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## Dualization in lattices given by ordered sets of irreducibles

Theoretical Computer Science. 2017. Vol. Volume 658, Part B. No. 7 January. P. 316-326.

Babin M. A., Kuznetsov S.

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 context). We show that in this case dualization is equivalent to the enumeration of so-called minimal hypotheses. In contrast to usual dualization setting, where a lattice is given by the ordered set of its elements, dualization in this case is shown to be impossible in output polynomial time unless P = NP. However, if the lattice is distributive, dualization is shown to be possible in subexponential time.

Publication based on the results of:

Poelmans J., Kuznetsov S., Ignatov D. I. et al., Expert Systems with Applications 2013 Vol. 40 No. 16 P. 6601-6623

This is the first part of a large survey paper in which we analyze recent literature on Formal Concept Analysis (FCA) and some closely related disciplines using FCA. We collected 1072 papers published between 2003 and 2011 mentioning terms related to Formal Concept Analysis in the title, abstract and keywords. We developed a knowledge browsing ...

Added: October 3, 2013

Kuznetsov S., Makhalova T., , in: CLA 2016: Proceedings of the Thirteenth International Conference on Concept Lattices and Their Applications. CEUR Workshop Proceedings. Vol. 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

Ignatov D. I., Kaminskaya A. Y., Konstantinova N. et al., , in: Proceedings of The 2014 IEEE/WIC/ACM International Joint Conference on Web Intelligence and Intelligent Agent Technology, WI-IAT 2014, 11-14 August 2014 Warsaw, Poland. .: Los Alamitos, Washington, Tokyo: IEEE Computer Society, 2014.. P. 327-335.

This paper discusses the recommender models and methods for crowdsourcing platforms. These models are based on modern methods of data analysis of object-attribute data, such as Formal Concept Analysis and biclustering. In particular, the paper is focused on the solution of two tasks – idea and antagonists recommendation – on the example of crowdsourcing platform ...

Added: June 9, 2014

Kuznetsov S., Poelman J., Elzinga P. et al., Lecture Notes in Computer Science 2012 Vol. 7377 LNAI P. 528-272

In this paper we introduce a novel human-centered data mining software system which was designed to gain intelligence from unstructured textual data. The architecture takes its roots in several case studies which were a collaboration between the Amsterdam-Amstelland Police, GasthuisZusters Antwerpen (GZA) hospitals and KU Leuven. It is currently being implemented by bachelor and master ...

Added: February 7, 2013

CEUR Workshop Proceedings, 2018

Added: November 25, 2018

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

Ignatov D. I., Kaminskaya A. Y., Malioukov A. et al., , in: Proceedings of International Conference on Conceptual Structures 2014. Vol. 8577: Graph-Based Representation and Reasoning.: Springer, 2014.. P. 287-292.

This paper considers a recommender part of the data anal- ysis system for the collaborative platform Witology. It was developed by the joint research team of the National Research University Higher School of Economics and the Witology company. This recommender sys- tem is able to recommend ideas, like-minded users and antagonists at the respective phases ...

Added: June 9, 2014

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., 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

Puppe C. D., Slinko A., Economic Theory 2019 Vol. 67 No. 1 P. 285-318

Condorcet domains are sets of linear orders with the property that, whenever the preferences of all voters of a society belong to this set, their majority relation has no cycles. We observe that, without loss of generality, every such domain can be assumed to be closed in the sense that it contains the majority relation ...

Added: May 18, 2020

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 Proceedings. Vol. 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

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

Poelmans J., Ignatov D. I., Viaene S. undefined. et al., , in: Advances in Data Mining. Applications and Theoretical Aspects. 12th Industrial Conference, ICDM 2012, Berlin, Germany, July 13-20, 2012. Proceedings. Vol. 7377.: Berlin, Heidelberg: Springer, 2012.. P. 273-287.

Formal Concept Analysis (FCA) is an unsupervised clustering technique and many scientific papers are devoted to applying FCA in Information Retrieval (IR) research. We collected 103 papers published between 2003-2009 which mention FCA and information retrieval in the abstract, title or keywords. Using a prototype of our FCA-based toolset CORDIET, we converted the pdf-files containing ...

Added: December 3, 2012

Ignatov D. I., Kaminskaya A. Y., Bezzubtseva A. A. et al., 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 года. Вып. 1.: М.: Национальный открытый университет «ИНТУИТ», 2012.. С. 16-26.

В работе описывается система анализа данных кол
лаборативной платформы компании Witology. Проект находится
в состоянии разработки, поэтому в статье отражены в основном
методологические аспекты и результаты первых экспериментов.
В основу системы положен ряд моделей и методов современного
анализа объектно-признаковых и неструктурированных данных
(текстов), таких как Анализ Формальных Понятий, мультимо
дальная кластеризация, поиск ассоциативных правил и извлече
ние ключевых словосочетаний и слов из текстов. ...

Added: January 30, 2013

Kanovich M., Kuznetsov S., Scedrov A., , in: Logic, Language, Information, and Computation: 26th International Workshop, WoLLIC 2019, Utrecht, The Netherlands, July 2-5, 2019, Proceedings. Vol. 11541: Lecture Notes in Computer Science.: Berlin, Heidelberg: Springer, 2019.. P. 373-391.

Language and relational models, or L-models and R-models, are two natural classes of models for the Lambek calculus. Completeness w.r.t. L-models was proved by Pentus and completeness w.r.t. R-models by Andréka and Mikulás. It is well known that adding both additive conjunction and disjunction together yields incompleteness, because of the distributive law. The product-free Lambek ...

Added: September 4, 2019

Springer, 2015

This book constitutes the refereed proceedings of the 13th International Conference on Formal Concept Analysis, ICFCA 2015, held in Neja, Spain, in June 2015. The 16 revised full papers presented were carefully reviewed and selected from 38 submissions. The topics in this volume cover theoretical aspects of FCA; methods and applications of FCA to different ...

Added: September 10, 2015

Springer, 2014

This book constitutes the proceedings of the 21st International Conference on Conceptual Structures, ICCS 2014, held in Iaşi, Romania, in July 2014. The 17 regular papers and 6 short papers presented in this volume were carefully reviewed and selected from 40 and 10 submissions, respectively. The topics covered are: conceptual structures, knowledge representation, reasoning, conceptual ...

Added: June 9, 2014

Ignatov D. I., Gnatyshak D. V., Kuznetsov S. 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

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

Obiedkov S., Lecture Notes in Computer Science 2012 Vol. 7278 P. 227-243

In this paper, we consider two types of preferences from preference logic and propose their interpretation in terms of formal concept analysis. We are concerned only with preferences between sets of attributes, or, viewed logically, between conjunctions of atomic formulas. We provide inference systems for the two types of preferences and study their relation to ...

Added: January 28, 2013

Poelmans J., Ignatov D. I., Kuznetsov S. et al., Expert Systems with Applications 2013 Vol. 40 No. 16 P. 6538-6560

This is the second part of a large survey paper in which we analyze recent literature on Formal Concept Analysis (FCA) and some closely related disciplines using FCA. We collected 1072 papers published between 2003 and 2011 mentioning terms related to Formal Concept Analysis in the title, abstract and keywords. We developed a knowledge browsing ...

Added: October 3, 2013

Ignatov D. I., Ненова Е. Н., Konstantinov A. V. et al., , in: Artificial Intelligence: Methodology, Systems, and Applications 16th International Conference, AIMSA 2014, Varna, Bulgaria, September 11-13, 2014. Proceedings. Vol. 8722.: Dordrecht, L., Cham, Heidelberg, NY: Springer, 2014.. P. 47-58.

We propose a new approach for Collaborative filtering which is based on Boolean Matrix Factorisation (BMF) and Formal Concept Analysis. In a series of experiments on real data (MovieLens dataset) we compare the approach with an SVD-based one in terms of Mean Average Error (MAE). One of the experimental consequences is that it is enough to ...

Added: October 20, 2014

Ignatov D. I., Kaminskaya A. Y., Bezzubtseva A. A. et al., , in: Перспективные направления исследований в области бизнес-информатики: Материалы XI международной конференции. .: Nizhny Novgorod: Higher School of Economics in Nizhny Novgorod, 2012.. P. 7-17.

In a crowdsourcing project several participants discuss and solve one common problem, propose their ideas, evaluate ideas of each other, etc. We propose the novel instrument CrowDM for analyzing data generated by collaborative platforms. The initial version of the system combines several innovative techniques for structured and unstructured data analysis. Formal Concept Analysis, multimodal clustering ...

Added: December 3, 2012