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Rees matrix constructions for clustering of data. (English) Zbl 1233.16021

Summary: This paper continues the investigation of semigroup constructions motivated by applications in data mining [A. V. Kelarev, J. L. Yearwood and M. A. Mammadov, Semigroup Forum 78, No. 2, 293-309 (2009; Zbl 1168.94007)]. 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.

MSC:

16S36 Ordinary and skew polynomial rings and semigroup rings
20M25 Semigroup rings, multiplicative semigroups of rings
68T05 Learning and adaptive systems in artificial intelligence
20M35 Semigroups in automata theory, linguistics, etc.
94B05 Linear codes (general theory)

Citations:

Zbl 1168.94007

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References:

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