all but very small sets. Nevertheless, both exact solution methods and heuristics are available.
In this paper we present the package seriation which provides an infrastructure for seriation with R. The infrastructure comprises data structures to represent linear orders as permutation vectors, a wide array of seriation methods using a consistent interface, a method to calculate the value of various loss and merit functions, and several visualization techniques which build on seriation.
To illustrate how easily the package can be applied for a variety of applications, a comprehensive collection of examples is presented.

Have you ever wondered how to sort a list or a folder of files where no strict sorting comparison operator like 'newer than' is quite right? It turns out that it is perfectly possible to loosen the definition of 'sorting' to something more approximate like 'try to minimize how different each item is from the next one'; this approximate or generalized sorting is called 'seriation'. It is obscure (I had never heard of the term until a year ago or so), but highly useful: it works for everything from seriating Egyptian graves by rough burial time to organizing tag entries by topic. Since we now have neural embeddings for just about every modality there is, that means you can seriate anything.

What might you use it for? I use it on Gwern.net (background) to organize the 'similar links' recommendations in a way much smarter than the naive k-NN embedding distance retrieval approach. If you just sort them by 'distance', it is mostly meaningless and produces a jumble (see for example any algorithmic set of recommendations, like YouTube video lists - if I open a cat video, I see cat/anime/Touhou/cat/CS/music/cat/...); if you seriate them, however, suddenly you see clear clusters/topics emerge out of the chaos, and it's easier to skim the list. Because it works so well, and is so simple to implement (simple greedy distance minimization heuristic worked surprisingly well for my use-case, no need for TSP solvers), I initially called it...

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