Rees matrix constructions for clustering of data
- Authors: Kelarev, Andrei , Watters, Paul , Yearwood, John
- Date: 2009
- Type: Journal article
- Relation: Journal of the Australian Mathematical Society Vol. 87, no. 3 (2009), p. 377-393
- Relation: http://purl.org/au-research/grants/arc/DP0211866
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- Description: This paper continues the investigation of semigroup constructions motivated by applications in data mining. We give a complete description of the error-correcting capabilities of a large family of clusterers based on Rees matrix semigroups well known in semigroup theory. This result strengthens and complements previous formulas recently obtained in the literature. Examples show that our theorems do not generalize to other classes of semigroups.
Optimal rees matrix constructions for analysis of data
- Authors: Kelarev, Andrei , Yearwood, John , Zi, Lifang
- Date: 2012
- Type: Text , Journal article
- Relation: Journal of the Australian Mathematical Society Vol. 92, no. 3 (2012), p. 357-366
- Relation: http://purl.org/au-research/grants/arc/LP0990908
- Relation: http://purl.org/au-research/grants/arc/DP0211866
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- Description: Abstract We introduce a new construction involving Rees matrix semigroups and max-plus algebras that is very convenient for generating sets of centroids. We describe completely all optimal sets of centroids for all Rees matrix semigroups without any restrictions on the sandwich matrices. © 2013 Australian Mathematical Publishing Association Inc.
- Description: 2003010862