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 Sib. Èlektron. Mat. Izv., 2015, Volume 12, Pages 1006–1031 (Mi semr650)

Mathematical logic, algebra and number theory

Formalization of «natural» classification and systematics as fix-points ofpredictions

E. E. Vityaeva, V. V. Martinovichb

a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Novosibirsk State University, Pirogova, 2, 630090, Novosibirsk, Russia

Abstract: Nowadays there exist many approaches to classification and clustering; for instance one can mention those based on compactness and various metrics on feature spaces, based on etalons, on distributions composition partitioning, etc. In contrast to these approaches, the task of “natural” classification is to discover a classification as a law of nature that satisfy some requirements promoted by naturalists. The sense of this law is in the compression of information by extracting the structure of natural objects. We propose a formalization of this law based on fix-points of probabilistic laws of special type. We prove that the probabilistic laws we define solve the problem of statistical ambiguity and thus they enable us to predict without contradictions and to provide consistent fix-points. These fix-points form a “natural” classification. Finally we present the results of a computer experiment on building and recognition of classes of transcription factors binding sites.

Keywords: natural classification, clustering, fix-points, formal notion, building of notions, notions.

 Funding Agency Grant Number Russian Foundation for Basic Research 15-07-03410-a

DOI: https://doi.org/10.17377/semi.2015.12.087

Full text: PDF file (969 kB)
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UDC: 519.7
MSC: 68T37
Received July 21, 2015, published December 24, 2015

Citation: E. E. Vityaev, V. V. Martinovich, “Formalization of «natural» classification and systematics as fix-points ofpredictions”, Sib. Èlektron. Mat. Izv., 12 (2015), 1006–1031

Citation in format AMSBIB
\Bibitem{VitMar15} \by E.~E.~Vityaev, V.~V.~Martinovich \paper Formalization of <<natural>> classification and systematics as fix-points ofpredictions \jour Sib. \Elektron. Mat. Izv. \yr 2015 \vol 12 \pages 1006--1031 \mathnet{http://mi.mathnet.ru/semr650} \crossref{https://doi.org/10.17377/semi.2015.12.087} `