A polynomial ring construction for the classification of data
- Authors: Kelarev, Andrei , Yearwood, John , Vamplew, Peter
- Date: 2009
- Type: Text , Journal article
- Relation: Bulletin of the Australian Mathematical Society Vol. 79, no. 2 (2009), p. 213-225
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- Description: Drensky and Lakatos (Lecture Notes in Computer Science, 357 (Springer, Berlin, 1989), pp. 181-188) have established a convenient property of certain ideals in polynomial quotient rings, which can now be used to determine error-correcting capabilities of combined multiple classifiers following a standard approach explained in the well-known monograph by Witten and Frank (Data Mining: Practical Machine Learning Tools and Techniques (Elsevier, Amsterdam, 2005)). We strengthen and generalise the result of Drensky and Lakatos by demonstrating that the corresponding nice property remains valid in a much larger variety of constructions and applies to more general types of ideals. Examples show that our theorems do not extend to larger classes of ring constructions and cannot be simplified or generalised.
Optimization and matrix constructions for classification of data
- Authors: Kelarev, Andrei , Yearwood, John , Vamplew, Peter , Abawajy, Jemal , Chowdhury, Morshed
- Date: 2011
- Type: Journal article
- Relation: New Zealand Journal of Mathematics Vol. 41, no. 2011 (2011), p. 65-73
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- Description: Max-plus alegbras and more general semirings have many useful applications and have been actively investigated. On the other hand, structural matrix rings are also well known and have been considered by many authors. The main theorem of this article completely describes all optimal ideas in the more general structural matrix semirings. Originally, our investigation of these ideals was motivated by applications in data mining for the design of multiple classification systems combining several individual classifiers.