TY - JOUR

T1 - Formalization of «natural» classification and systematics as fix-points ofpredictions

AU - Vityaev, Evgenii Evgen evich

AU - Martinovich, Vitalii Valer evich

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - Building of notions

KW - Clustering

KW - Fix-points

KW - Formal notion

KW - Natural classification

KW - Notions

UR - http://www.scopus.com/inward/record.url?scp=85007481397&partnerID=8YFLogxK

U2 - 10.17377/semi.2015.12.087

DO - 10.17377/semi.2015.12.087

M3 - Article

AN - SCOPUS:85007481397

VL - 12

SP - 1006

EP - 1031

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -