Centroid sets with largest weight in Munn semirings for data mining applications

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Abawajy, Jemal, Kelarev, Andrei and Zeleznikow, John (2013) Centroid sets with largest weight in Munn semirings for data mining applications. Semigroup Forum, 86 (2). ISSN 0037-1912 (Print) 1432-2137 (Online)

Abstract

Our main results show that Munn semirings over idempotent semifields possess more convenient properties than the Munn rings over fields. First, we describe all centroid sets that can be generated as ideals of the largest weight in Munn semirings over idempotent semifields. Second, we handle the more general case of all onesided ideals too. The multiplication in the Munn semirings is not commutative and the family of arbitrary one-sided ideals is larger than that of two-sided ideals. It is essential to consider all ideals not only in order to develop theoretical foundations, but also since the larger set of ideals may lead to design of classification and clustering systems with better properties. Our main theorem describes all ideals and one-sided ideals with the largest weight in Munn semirings over idempotent semifields.

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Item type Article
URI https://vuir.vu.edu.au/id/eprint/22294
DOI https://doi.org/10.1007/s00233-013-9488-5
Official URL http://link.springer.com/content/pdf/10.1007%2Fs00...
Funders http://purl.org/au-research/grants/arc/DP0880501
Subjects Historical > FOR Classification > 0101 Pure Mathematics
Historical > FOR Classification > 0806 Information Systems
Historical > Faculty/School/Research Centre/Department > College of Business
Keywords algebra, mathematics, classification system, Munn semiring, classifier, clusterer, Rees matrix semigroup
Citations in Scopus 2 - View on Scopus
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