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On Containment of Triclusters Collections Generated by Quantified Box Operators
P. 573–579.
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.
Publication based on the results of:
In book
Birkhauser/Springer, 2017.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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