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Clustering with Stable Pattern Concepts
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. Stable concepts are considered as cluster candidates and the SOFIA algorithm is used to discover the set of stable concepts in linear time. Then an algorithm inspired by a rare itemset mining algorithm is designed to build a clustering with good properties, i.e., high internal cohesion within a cluster and high external separation between the clusters. Some interestingness measures allowing us to choose the best clustering are discussed. Finally the present approach is compared to some other well-known algorithms such as KMeans, DBScan, and Optic.
Publication based on the results of:
In book
Vol. 3911. , CEUR Workshop Proceedings, 2024.
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
Dudyrev E., Couceiro M., Kaytoue M. et al., , in: Second International Joint Conference, CONCEPTS 2025, Cluj-Napoca, Romania, September 8–12, 2025, Proceedings. Conceptual Knowledge Structures. LNCS, volume 15941.: Cham: Springer, 2025. P. 178–194.
Pattern Structures is a framework in FCA allowing objects to have complex descriptions, only requiring that the set of descriptions forms a complete meet-semi-lattice. However, some particular descrip tions or patterns, such as subgraphs and subsequences, do not necessarily ensure that every pair of descriptions has a unique infimum and ask for additional operations, e.g., ...
Added: December 1, 2025
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
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
Parakal E. G., Dudyrev E., Sergei O. Kuznetsov et al., Lecture Notes in Computer Science 2024 Vol. 14914 P. 286–301
This paper proposes an approach and an associated system
based on pattern structures, aimed at the classification of documents
represented as graphs. The representation of documents relies on Abstract
Meaning Representation (AMR) document graphs. Given a set of AMR
document graphs, the system learns characteristic graph patterns, that
can be reused by an aggregate rule classifier to predict the class ...
Added: September 10, 2024
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
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
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
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
Makhalova T., Ilvovsky D., Galitsky B. et al., , in: RAAI 2020 Russian Advances in Artificial Intelligence 2020 Selected Contributions of the "Russian Advances in Artificial Intelligence" Track at RCAI 2020 co-located with 18th Russian Conference on Artificial Intelligence (RCAI 2020)Vol. 2648.: CEUR-WS, 2020. P. 144–156.
Information retrieval (IR) chatbot is a special class of virtual assistants, which is widely used nowadays in customer support services. However, the work of modern IR retrieval systems is limited by simple queries to the database, which does not utilize all the potential of interaction with the user. In this paper we implement an FCA-based ...
Added: September 15, 2020
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
Obiedkov S., Sertkaya B., Zolotukhin D., , in: 32nd International Workshop on Description Logics, DL 2019; Oslo; Norway; 18 June 2019 through 21 June 2019.: CEUR-WS.org, 2019. P. 1–10.
We propose an approach for approximately completing a TBox w.r.t. a fixed model. By asking implication questions to a domain expert, our method approximates the subsumption relationships that hold in expert’s model and enriches the TBox with the newly discovered relationships between a given set of concept names. Our approach is based on Angluin’s exact ...
Added: October 29, 2019
Borchmann D., Hanika T., Obiedkov S., Discrete Applied Mathematics 2020 Vol. 273 P. 30–42
We propose an algorithm for learning the Horn envelope of an arbitrary domain using an expert, or an oracle, capable of answering certain types of queries about this domain. Attribute exploration from formal concept analysis is a procedure that solves this problem, but the number of queries it may ask is exponential in the size ...
Added: October 29, 2019
Obiedkov S., , in: Formal Concept Analysis. ICFCA 2019.: Springer, 2019. P. 32–44.
In this paper, we consider computational problems related to finding implications in an explicitly given formal context or via queries to an oracle. We are concerned with two types of problems: enumerating implications (or association rules) and finding a single implication satisfying certain conditions. We present complexity results for some of these problems and leave ...
Added: October 29, 2019
Springer, 2019.
This book constitutes the proceedings of the 15th International Conference on Formal Concept Analysis, ICFCA 2019, held in Frankfurt am Main, Germany, in June 2019.
The 15 full papers and 5 short papers presented in this volume were carefully reviewed and selected from 36 submissions. The book also contains four invited contributions in full paper length.
The ...
Added: October 29, 2019
Metric Generalization and Modification of Classification Algorithms Based on Formal Concept Analysis
Evgeny Kolmakov, , in: Proceedings of the International Workshop "What can FCA do for Artificial Intelligence?" (FCA4AI at ECAI 2014)Vol. 1257.: Prague: CEUR Workshop Proceedings, 2014. P. 43–50.
Added: December 5, 2018