TY - GEN

T1 - Representation of “Natural” Concepts and Classes by a Hypernet Lattice of (Probabilistic) Formal Concepts

AU - Vityaev, Evgenii

N1 - Funding Information: This work is supported by the RFBR grant #19-01-00331-a. Publisher Copyright: © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021

Y1 - 2021

N2 - In previous works, a probabilistic generalization of formal concepts was developed that is resistant to noise and is capable of restoring formal concepts. In this paper, we show that probabilistic formal concepts have a deeper meaning than the restoration of formal concepts. Probabilistic formal concepts model “natural” concepts explored in cognitive sciences and “natural” classes explored in the “natural” classification. The hyper network of probabilistic formal concepts reflects the hierarchical structure of complex patterns – a hierarchy of secondary, increasingly complex features that are found as a result of deep learning. This hierarchy, obtained by logical-probabilistic methods, in addition to being “natural”, is also explanatory, since it can give descriptions of its classes in logical-probabilistic terms. Thus, the hierarchy of probabilistic formal concepts discovered on complex images yields logical-probabilistic deep learning. The vertices of the hyper simplexes of the hyper network of probabilistic formal concepts reflect the content of “natural” concepts and classes, as they are inextricably linked with the underlying features. These vertices determine the meanings of “natural” concepts and classes, which are not reducible to the features that form them.

AB - In previous works, a probabilistic generalization of formal concepts was developed that is resistant to noise and is capable of restoring formal concepts. In this paper, we show that probabilistic formal concepts have a deeper meaning than the restoration of formal concepts. Probabilistic formal concepts model “natural” concepts explored in cognitive sciences and “natural” classes explored in the “natural” classification. The hyper network of probabilistic formal concepts reflects the hierarchical structure of complex patterns – a hierarchy of secondary, increasingly complex features that are found as a result of deep learning. This hierarchy, obtained by logical-probabilistic methods, in addition to being “natural”, is also explanatory, since it can give descriptions of its classes in logical-probabilistic terms. Thus, the hierarchy of probabilistic formal concepts discovered on complex images yields logical-probabilistic deep learning. The vertices of the hyper simplexes of the hyper network of probabilistic formal concepts reflect the content of “natural” concepts and classes, as they are inextricably linked with the underlying features. These vertices determine the meanings of “natural” concepts and classes, which are not reducible to the features that form them.

KW - Clustering

KW - Concept

KW - Hypernet lattice

KW - Probabilistic formal concept

UR - http://www.scopus.com/inward/record.url?scp=85105884637&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-71637-0_77

DO - 10.1007/978-3-030-71637-0_77

M3 - Conference contribution

AN - SCOPUS:85105884637

SN - 9783030716363

T3 - Advances in Intelligent Systems and Computing

SP - 671

EP - 676

BT - Advances in Cognitive Research, Artificial Intelligence and Neuroinformatics - Proceedings of the 9th International Conference on Cognitive Sciences, Intercognsci-2020

A2 - Velichkovsky, Boris M.

A2 - Balaban, Pavel M.

A2 - Ushakov, Vadim L.

PB - Springer Science and Business Media Deutschland GmbH

T2 - 9th International Conference on Cognitive Sciences, Intercognsci 2020

Y2 - 10 October 2020 through 16 October 2020

ER -