Journal article
Mathematical models of functional extreme leaning machins: operator-algebraic and free-probabilistic approaches
Aequationes mathematicae, Vol.99(3), pp.949-988
06/2025
DOI: 10.1007/s00010-024-01096-8
Abstract
In this paper, we establish mathematical models for an arbitrarily fixed functional extreme learning machine (FELM). From a FELM M, we construct a direct graph G induced by M, and then define the graph groupoid G of G. Then the graph-groupoid C∗-algebra MG of G generated by G is well-determined. This C∗-algebra MG is realized on a certain Hilbert space HG up to a canonical representation. It means that the FELM M is analyzed in a representation-depending structure in terms of operator algebra theory. By defining a natural free probability on MG, one can have an assessment tool of the operator algebra on MG, too.
Details
- Title: Subtitle
- Mathematical models of functional extreme leaning machins: operator-algebraic and free-probabilistic approaches
- Creators
- Ilwoo Cho - Saint Ambrose UniversityPalle E. T. Jorgensen
- Resource Type
- Journal article
- Publication Details
- Aequationes mathematicae, Vol.99(3), pp.949-988
- DOI
- 10.1007/s00010-024-01096-8
- ISSN
- 0001-9054
- eISSN
- 1420-8903
- Publisher
- Springer
- Language
- English
- Electronic publication date
- 06/24/2024
- Date published
- 06/2025
- Academic Unit
- Mathematics
- Record Identifier
- 9984649959402771
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