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.
Optimization of classifiers for data mining based on combinatorial semigroups
- Authors: Kelarev, Andrei , Yearwood, John , Watters, Paul
- Date: 2011
- Type: Text , Journal article
- Relation: Semigroup Forum Vol. 82, no. 2 (2011), p. 1-10
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- Description: The aim of the present article is to obtain a theoretical result essential for applications of combinatorial semigroups for the design of multiple classification systems in data mining. We consider a novel construction of multiple classification systems, or classifiers, combining several binary classifiers. The construction is based on combinatorial Rees matrix semigroups without any restrictions on the sandwich-matrix. Our main theorem gives a complete description of all optimal classifiers in this novel construction. © 2011 Springer Science+Business Media, LLC.
Internet security applications of Grobner-Shirvov bases
- Authors: Kelarev, Andrei , Yearwood, John , Watters, Paul
- Date: 2010
- Type: Text , Journal article
- Relation: Asian-European Journal of Mathematics Vol. 3, no. 3 (2010), p. 435-442
- Relation: http://purl.org/au-research/grants/arc/DP0211866
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A Grobner-Shirshov Algorithm for Applications in Internet Security
- Authors: Kelarev, Andrei , Yearwood, John , Watters, Paul , Wu, Xinwen , Ma, Liping , Abawajy, Jemal , Pan, L.
- Date: 2011
- Type: Text , Journal article
- Relation: Southeast Asian Bulletin of Mathematics Vol. 35, no. (2011), p. 807-820
- Full Text: false
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- Description: The design of multiple classication and clustering systems for the detection of malware is an important problem in internet security. Grobner-Shirshov bases have been used recently by Dazeley et al. [15] to develop an algorithm for constructions with certain restrictions on the sandwich-matrices. We develop a new Grobner-Shirshov algorithm which applies to a larger variety of constructions based on combinatorial Rees matrix semigroups without any restrictions on the sandwich-matrices.