Optimization and Matrix Constructions for Classification of Data


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New Zealand Journal of Mathematics

Vol. 41, (2011), Pages 55-64

A.V. Kelarev, J.L. Yearwood, P.W. Vamplew

School of Science, Information Technology and Engineering

University of Ballarat, P.O. Box 663,

Ballarat, Victoria 3353, Australia


J. Abawajy, M. Chowdhury

School of Information Technology, Deakin University

221 Burwood Highway, Burwood, Victoria 3125, Australia


Abstract Max-plus algebras and more general semirings have many useful applications and have been actively investigated. On the other hand, structural matrix rings are also well known and have been considered by many authors. The main theorem of this article completely describes all optimal ideals in the more general structural matrix semirings. Originally, our investigation of these ideals was motivated by applications in data mining for the design of centroid-based classification systems, as well as for the design of multiple classification systems combining several individual classifiers.

Keywords matrix constructions, ideals, semirings, optimization system

Classification (MSC2000) 16S50, 40C05, 65F30.

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