Nucleus I: Adjunction spectra in recommender systems and descent

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 recommen...

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Bibliographic Details
Published in:arXiv.org 2023-10
Main Authors: Pavlovic, Dusko, Hughes, Dominic J D
Format: Article
Language:English
Subjects:
Algebra
Categories
Data analysis
Displays
Linear operators
Operators (mathematics)
Singular value decomposition
Topology
Online Access:Get full text
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Summary: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.
ISSN:2331-8422