A data mining application of the incidence semirings
- Authors: Abawajy, Jemal , Kelarev, Andrei , Yearwood, John , Turville, Christopher
- Date: 2013
- Type: Text , Journal article
- Relation: Houston Journal of Mathematics Vol. 39, no. 4 (2013), p. 1083-1093
- Relation: http://purl.org/au-research/grants/arc/LP0990908
- Full Text: false
- Reviewed:
- Description: This paper is devoted to a combinatorial problem for incidence semirings, which can be viewed as sets of polynomials over graphs, where the edges are the unknowns and the coefficients are taken from a semiring. The construction of incidence rings is very well known and has many useful applications. The present article is devoted to a novel application of the more general incidence semirings. Recent research on data mining has motivated the investigation of the sets of centroids that have largest weights in semiring constructions. These sets are valuable for the design of centroid-based classification systems, or classifiers, as well as for the design of multiple classifiers combining several individual classifiers. Our article gives a complete description of all sets of centroids with the largest weight in incidence semirings.
Classification systems based on combinatorial semigroups
- Authors: Abawajy, Jemal , Kelarev, Andrei
- Date: 2013
- Type: Text , Journal article
- Relation: Semigroup forum Vol. 86, no. 3 (2013), p. 603-612
- Full Text: false
- Reviewed:
- Description: The present article continues the investigation of constructions essential for applications of combinatorial semigroups to the design of multiple classification systems in data mining. Our main theorem gives a complete description of all optimal classification systems defined by one-sided ideals in a construction based on combinatorial Rees matrix semigroups. It strengthens and generalizes previous results, which handled the more narrow case of two-sided ideals.
Classification systems based on combinatorial semigroups
- Authors: Abawajy, Jemal , Kelarev, Andrei
- Date: 2013
- Type: Text , Journal article
- Relation: Semigroup Forum Vol. 86, no. 3 (2013), p. 603-612
- Full Text:
- Reviewed:
- Description: The present article continues the investigation of constructions essential for applications of combinatorial semigroups to the design of multiple classification systems in data mining. Our main theorem gives a complete description of all optimal classification systems defined by one-sided ideals in a construction based on combinatorial Rees matrix semigroups. It strengthens and generalizes previous results, which handled the more narrow case of two-sided ideals. © 2012 Springer Science+Business Media New York.
- Description: 2003011021
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
- Reviewed:
- 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.
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
- Full Text: false
- Reviewed:
An algorithm for the optimization of multiple classifers in data mining based on graphs
- Authors: Kelarev, Andrei , Ryan, Joe , Yearwood, John
- Date: 2009
- Type: Text , Journal article
- Relation: The Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 71, no. (2009), p. 65-85
- Full Text: false
- Reviewed:
- Description: This article develops an efficient combinatorial algorithm based on labeled directed graphs and motivated by applications in data mining for designing multiple classifiers. Our method originates from the standard approach described in [37]. It defines a representation of a multiclass classifier in terms of several binary classifiers. We are using labeled graphs to introduce additional structure on the classifier. Representations of this sort are known to have serious advantages. An important property of these representations is their ability to correct errors of individual binary classifiers and produce correct combined output. For every representation like this we develop a combinatorial algorithm with quadratic running time to compute the largest number of errors of individual binary classifiers which can be corrected by the combined multiple classifier. In addition, we consider the question of optimizing the classifiers of this type and find all optimal representations for these multiple classifiers.
- Description: 2003007563