• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Book chapter
  • On Containment of Triclusters Collections Generated by Quantified Box Operators
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
June 5, 2026
Neural Network Maps as a Method for Constructing Mathematical Models
Scientists from HSE University–Nizhny Novgorod and the Institute of Physics Belgrade, Serbia, are jointly exploring the application of machine learning techniques and neural networks to the study of nonlinear dynamics. Natalya Stankevich, Leading Research Fellow at the Laboratory of Topological Methods in Dynamics of the Faculty of Informatics, Mathematics, and Computer Science at HSE University–Nizhny Novgorod, spoke to the HSE News Service about this international project.
June 5, 2026
‘In the Age of Technology, It Is Interesting to Look into the Past and Think about What We Can Take from It
Polina Tabakova decided to apply for a Philology degree at HSE in Nizhny Novgorod because she grew up in Mari El and did not want to move far away from the Russian forests. In an interview for the Young Scientists of HSE University project, she spoke about the genre of the campus novel, the existential drama of Kolobok, and a blackout version of Eugene Onegin.
June 5, 2026
HSE Scientists Develop Method to Compress Large Language Models Without Losing Quality
Researchers from the AI and Digital Science Institute at the HSE Faculty of Computer Science have developed a new compression method for large language models such as GPT and LLaMA that reduces their size by 25–36% without additional training or significant loss of accuracy. This is the first approach to use mathematical transformations—specifically, rotations of model weights—to make models more amenable to compression with structured matrices. The study results have been published in ACL Findings 2025. The code is available on GitHub.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

On Containment of Triclusters Collections Generated by Quantified Box Operators

P. 573–579.
Egurnov D., Ignatov D. I., MEPHU NGUIFO E.

Analysis of polyadic data (for example n-ary relations) becomes a popular task nowadays. While several data mining techniques exist for dyadic contexts, their extensions to triadic case are not obvious. In this work, we study development of ideas of Formal Concept Analysis for processing three-dimensional data, namely OAC-triclustering (from Object, Attribute, Condition). We consider several similar methods, study relations between their outputs and organize them in an ordered structure.

Language: English
DOI
Text on another site
Keywords: triclusteringThree-way data miningTriadic Formal Concept AnalysisOAC-triclustering
Publication based on the results of:
Explanation-oriented Methods of  Data Analysis for Semantically Rich Data and Their Applications (2017)

In book

23rd International Symposium on Methodologies for Intelligent Systems - Proceedings
Birkhauser/Springer, 2017.
Similar publications
Triclusters of Close Values for the Analysis of 3D Data
Egurnov D., Ignatov D. I., Automation and Remote Control 2022 Vol. 83 No. 6 P. 894–902
Abstract: The paper deals with the problem of triclustering in multivalued triadic contexts in termsof one multidimensional extension of formal concept analysis; triclustering can be viewed as asearch for dense subtensors in three-dimensional tensors over the field of real numbers. Twomethods are proposed for solving this problem, namely, NOAC—a version of the OACtriclustering method for ...
Added: November 1, 2022
Triclustring Toolbox
Ignatov D. I., Egurnov D., , in: Supplementary Proceedings ICFCA 2019 Conference and WorkshopsVol. 2378.: CEUR Workshop Proceedings, 2019. P. 65–69.
Triclustring Toolbox is a collection of triclustering methods consolidated into a single interface. It provides access to both box- and prime-based OAC (Object-Attribute-Condition) triclustering, Spectral triclustering and features implementations of DataPeeler and Trias. The application also contains algorithms for mining triclusters of similar values: NOAC and Tri-K-Means. Quality of triclusters is measured in terms of ...
Added: October 31, 2019
Multimodal Clustering of Boolean Tensors on MapReduce: Experiments Revisited
Ignatov D. I., Egurnov D., Точилкин Д. С., , in: Supplementary Proceedings ICFCA 2019 Conference and WorkshopsVol. 2378.: CEUR Workshop Proceedings, 2019. P. 137–151.
This paper presents further development of distributed multimodal clustering. We introduce a new version of multimodal clustering algorithm for distributed processing in Apache Hadoop on computer clusters. Its implementation allows a user to conduct clustering on data with modality greater than two. We provide time and space complexity of the algorithm and justify its relevance. ...
Added: October 31, 2019
On closure operators related to maximal tricliques in tripartite hypergraphs
Ignatov D. I., Discrete Applied Mathematics 2018 Vol. 249 P. 74–84
Triadic Formal Concept Analysis (3FCA) was introduced by Lehman and Wille almost two decades ago. Many researchers work in Data Mining and Formal Concept Analysis using the notions of closed sets, Galois and closure operators, and closure systems. However, a proper closure operator for enumeration of triconcepts, i.e. maximal triadic cliques of tripartite hypergraphs, was not introduced. In this ...
Added: December 15, 2017
Mining Triclusters of Similar Values in Triadic Real-Valued Contexts
Egurnov D., Ignatov D. I., MEPHU NGUIFO E., , in: 14th International Conference on Formal Concept Analysis - Supplementary Proceedings.: University Rennes 1, 2017. P. 31–47.
Analysis of polyadic data (for example, multi-way tensors and n-ary relations) becomes more and more popular task nowadays. While several datamining techniques exist for (numeric) dyadic contexts, their extensions to the triadic case are not obvious, if possible at all. In this work, we study development of the ideas of Formal Concept Analysis for processing ...
Added: June 21, 2017
Putting OAC-triclustering on MapReduce
Зудин С., Gnatyshak D. V., Ignatov D. I., , in: Proceedings of the Twelfth International Conference on Concept Lattices and Their Applications Clermont-Ferrand, France, October 13-16, 2015Vol. 1466.: Clermont-Ferrand: CEUR Workshop Proceedings, 2015. P. 47–58.
In our previous work an efficient one-pass online algorithm for triclustering of binary data (triadic formal contexts) was proposed. This algorithm is a modified version of the basic algorithm for OAC-triclustering approach; it has linear time and memory complexities. In this paper we parallelise it via map-reduce framework in order to make it suitable for big datasets. The results of ...
Added: October 23, 2015
Triadic Formal Concept Analysis and triclustering: searching for optimal patterns
Ignatov D. I., Gnatyshak D. V., Sergei O. Kuznetsov et al., Machine Learning 2015 Vol. 101 No. 1 P. 271–302
This paper presents several definitions of “optimal patterns” in triadic data and results of experimental comparison of five triclustering algorithms on real-world and synthetic datasets. The evaluation is carried over such criteria as resource efficiency, noise tolerance and quality scores involving cardinality, density, coverage, and diversity of the patterns. An ideal triadic pattern is a totally dense ...
Added: April 15, 2015
A One-Pass Triclustering Approach: Is There any Room for Big Data?
Gnatyshak D. V., Ignatov D. I., Kuznetsov S. et al., , in: CLA 2014: Proceedings of the Eleventh International Conference on Concept Lattices and Their Applications.: Kosice: Pavol Jozef Safarik University, 2014. P. 231–242.
An efficient one-pass online algorithm for triclustering of binary data (triadic formal contexts) is proposed. This algorithm is a modified version of the basic algorithm for OAC-triclustering approach, but it has linear time and memory complexities with respect to the cardinality of the underlying ternary relation and can be easily parallelized in order to be ...
Added: October 8, 2014
Greedy Modifications of OAC-triclustering Algorithm
Gnatyshak D. V., , in: Procedia Computer Science. 2nd International Conference on Information Technology and Quantitative Management, ITQM 2014. National Research University Higher School of Economics (HSE) in Moscow (Russia) on June 3-5, 2014Vol. 31.: Amsterdam: Elsevier, 2014. P. 1116–1123.
In this paper we propose several possible modifications to the OAC-triclustering algorithms based on the prime operators. This method based on the framework of Formal Concept Analysis showed some rather promising results in the previous research. But while it is fast and ecient with respect to such measures as average density of the output, diversity, ...
Added: September 11, 2014
Визуальная аналитика в задаче трикластеризации данных социальных сетей
Kashnitsky Y., В кн.: Труды Международной конференции по физико-технической информатике CPT-2013, 12-19 мая 2013 г., Ларнака, Республика Кипр.: М., Протвино: Изд-во ИФТИ, 2013. С. 251–258.
Triclustering is an outgrowth of Formal Concept Analysis intented to detect groups of objects with similar properties (clusters) in a context of three sets of entities. In case of social network analysis, for instance, these sets might be users, their interests and events they take part in. Triclustering here can help to detect users with similar ...
Added: January 27, 2014
Визуальная аналитика в задаче трикластеризации многомерных данных
Kashnitsky Y., Труды Московского физико-технического института 2014 Т. 6 № 3 С. 43–56
Triclustering is an outgrowth of Formal Concept Analysis intented to detect groups of objects with similar properties (clusters) in a context of three sets of entities. In case of social network analysis, for instance, these sets might be users, their interests and events they take part in. Triclustering here can help to detect users with ...
Added: November 8, 2013
From Triadic FCA to Triclustering: Experimental Comparison of Some Triclustering Algorithms
Dmitry V. Gnatyshak, Dmitry I. Ignatov, Sergei O. Kuznetsov, , in: CLA 2013 Proceedings of the Tenth International Conference on Concept Lattices and Their Applications.: La Rochelle: Laboratory L3i, University of La Rochelle, 2013. P. 249–260.
In this paper we show the results of the experimental comparison of ve triclustering algorithms on real-world and synthetic data wrt. resource eciency and 4 quality measures. One of the algorithms, the OAC-triclustering based on prime operators, is presented rst time in this paper. Interpretation of results for real-world datasets is provided. ...
Added: October 18, 2013
Can triconcepts become triclusters?
Ignatov D. I., Kuznetsov S., Zhukov L. E. et al., International Journal of General Systems 2013 Vol. 42 No. 6 P. 572–593
formal concept analysis,  data mining,  triclustering,  three-way data,  folksonomy,  spectral triclustering ...
Added: October 16, 2013
Approximate bicluster and tricluster boxes in the analysis of binary data
Mirkin B., Lecture Notes in Computer Science 2011 Vol. 6743 P. 248–256
A disjunctive model of box bicluster and tricluster analysis is considered. A least-squares locally-optimal one cluster method is proposed, oriented towards the analysis of binary data. The method involves a parameter, the scale shift, and is proven to lead to ”contrast” box biand tri-clusters. An experimental study of the method is reported. ...
Added: February 1, 2012
Gaining insight in social networks with biclustering and triclustering
Gnatyshak D. V., Ignatov D. I., Semenov A., Lecture Notes in Business Information Processing 2012 Vol. 128 LNBIP P. 162–171
We combine bi- and triclustering to analyse data collected from the Russian online social network Vkontakte. Using biclustering we extract groups of users with similar interests and find communities of users which belong to similar groups. With triclustering we reveal users' interests as tags and use them to describe Vkontakte groups. After this social tagging ...
Added: February 7, 2013
Метод спектральной трикластеризации для систем совместного пользования ресурсами
Секинаева З. Р., Ignatov D. I., В кн.: Анализ изображений, сетей и текстов. Доклады всероссийской научной конференции АИСТ'12. Модели, алгоритмы и инструменты анализа данных; результаты и возможности для анализа изображений, сетей и текстов. Екатеринбург, 16 – 18 марта 2012 годаВып. 1.: М.: Национальный открытый университет «ИНТУИТ», 2012. С. 246–254.
Статья посвящена разработке метода трикластеризации на основе графовой спектральной кластеризации. В серии экспериментов на реальных данных исследована эффективность и пригодность метода к анализу данных систем совместного пользования ресурсами, т.н. фолксономий ...
Added: January 30, 2013
From Triconcepts to Triclusters
Ignatov D. I., Kuznetsov S., Zhukov L. E., , in: Rough Sets, Fuzzy Sets, Data Mining and Granular Computing: 13th International Conference, RSFDGrC 2011, Moscow, Russia, June 25-27, 2011. ProceedingsVol. 6743.: Berlin, Heidelberg: Springer, 2011. P. 257–264.
A novel approach to triclustering of a three-way binary data is proposed. Tricluster is defined in terms of Triadic Formal Concept Analysis as a dense triset of a binary relation Y , describing relationship between objects, attributes and conditions. This definition is a relaxation of a triconcept notion and makes it possible to find all ...
Added: December 3, 2012
Gaining Insight in Social Networks with Biclustering and Triclustering
Gnatyshak D. V., Ignatov D. I., Semenov A. et al., , in: Perspectives in Business Informatics Research. 11th International Conference, BIR 2012, Nizhny Novgorod, Russia, September 2012 ProceedingsIssue 128.: Berlin, Heidelberg: Springer, 2012. P. 162–171.
We combine bi- and triclustering to analyse data collected from the Russian online social network Vkontakte. Using biclustering we extract groups of users with similar interests and find communities of users which belong to similar groups. With triclustering we reveal users' interests as tags and use them to describe Vkontakte groups. After this social tagging ...
Added: December 3, 2012
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit