Nick Harris

Matthew Pugh, Jo Grundy, Corina Cirstea et al.

This paper is the first to construct and motivate a Machine Learning algorithm solely with Enriched Category Theory, supplementing evidence that Category Theory can provide valuable insights into the construction and explainability of Machine Learning algorithms. It is shown that a series of reasonable assumptions about a dataset lead to the construction of the Nearest Neighbours Algorithm. This construction is produced as an extension of the original dataset using profunctors in the category of Lawvere metric spaces, leading to a definition of an Enriched Nearest Neighbours Algorithm, which, consequently, also produces an enriched form of the Voronoi diagram. Further investigation of the generalisations this construction induces demonstrates how the $k$ Nearest Neighbours Algorithm may also be produced. Moreover, how the new construction allows metrics on the classification labels to inform the outputs of the Enriched Nearest Neighbour Algorithm: Enabling soft classification boundaries and dependent classifications. This paper is intended to be accessible without any knowledge of Category Theory.

Matthew Pugh, Jo Grundy, Corina Cirstea et al.

Previous work has demonstrated that efficient algorithms exist for computing Kan extensions and that some Kan extensions have interesting similarities to various machine learning algorithms. This paper closes the gap by proving that all error minimisation algorithms may be presented as a Kan extension. This result provides a foundation for future work to investigate the optimisation of machine learning algorithms through their presentation as Kan extensions. A corollary of this representation of error-minimising algorithms is a presentation of error from the perspective of lossy and lossless transformations of data.