Nucleus I: Adjunction spectra in recommender systems and descent
This work bridges a large technical gap between two vast research areas, potentially offering new insights for data analysis and theoretical foundations, though it appears incremental as part of a series of earlier efforts.
The paper tackles the problem of linking recommender systems with descent theory in algebraic geometry and topology, revealing a formal connection that emerged unexpectedly from data analysis challenges, leading to a novel solution in category theory.
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.