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Approximate clusters, biclusters and n-clusters in the analysis of binary and general data matrices
P. 7–8.
Аpproximate cluster structures are those of formal concepts and n-concepts with added numerical intensity weights. The talk presents theoretical results and computational methods for approximate clustering and n-clustering as extensions of the algebraic-geometrical properties of numerical matrices (SVD and the like) to the situations where one or most of elements of the solutions to be found are expressed by binary vectors. The theory embraces such methods as k-means, consensus clustering, network clustering, biclusters and triclusters and provides natural data analysis criteria, effective algorithms and interpretation tools.
Language:
English
In book
Vol. 1624. , M.: Higher School of Economics, National Research University, 2016.
Ignatov D. I., , in: 11th International Conference, AIST 2023, Yerevan, Armenia, September 28–30, 2023, Revised Selected Papers. Analysis of Images, Social Networks and Texts. Lecture Notes in Computer Science (LNCS, volume 14486).: Cham: Springer, 2024. P. 349 – 361.
This paper dates back to the asymptotic solutions of Rota’s problem on the size of maximum antichain in the set partition lattice by Canfield and Harper and others. The knowledge of asymptotic coefficients could pave the way to the asymptotic solutions of such problems as (maximal) antichain counting in partition lattices. In addition to our ...
Added: January 23, 2026
Ignatov D. I., Khvorykh G., Khrunin A. et al., , in: Recent Trends in Analysis of Images, Social Networks and Texts. 9th International Conference, AIST 2020, Skolkovo, Moscow, Russia, October 15–16, 2020 Revised Supplementary ProceedingsVol. 12602.: Springer, 2021. P. 185–204.
© 2021, Springer Nature Switzerland AG.Missing genotypes can affect the efficacy of machine learning approaches to identify the risk genetic variants of common diseases and traits. The problem occurs when genotypic data are collected from different experiments with different DNA microarrays, each being characterised by its pattern of uncalled (missing) genotypes. This can prevent the ...
Added: November 1, 2022
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
CEUR-WS.org, 2020.
The CLA conference is an international forum for researchers, practitioners and students dedicated to the practice of Formal Concept Analysis (FCA) and areas closely related to it, including data analysis and mining, information retrieval, knowledge management, knowledge engineering, logic, algebra and lattice theory.
The 15th of CLA, CLA 2020, was going to be held in Tallinn, Estonia ...
Added: October 30, 2020
CEUR Workshop Proceedings, 2018.
Added: November 25, 2018
Ignatov D. I., Semenov A., Комиссарова Д. В. et al., , in: Formal Concept Analysis of Social Networks.: Springer, 2017. Ch. 4 P. 59–96.
Multimodal clustering is an unsupervised technique for mining interesting patterns in n-ary relations or n-mode networks. Among different types of such generalised patterns one can find biclusters and formal concepts (maximal bicliques) for two-mode case, triclusters and triconcepts for three-mode case, closed n-sets for n-mode case, etc. Object-attribute biclustering (OA-biclustering) for mining large binary datatables (formal contexts or two-mode ...
Added: December 17, 2017
Masyutin A., Kashnitsky Y., , in: Foundations of Intelligent Systems.: Warsz.: Springer, 2017. P. 664–673.
The cornerstone of retail banking risk management is the estimation of the expected losses when granting a loan to the borrower. The key driver for loss estimation is probability of default (PD) of the borrower. Assessing PD lies in the area of classification problem. In this paper we apply FCA query-based classification techniques to Kaggle ...
Added: July 6, 2017
University Rennes 1, 2017.
This volume is the supplementary volume of the 14th International Conference on Formal Concept Analysis (ICFCA 2017), held from June 13th to 16th 2017, at IRISA, Rennes. The ICFCA conference series is one of the major venues for researches from the field of Formal Concept Analysis and related areas to present and discuss their recent ...
Added: June 19, 2017
Babin M. A., Kuznetsov S., Theoretical Computer Science 2017 Vol. Volume 658, Part B No. 7 January P. 316–326
Dualization of a monotone Boolean function on a finite lattice can be represented by transforming the set of its minimal 1 values to the set of its maximal 0 values. In this paper we consider finite lattices given by ordered sets of their meet and join irreducibles (i.e., as a concept lattice of a formal ...
Added: February 9, 2017
Бочаров А. А., Gnatyshak D. V., Ignatov D. I. et al., , in: CLA 2016: Proceedings of the Thirteenth International Conference on Concept Lattices and Their Applications. CEUR Workshop ProceedingsVol. 1624.: M.: Higher School of Economics, National Research University, 2016. P. 45–56.
We propose a new algorithm for consensus clustering, FCA-Consensus, based on Formal Concept Analysis. As the input, the algorithm takes T partitions of a certain set of objects obtained by k-means algorithm after T runs from different initialisations. The resulting consensus partition is extracted from an antichain of the concept lattice built on a formal ...
Added: October 24, 2016
Kuznetsov S., Makhalova T., , in: CLA 2016: Proceedings of the Thirteenth International Conference on Concept Lattices and Their Applications. CEUR Workshop ProceedingsVol. 1624.: M.: Higher School of Economics, National Research University, 2016. P. 245–253.
Triadic concept analysis has become a popular research direction, since triadic relations give natural models of many data collections. In this paper we address the problem of selecting most interesting concepts by proposing triadic stability indices ...
Added: October 11, 2016
Kashnitsky Y., Kuznetsov S., , in: Proceedings of the International Workshop "What can FCA do for Artificial Intelligence?" (FCA4AI at ECAI 2016).: M.: [б.и.], 2016. P. 105–112.
Decision tree learning is one of the most popular classifica- tion techniques. However, by its nature it is a greedy approach to finding a classification hypothesis that optimizes some information-based crite- rion. It is very fast but may lead to finding suboptimal classification hy- potheses. Moreover, in spite of decision trees being easily interpretable, ensembles ...
Added: October 6, 2016
M.: [б.и.], 2016.
The four preceding editions of the FCA4AI Workshop showed that many researchers working in Artificial Intelligence are deeply interested by a well-founded method for classi- fication and mining such as Formal Concept Analysis (see http://www.fca4ai.hse.ru/). The first edition of FCA4AI was co-located with ECAI 2012 in Montpellier, the second one with IJCAI 2013 in Beijing, ...
Added: October 6, 2016
Kashnitsky Y., Kuznetsov S., , in: CLA 2016: Proceedings of the Thirteenth International Conference on Concept Lattices and Their Applications. CEUR Workshop ProceedingsVol. 1624.: M.: Higher School of Economics, National Research University, 2016. Ch. 19 P. 189–202.
Nowadays decision tree learning is one of the most popular classification and regression techniques. Though decision trees are not accurate on their own, they make very good base learners for advanced tree-based methods such as random forests and gradient boosted trees. However, applying ensembles of trees deteriorates interpretability of the final model. Another problem is ...
Added: October 6, 2016
M.: Higher School of Economics, National Research University, 2016.
The 13th International Conference on “Concept Lattices and Applications (CLA 2016)” was held at National Research University Higher School of Economics, Moscow, Russia from July 18 until July 22, 2016. The CLA conference, organized since 2002, aims to provide to everyone interested in Formal Concept Analysis and more generally in Concept Lattices or Galois Lattices, ...
Added: October 6, 2016
Kashnitsky Y., , in: Supplementary Proceedings of the 5th International Conference on Analysis of Images, Social Networks and Texts (AIST-SUP 2016), Yekaterinburg, Russia, April 7-9, 2016.Vol. 1710.: Aachen: CEUR Workshop Proceedings, 2016. Ch. 8 P. 73–84.
In this paper, we address machine learning classification problem and classify each test instance with a set of interpretable and accurate rules. We resort to the idea of lazy classification and mathematical apparatus of formal concept analysis to develop an abstract framework for this task.
In a set of benchmarking experiments, we compare the proposed ...
Added: October 6, 2016
Greene G., Dunaiski M., Fischer B. et al., , in: RuZA 2015 Workshop. Proceedings of Russian and South African Workshop on Knowledge Discovery Techniques Based on Formal Concept Analysis (RuZA 2015). November 30 - December 5, 2015, Stellenbosch, South AfricaVol. 1552.: Aachen: CEUR Workshop Proceedings, 2015. P. 10–22.
In order to find research on a specific topic or to get an overview of the topics that are published at different academic venues, academics need to browse data from existing academic publications. The title and abstract of publications contains useful key-phrases indicating the topic of the publication, but these need to be directly extracted ...
Added: June 14, 2016
Neznanov A., Parinov A., , in: RuZA 2015 Workshop. Proceedings of Russian and South African Workshop on Knowledge Discovery Techniques Based on Formal Concept Analysis (RuZA 2015). November 30 - December 5, 2015, Stellenbosch, South AfricaVol. 1552.: Aachen: CEUR Workshop Proceedings, 2015.
The speed of full-text search directly affects the process of text analysis. Search engine creates a text index, which is used for fast full-text search. Solr and ElasticSearch are two popular search engines. A text analysis system requires fast implementing searching and indexing at the same time. This paper describes preprocessing workflow of the analysis ...
Added: June 14, 2016
Neznanov A., Kourie D. G., , in: RuZA 2015 Workshop. Proceedings of Russian and South African Workshop on Knowledge Discovery Techniques Based on Formal Concept Analysis (RuZA 2015). November 30 - December 5, 2015, Stellenbosch, South AfricaVol. 1552.: Aachen: CEUR Workshop Proceedings, 2015.
Formal Concept Analysis Research Toolbox (FCART) is an integrated environment for knowledge and data engineers with a set of research tools based on Formal Concept Analysis (FCA). In the paper we consider main FCA workflow and some applications in the field of the text pattern matching. ...
Added: June 14, 2016
Kashnitsky Y., Ignatov D. I., Интеллектуальные системы. Теория и приложения 2015 Т. 19 № 4 С. 37–55
The paper makes a brief introduction into multiple classifier systems and describes a particular algorithm which improves classification accuracy by making a recommendation of an algorithm to an object. This recommendation is done under a hypothesis that a classifier is likely to predict the label of the object correctly if it has correctly classified its ...
Added: December 7, 2015
Ignatov D. I., Корнилов Д. И., , in: Proceedings of the International Workshop "What can FCA do for Artificial Intelligence?" (FCA4AI at IJCAI 2015).: Buenos Aires: [б.и.], 2015. P. 87–98.
We propose a new algorithm for recommender systems with numeric ratings which is based on Pattern Structures (RAPS). As the input the algorithm takes rating matrix, e.g., such that it contains movies rated by users. For a target user, the algorithm returns a rated list of items (movies) based on its previous ratings and ratings ...
Added: October 23, 2015