yearwood-optimizationofmatrix-2011.pdf (178.29 kB)
Optimization of matrix semirings for classification systems
journal contribution
posted on 2011-12-01, 00:00 authored by D Y Gao, A V Kelarev, John YearwoodJohn YearwoodThe max-plus algebra is well known and has useful applications in the investigation of discrete event systems and affine equations. Structural matrix rings have been considered by many authors too. This article introduces more general structural matrix semirings, which include all matrix semirings over the max-plus algebra. We investigate properties of ideals in this construction motivated by applications to the design of centroid-based classification systems, or classifiers, as well as multiple classifiers combining several initial classifiers. The first main theorem of this paper shows that structural matrix semirings possess convenient visible generating sets for ideals. Our second main theorem uses two special sets to determine the weights of all ideals and describe all matrix ideals with the largest possible weight, which are optimal for the design of classification systems.
History
Journal
Bulletin of the Australian mathematical societyVolume
84Issue
3Pagination
492 - 503Publisher
Cambridge University PressLocation
Cambridge, Eng.Publisher DOI
ISSN
0004-9727eISSN
1755-1633Language
engPublication classification
C1.1 Refereed article in a scholarly journalCopyright notice
2011, Australian Mathematical Publishing Association Inc.Usage metrics
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