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
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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Cayley graphs as classifiers for data mining : The influence of asymmetries
- Authors: Kelarev, Andrei , Ryan, Joe , Yearwood, John
- Date: 2009
- Type: Text , Journal article
- Relation: Discrete Mathematics Vol. 309, no. 17 (2009), p. 5360-5369
- Relation: http://purl.org/au-research/grants/arc/DP0211866
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- Description: The endomorphism monoids of graphs have been actively investigated. They are convenient tools expressing asymmetries of the graphs. One of the most important classes of graphs considered in this framework is that of Cayley graphs. Our paper proposes a new method of using Cayley graphs for classification of data. We give a survey of recent results devoted to the Cayley graphs also involving their endomorphism monoids. © 2008 Elsevier B.V. All rights reserved.
Optimization methods and the k-committees algorithm for clustering of sequence data
- Authors: Yearwood, John , Bagirov, Adil , Kelarev, Andrei
- Date: 2009
- Type: Text , Journal article
- Relation: Applied and Computational Mathematics Vol. 8, no. 1 (2009), p. 92-101
- Relation: http://purl.org/au-research/grants/arc/DP0211866
- Relation: http://purl.org/au-research/grants/arc/DP0666061
- Full Text: false
- Description: The present paper is devoted to new algorithms for unsupervised clustering based on the optimization approaches due to [2], [3] and [4]. We consider a novel situation, where the datasets consist of nucleotide or protein sequences and rather sophisticated biologically significant alignment scores have to be used as a measure of distance. Sequences of this kind cannot be regarded as points in a finite dimensional space. Besides, the alignment scores do not satisfy properties of Minkowski metrics. Nevertheless the optimization approaches have made it possible to introduce a new k-committees algorithm and compare its performance with previous algorithms for two datasets. Our experimental results show that the k-committees algorithms achieves intermediate accuracy for a dataset of ITS sequences, and it can perform better than the discrete k-means and Nearest Neighbour algorithms for certain datasets. All three algorithms achieve good agreement with clusters published in the biological literature before and can be used to obtain biologically significant clusterings.
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.