Nucleus I: Adjunction spectra in recommender systems and descent
Abstract
Recommender systems build user profiles using concept analysis of usage matrices. The concepts are mined as spectra and form Galois connections. Descent is a general method for spectral decomposition in algebraic geometry and topology which also leads to generalized Galois connections. Both recommender systems and descent theory are vast research areas, separated by a technical gap so large that trying to establish a link would seem foolish. Yet a formal link emerged, all on its own, bottom-up, against authors' intentions and better judgment. Familiar problems of data analysis led to a novel solution in category theory. The present paper arose from a series of earlier efforts to provide a top-down account of these developments.
Keywords
Cite
@article{arxiv.2004.07353,
title = {Nucleus I: Adjunction spectra in recommender systems and descent},
author = {Dusko Pavlovic and Dominic J. D. Hughes},
journal= {arXiv preprint arXiv:2004.07353},
year = {2023}
}
Comments
46 pages, 40 figures. For readability, the previous longer version has now been split into several papers. This is part I