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## Is Concept Stability a Measure for Pattern Selection?

Procedia Computer Science. 2014. Vol. 31. P. 918-927.

There is a lot of usefulness measures of patterns in data mining. This paper is focused on the measures used in Formal Concept Analysis (FCA). In particular, concept stability is a popular relevancy measure in FCA. Experimental results of this paper show that high stability of a pattern in a given dataset derived from the general population suggests that the stability of that pattern is high in another dataset derived from the same population. At the second part of the paper, a new estimate of stability is introduced and studied. It es performance is evaluated experimentally. And it is shown that it is more efficient.

СПб. : Издательский дом Федоровой Г.В., 2015

Proceedings of the III International Conference in memory of V.I. Zubov "Stability and Control Processes (SCP 2015)". ...

Added: October 14, 2015

Alam M., Buzmakov A. V., Napoli A., Discrete Applied Mathematics 2018 Vol. 249 P. 2-17

With an increased interest in machine processable data and with the progress of semantic technologies, many datasets are now published in the form of RDF triples for constituting the so-called Web of Data. Data can be queried using SPARQL but there are still needs for integrating, classifying and exploring the data for data analysis and ...

Added: September 26, 2017

Kaytoue M., Kuznetsov S., Macko J. et al., Annals of Mathematics and Artificial Intelligence 2014 Vol. 70 No. 1 P. 55-79

Biclustering numerical data became a popular data-mining task at the beginning of 2000’s, especially for gene expression data analysis and recommender systems. A bicluster reflects a strong association between a subset of objects and a subset of attributes in a numerical object/attribute data-table. So-called biclusters of similar values can be thought as maximal sub-tables with ...

Added: October 27, 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

Ignatov D. I., Shestakoff A., Lecture Notes in Computer Science 2013

We propose a new FCA-based algorithm for consensus clustering FCA-Consensus. As the input the algorithm takes $n$ partitions of a certain set of objects obtained by k-means algorithm after its $n$ different executions. The resulting consensus partition is extracted from a (partial) antichain of the concept lattice built on formal context $objects \times classes$, where ...

Added: October 26, 2013

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

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

Ignatov D. I., Chubis Y., Konstantinov A. V., Lecture Notes in Computer Science 2013 Vol. 7814 P. 722-725

We proposed a prototype of near-duplicate detection system for web-shop owners. It’s a typical situation for this online businesses to buy description of their goods from so-called copyrighters. Copyrighter can cheat from time to time and provide the owner with some almost identical descriptions for different items. In this paper we demonstrated how we can ...

Added: October 10, 2013

Zlotnik Alexander, Zlotnik Ilya, Computational Methods in Applied Mathematics 2015 Vol. 15 No. 2 P. 233-245

We consider the Cauchy problem for the 1D generalized Schrὅdinger equation on the whole axis. To solve it, any order finite element in space and the Crank-Nicolson in time method with the discrete transpa\-rent boundary conditions (TBCs) has recently been constructed. Now we engage the global Richardson extrapolation in time to derive the high order ...

Added: March 3, 2015

Buzmakov A. V., Egho E., Jay N. et al., International Journal of General Systems 2016 Vol. 45 No. 2 P. 135-159

Nowadays data-sets are available in very complex and heterogeneous ways. Mining of such data collections is essential to support many real-world applications ranging from healthcare to marketing. In this work, we focus on the analysis of “complex” sequential data by means of interesting sequential patterns. We approach the problem using the elegant mathematical framework of ...

Added: February 25, 2016

Aachen : CEUR Workshop Proceedings, 2013

Formal Concept Analysis (FCA) is a mathematically well-founded theory aimed at data analysis and classication, introduced and detailed in the book of Bernhard Ganter and Rudolf Wille, \Formal Concept Analysis", Springer 1999. The area came into being in the early 1980s and has since then spawned over 10000 scientic publications and a variety of practically ...

Added: October 10, 2013

М. : Физматлит, 2013

This volume is dedicated to the 80th anniversary of academician V. M. Matrosov. The book contains reviews and original articles, which address the issues of development of the method of vector Lyapunov functions, questions of stability and stabilization control in mechanical systems, stability in differential games, the study of systems with multirate time and other. ...

Added: March 7, 2014

Protasov V., Systems and Control Letters 2016 Vol. 90 P. 54-60

We prove the existence of positive linear switching systems (continuous time), whose trajectories grow to infinity, but slower than a given increasing function. This implies that, unlike the situation with linear ODE, the maximal growth of trajectories of linear systems may be arbitrarily slow. For systems generated by a finite set of matrices, this phenomenon ...

Added: February 22, 2016

Poelmans J., Ignatov D. I., Kuznetsov S. et al., International Journal of General Systems 2014 Vol. 43 No. 2 P. 105-134

Formal Concept Analysis (FCA) is a mathematical technique that has been extensively applied to Boolean data in knowledge discovery, information retrieval, web mining, etc. applications. During the past years, the research on extending FCA theory to cope with imprecise and incomplete information made significant progress. In this paper, we give a systematic overview of the ...

Added: June 9, 2014

Buzmakov A. V., Kuznetsov S., Napoli A., , in : 2017 IEEE 17th International Conference on Data Mining (ICDM). : New Orleans : IEEE, 2017. Ch. 89. P. 757-762.

A scalable method for mining graph patterns stable under subsampling is proposed.
The existing subsample stability and robustness measures are not antimonotonic according to definitions known so far.
We study a broader notion of antimonotonicity for graph patterns, so that measures of subsample stability become antimonotonic. Then we propose gSOFIA for mining the most subsample-stable graph patterns.
The ...

Added: September 26, 2017

Springer, 2017

The book studies the existing and potential connections between Social Network Analysis (SNA) and Formal Concept Analysis (FCA) by showing how standard SNA techniques, usually based on graph theory, can be supplemented by FCA methods, which rely on lattice theory.
The book presents contributions to the following areas: acquisition of terminological knowledge from social networks, knowledge ...

Added: December 17, 2017

Ignatov D. I., Khvorykh G. V., Khrunin A. V. et al., / Springer. Series LNCS "Lecture Notes in Computer Science". 2020.

Missing genotypes can affect the effcacy 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 machine learning classifier from assigning ...

Added: November 10, 2020

Ducomet B., Zlotnik A., Zlotnik I. A., / Cornell University. Series math "arxiv.org". 2013. No. arxiv: 1303.3471.

We consider an initial-boundary value problem for a generalized 2D time-dependent Schrödinger equation on a semi-infinite strip. For the Crank-Nicolson finite-difference scheme with approximate or discrete transparent boundary conditions (TBCs), the Strang-type splitting with respect to the potential is applied. For the resulting method, the uniform in time L2-stability is proved. Due to the ...

Added: March 16, 2013

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

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

Zlotnik A., Čiegis R., / Cornell University. Series arXiv "math". 2020. No. 2012.01000 [math.NA].

We study necessary conditions for stability of a Numerov-type compact higher-order finite-diffe\-rence scheme for the 1D homogeneous wave equation in the case of non-uniform spatial meshes. We first show that the uniform in time stability cannot be valid in any spatial norm provided that the complex eigenvalues appear in the associated mesh eigenvalue problem. Moreover, we prove ...

Added: December 3, 2020

Злотник А.А., Лапухина А., Проблемы математического анализа 2010 № 47 С. 77-88

Нестационарное уравнение Шрёдингера относится к основным уравнениям математической физики и находит многочисленные приложения. Очень часто его приходится численно решать в неограниченных по пространству областях. Для этой цели разработан ряд подходов, связанных с постановкой искусственных или приближенных прозрачных граничных условий (ПГУ) на искусственных границах. Среди них следует выделить подход, использующий так называемые дискретные ПГУ. Серьезный практический ...

Added: December 22, 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

Trautmann P., Vexler B., Zlotnik A., / Cornell University. Series "Working papers by Cornell University". 2017. No. 1702.00362.

This work is concerned with the optimal control problems governed by the 1D wave equation with variable coefficients and the control spaces $\mathcal M_T$ of either measure-valued functions $L^2(I,\mathcal M(\Omega))$
or vector measures $\mathcal M(\Omega,L^2(I))$. The cost functional involves the standard quadratic terms and the regularization term $\alpha\|u\|_{\mathcal M_T}$, $\alpha>0$. We construct and study three-level in time bilinear ...

Added: February 2, 2017