Geodesic
On decomposition of a binary context without losing formal concepts
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 3, pp. 323-330.

Voir la notice de l'article provenant de la source Math-Net.Ru

The $\#P$-complete problem of finding all the formal concepts of a given context and the decomposition method for its solving are investigated. As parts of the decomposition is proposed to use fragments of the initial context, called boxes. Such decomposition allows to decompose the given context without losing formal concepts and thereby to reduce the execution time of the algorithms for solving considered task. The number of boxes, obtained at each iteration of the decomposition, is determined based on studies of the boxes structure and the rules for stopping of the decomposition process are established.
Keywords: formal concept analysis, decomposition of the binary context. 
@article{JSFU_2019_12_3_a6,
     author = {Choduraa M. Mongush and Valentina V. Bykova},
     title = {On decomposition of a binary context without losing formal concepts},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {323--330},
     publisher = {mathdoc},
     volume = {12},
     number = {3},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2019_12_3_a6/}
}
TY  - JOUR
AU  - Choduraa M. Mongush
AU  - Valentina V. Bykova
TI  - On decomposition of a binary context without losing formal concepts
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2019
SP  - 323
EP  - 330
VL  - 12
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2019_12_3_a6/
LA  - en
ID  - JSFU_2019_12_3_a6
ER  - 
%0 Journal Article
%A Choduraa M. Mongush
%A Valentina V. Bykova
%T On decomposition of a binary context without losing formal concepts
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2019
%P 323-330
%V 12
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2019_12_3_a6/
%G en
%F JSFU_2019_12_3_a6
Choduraa M. Mongush; Valentina V. Bykova. On decomposition of a binary context without losing formal concepts. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 3, pp. 323-330. http://geodesic.mathdoc.fr/item/JSFU_2019_12_3_a6/

[1] A.A. Barseghyan, M.S. Kupriyanov, V.V. Stepanenko, I.I. Kholod, Data Analysis Technology: Data Mining, Visual Mining, Text Mining, OLAP, Piter, St. Peterburg, 2008 (in Russian)

[2] B. Ganter, R. Wille, Formal Concept Analyses: mathematical foundations, Springer Science and Business Media, 2012 | MR

[3] B. Ganter, S.A. Obiedkov, Conceptual Exploration, Springer, Berlin–Heidelberg, 2016 | MR | Zbl

[4] S.O. Kuznetsov, S.A. Obiedkov, “Comparing Performance of Algorithms for Generating Concept Lattices”, Journal of Experimental and Theoretical Artificial Intelligence, 14:2–3 (2002), 189–216 | DOI | Zbl

[5] A.A. Simon, ““Best-of-Breed” approach for designing a fast algorithm for computing fixpoints of Galois Connections”, Information Sciences, 265 (2015), 633–649

[6] V.V. Bykova, Ch.M. Mongush, “On Algebraic Approach of R. Wille and B. Ganter in the Investigation of Texts”, Journal of Siberian Federal University, 10:3 (2017), 372–384 | DOI | MR

[7] V.V. Bykova, “Mathematical methods for analyzing recursive algorithms”, Journal of Siberian Federal University. Mathematics and Physics, 3:1 (2008), 236–246 (in Russian) | MR

[8] E. Harzheim, Ordered Sets, Springer, New York, 2015 | MR