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On the Usability of Probably Approximately Correct Implication Bases
P. 72–88.
Borchmann D., Hanika T., Obiedkov S.
We revisit the notion of probably approximately correct implication bases from the literature and present a first formulation in the language of formal concept analysis, with the goal to investigate whether such bases represent a suitable substitute for exact implication bases in practical use cases. To this end, we quantitatively examine the behavior of probably approximately correct implication bases on artificial and real-world data sets and compare their precision and recall with respect to their corresponding exact implication bases. Using a small example, we also provide evidence suggesting that implications from probably approximately correct bases can still represent meaningful knowledge from a given data set.
Publication based on the results of:
In book
Vol. 10308. , Cham: Springer, 2017.
Parkhomenko V., Kulikova S., Buzmakov A. V., Lobachevskii Journal of Mathematics 2026 Vol. 47 No. 6 P. 2979–2992
The stability of formal concepts and its generalization as robustness are considered in the paper. We use an approximation of stability in the form of Δ-measure for fast calculations. A computationally efficient method for calculating robustness based on subcontexts is presented. We also present a new method to analytically evaluate the number of preimages for ...
Added: October 14, 2026
Kanaev E., Southeast Asia: Actual Problems of Development 2026 Vol. 2 No. 2(71) P. 11–22
The author focuses on a strengthening digital component in the evolution of the South China Sea issue in the context of ASEAN’s evolving approach to the deepening contradictions and its policy in the digital field. On outlining ASEAN’s policy on the South China Sea issue, the author proceeds to exploring the digital agenda of ASEAN’s ...
Added: July 30, 2026
Junyu B., Fei H., Huilin F. et al., International Journal of Approximate Reasoning 2025 Vol. 187 Article 109541
In Formal Concept Analysis (FCA), concept reduction serves as an important means of simplification. The application scenarios of concept reduction cover various aspects such as data mining, knowledge discovery, strategic decision-making, and rule learning. For symmetric formal contexts, a specialized class of concept reduction exists that can fully recover all knowledge. However, most existing concept ...
Added: December 1, 2025
Dudyrev E., Mariia Zueva, Kuznetsov S. et al., , in: FCA4AI 2024: The 12th International Workshop "What can FCA do for Artificial Intelligence?", October 19 2024, Santiago de Compostela, SpainVol. 3911.: CEUR Workshop Proceedings, 2024. P. 47–58.
Clustering aims at finding disjoint groups of similar objects in data and is one major task in Machine Learning. It is also gaining more attention in Formal Concept Analysis community in these last years. This paper proposes an original approach to the clustering of complex data based on Formal Concept Analysis (FCA) and Pattern Structures. ...
Added: April 30, 2025
CEUR Workshop Proceedings, 2024.
The eleven preceding editions of the FCA4AI Workshop showed that many researchers working in Articial Intelligence are deeply interested in a well-founded method for classication and data mining such as Formal Concept Analysis (see https://upriss.github.io/fca/fca.html).
The FCA4AI Workshop Series started with ECAI 2012 (Montpellier) and the last edition was co-located with IJCAI 2023 (Macao, China). The ...
Added: April 29, 2025
Kanaev E., Garaeva A., Fedorenko D. O., , in: Cooperation in Asia-Pacific: Transition to a New World Order.: M.: IOS RAS, 2025. P. 8–10.
The chapter discusses the implications of the US-China technological rivalry for ASEAN and its digital projects. ...
Added: April 5, 2025
Dudyrev E., Kuznetsov S., Napoli A., , in: FCA4AI 2023 What can FCA do for Artificial Intelligence 2023 Proceedings of the 11th International Workshop "What can FCA do for Artificial Intelligence?" co-located with the 32nd International Joint Conference on Artificial Intelligence (IJCAI 2023) Macao, S.A.R. China; August 20, 2023Vol. 3489.: CEUR-WS.org, 2023. P. 69–80.
Rule Learning and Formal Concept Analysis (FCA) are two fields of science that study similar topic yet speak in a very different terms. This paper describes rule-based machine learning models with FCA-based terminology which results in decision quiver model. A decision quiver, discussed in the paper, is a supervised machine learning model that is based ...
Added: October 4, 2023
Dudyrev E., Kuznetsov S., Napoli A., , in: 17th International Conference, ICFCA 2023, Kassel, Germany, July 17–21, 2023, Proceedings. Formal Concept Analysis, (LNCS, volume 13934).: Switzerland: Springer, 2023. P. 127–142.
In this paper we introduce and study description quivers as compact representations of concept lattices and respective ensembles of decision trees. Formally, description quivers are directed multigraphs where vertices represent concept intents and (multiple) edges represent generators of intents. We study some properties of description quivers and shed light on their use for describing state-of-the-art symbolic machine ...
Added: October 4, 2023
Kanaev E., Luzyanin S., , in: The global reset: insights from regions.: M.: Advanced Solutions, 2022. P. 4–11.
The chapter points out salient features of the present-day globalization and outlines major changes that have been generated by the policies of Asia-Pacific economic actors. ...
Added: June 11, 2023
Kanaev E., Terskikh M., , in: The global reset: insights from regions.: M.: Advanced Solutions, 2022.
The chapter analyses Russia’s position on the Indo-Pacifi c region, its perception in the Russian expert and political communities, as well as its impact on Russia’s interests. The paper offers insights into Russia’s expert assessments of the Indo-Pacifi c region, presents mainstream points of view from a political and security perspective. The authors trace Russia’s ...
Added: June 11, 2023
terskikh M., , in: The global reset: insights from regions.: M.: Advanced Solutions, 2022. P. 88–97.
The chapter analyses Russia’s position on the Indo-Pacifi c region, its perception in the Russian expert and political communities, as well as its impact on Russia’s interests. The paper offers insights into Russia’s expert assessments of the Indo-Pacifi c region, presents mainstream points of view from a political and security perspective. The authors trace Russia’s ...
Added: June 11, 2023
Egurnov D., Точилкин Д. С., Ignatov D. I., , in: Complex Data Analytics with Formal Concept Analysis.: Springer, 2022. P. 239–258.
In this paper, we describe versions of triclustering algorithms adapted for efficient calculations in distributed environments with MapReduce model or parallelisation mechanism provided by modern programming languages. OAC-family of triclustering algorithms shows good parallelisation capabilities due to the independent processing of triples of a triadic formal context. We provide time and space complexity of the ...
Added: November 1, 2022
Springer, 2022.
FCA is an important formalism that is associated with a variety of research areas such as lattice theory, knowledge representation, data mining, machine learning, and semantic Web. It is successfully exploited in an increasing number of application domains such as software engineering, information retrieval, social network analysis, and bioinformatics. Its mathematical power comes from its concept ...
Added: November 1, 2022
Galitsky B., Ilvovsky D., Goncharova E., , in: Proceedings of the 10th International Workshop "What can FCA do for Artificial Intelligence?"Vol. 3233.: CEUR Workshop Proceedings, 2022. P. 75–87.
Supported decision trees that have been first proposed to boost the performance and the explainability of the expert systems built upon the texts can become a great basis for the machine reading comprehension (MRC) systems. The supported decision tree is based on building and combining the corresponding discourse trees for the text passage. In this work, ...
Added: November 1, 2022
Dudyrev E., Kuznetsov S., , in: Proceedings of the 10th International Workshop "What can FCA do for Artificial Intelligence?"Vol. 3233.: CEUR Workshop Proceedings, 2022. P. 23–34.
Studies on Explainable Artificial Intelligence show that a model should be small in order to be human understandable. The restriction on the size of a model drastically reduces the space of possible solutions. Many rule learning models still rely on greedy algorithms for generating ensembles of decision trees. This paper discusses FCA-inspired mathematical and engineering ...
Added: November 1, 2022
Bansal S., Kailasam S., Obiedkov S., , in: Formal Concept Analysis: 16th International Conference, ICFCA 2021, Strasbourg, France, June 29 – July 2, 2021, Proceedings.: Springer, 2021. P. 107–122.
We adapt a polynomial-time approximation algorithm for computing the canonical basis of implications to approximately compute frequent implications, also known as exact association rules. To this end, we define a suitable notion of approximation that takes into account the frequency of attribute subsets and show that our algorithm achieves a desired approximation with high probability. ...
Added: December 9, 2021
Dudyrev E., Kuznetsov S., , in: Proceedings of the 9th International Workshop "What can FCA do for Artificial Intelligence?" (FCA4AI 2021)Vol. 2972.: CEUR-WS, 2021. Ch. 9 P. 99–104.
Ensembles of decision trees, like Random Forests are efficient machine learning models with state-of-the-art prediction quality. However, their predictions are much less transparent than those of a single decision tree. In this paper, we describe a prediction model based on a single decision tree in terms of Formal Concept Analysis. We define a differential way ...
Added: December 8, 2021
Buzmakov A. V., Kuznetsov S., Makhalova T. et al., , in: Proceedings of the 9th International Workshop "What can FCA do for Artificial Intelligence?" (FCA4AI 2021)Vol. 2972.: CEUR-WS, 2021. Ch. 2 P. 19–26.
Added: December 7, 2021
Goncharova E., Ilvovsky D., Galitsky B., , in: Proceedings of the 9th International Workshop "What can FCA do for Artificial Intelligence?" (FCA4AI 2021)Vol. 2972.: CEUR-WS, 2021. P. 51–58.
Added: October 28, 2021
Springer, 2021.
This book constitutes the proceedings of the 16th International Conference on Formal Concept Analysis, ICFCA 2021, held in Strasbourg, France, in June/July 2021.
The 14 full papers and 5 short papers presented in this volume were carefully reviewed and selected from 32 submissions. The book also contains four invited contributions in full paper length.
The research part ...
Added: July 10, 2021
Belfodil A., Kuznetsov S., Kaytoue M., International Journal of General Systems 2020 Vol. 49 No. 8 P. 785–818
Order and lattice theory provides convenient mathematical tools for pattern mining, in particular for condensed irredundant representations of pattern spaces and their efficient generation. Formal Concept Analysis (FCA) offers a generic framework, called pattern structures, to formalize many types of patterns, such as itemsets, intervals, graphs, and sequence sets. Moreover, FCA provides generic algorithms to generate irredundantly all ...
Added: January 25, 2021
Yarullin R., Obiedkov S., International Journal of Approximate Reasoning 2020 Vol. 127 P. 1–16
In Angluin's exact-learning framework, equivalence queries can be simulated by stochastic equivalence testing to achieve a probably approximately correct identification of an unknown concept. We present an analysis of the number of samples that need to be generated in the process leading to a theoretical improvement on an earlier approach. We apply this modification to ...
Added: October 6, 2020