A scheme for constructing algorithms for correcting a local perturbation in a finite semimetric

• Published in: Computational mathematics and mathematical physics Vol. 50; no. 7; pp. 1249 - 1259
• Main Author: Gromov, I. A.
• Format: Journal Article
• Language: English
• Published: Dordrecht SP MAIK Nauka/Interperiodica 01.07.2010; Springer Nature B.V
• Subjects: Algorithms; Computational mathematics; Computational Mathematics and Numerical Analysis; Construction; Data mining; Functionals; Information processing; Mathematical analysis; Mathematical models; Mathematics; Mathematics and Statistics; Optimization; Perturbation methods; Preserves; Similarity; Studies; semimetric on a finite set; preprocessing of metric information; similarity of semimetrics; metric recognition algorithms; data mining
• ISSN: 0965-5425; 1555-6662
• DOI: 10.1134/S0965542510070134

A three-step scheme for constructing algorithms for transforming metric information in data mining is proposed and investigated. The correction problem of a local perturbation of a semimetric on a finite set of objects is considered. In the framework of the proposed scheme, algorithms correcting the changes of the distance between a pair of objects by a given quantity that preserve the metric properties are examined. Sufficient conditions under which the correction of semimetrics using the proposed three-step scheme actually completes in two steps and in some special cases even after the first step are obtained. Semimetric similarity functionals are considered, and the correction algorithms are matched to those functionals.