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NextClosures: parallel computation of the canonical base with background knowledge

Francesco Kriegel, Daniel Borchmann
2017 International Journal of General Systems  
Consequently, several algorithms for the computation of this base have been proposed.  ...  In this paper, we shall introduce an approach that remedies this deficit by allowing the canonical base to be computed in a parallel manner with respect to arbitrary implicational background knowledge.  ...  The benchmarks were performed on servers at the Institute of Theoretical Computer Science, and the Centre for Information Services and High Performance Computing (ZIH) at TU Dresden.  ... 
doi:10.1080/03081079.2017.1349570 fatcat:gnrogf6kizdgtga4r3szeagkzi

NextClosures with Constraints

Francesco Kriegel
2016 International Conference on Concept Lattices and their Applications  
In a former paper, the algorithm NextClosures for computing the set of all formal concepts as well as the canonical base for a given formal context has been introduced.  ...  Additionally, we show how the algorithm can be modified in order to do parallel Attribute Exploration for unconstrained closure operators, as well as give a reason for the impossibility of (parallel) Attribute  ...  Acknowledgements The author gratefully thanks the anonymous reviewers for their constructive hints and helpful remarks.  ... 
dblp:conf/cla/Kriegel16 fatcat:vgbn3cxstnbhnmmo2gzp5qrwri

Advances in Algorithms Based on CbO

Petr Krajca, Jan Outrata, Vilém Vychodil
2010 International Conference on Concept Lattices and their Applications  
First, we present an extension of CbO, so called FCbO, and an improved canonicity test that significantly reduces the number of formal concepts which are computed multiple times.  ...  Second, we outline a parallel version of the proposed algorithm and discuss various scheduling strategies and their impact on the overall performance and scalability of the algorithm.  ...  A parallel algorithm based on these ideas shall be called Parallel Fast Close-byOne (PFCbO).  ... 
dblp:conf/cla/KrajcaOV10 fatcat:3apfn4rzbnedpo5uvurdcsn5fy

Fast algorithm for computing fixpoints of Galois connections induced by object-attribute relational data

Jan Outrata, Vilem Vychodil
2012 Information Sciences  
The algorithm, called FCbO, results as a modification of Kuznetsov's CbO in which we use more efficient canonicity test.  ...  We describe the algorithm, prove its correctness, discuss efficiency issues, and present an experimental evaluation of its performance and comparison with other algorithms.  ...  The present paper is aimed as a detailed explanation of the algorithm with emphasis on the canonicity test.  ... 
doi:10.1016/j.ins.2011.09.023 fatcat:leyx7zjd3za2jhchkcnq5wqezi

Distributed Algorithm for Computing Formal Concepts Using Map-Reduce Framework [chapter]

Petr Krajca, Vilem Vychodil
2009 Lecture Notes in Computer Science  
In this paper we introduce a scalable distributed algorithm for computing maximal rectangles that uses the map-reduce approach to data processing.  ...  Several algorithms for computing particular patterns represented by maximal rectangles in binary matrices were proposed but their major drawback is their computational complexity limiting their application  ...  The test (so-called canonicity test) is based on comparing B ∩ Y j = D ∩ Y j where Y j ⊆ Y is defined as follows: Y j = {y ∈ Y | y < j}. (5) The role of the canonicity test is to prevent computing the  ... 
doi:10.1007/978-3-642-03915-7_29 fatcat:mdgj7zglp5dwrbbtceztmlbuui

A parallel version of the in-close algorithm

Nuwan Kodagoda, Simon Andrews, Koliya Pulasinghe
2017 2017 6th National Conference on Technology and Management (NCTM)  
The paper presents the key parallelization strategy used and presents experimental results of the parallelization using the OpenMP framework.  ...  This research paper presents a new parallel algorithm for computing the formal concepts in a formal context.  ...  ACKNOWLEDGEMENTS This work used the ARCHER UK National Supercomputing Service (  ... 
doi:10.1109/nctm.2017.7872818 fatcat:mh6ut454vzb7jffwz73352xexi

Implications over Probabilistic Attributes [chapter]

Francesco Kriegel
2017 Lecture Notes in Computer Science  
In case of finiteness of the input data to be analyzed, the constructed axiomatization is finite, too, and can be computed in finite time.  ...  In case of finiteness of the input data to be analyzed, the constructed axiomatization is finite, too, and can be computed in finite time. an implication set L entails an implication X → Y , symbolized  ...  The author gratefully thanks the anonymous reviewers for their constructive hints and helpful remarks.  ... 
doi:10.1007/978-3-319-59271-8_11 fatcat:wr34ilbzmzc2naqt37tjzzlyke

Attribute Exploration with Multiple Contradicting Partial Experts [article]

Maximilian Felde, Gerd Stumme
2022 arXiv   pre-print
Each expert has their own view of the domain and the views of multiple experts may contain contradicting information.  ...  In this paper we present an extension of attribute exploration that allows for a group of domain experts and explores their shared views.  ...  It works by asking the expert questions about the validity of implications in the domain. The basic approach [7] computes the canonical base.  ... 
arXiv:2205.15714v1 fatcat:xasdirzefzdktpxlovp3mxgv7u

Merge-Based Computation of Minimal Generators [chapter]

Céline Frambourg, Petko Valtchev, Robert Godin
2005 Lecture Notes in Computer Science  
The volatility of many real-world datasets has motivated the study of the evolution in the concept set under various modifications of the initial context.  ...  In the present paper, we build up on previous work about the incremental maintenance of the mingen family of a context to investigate the case of lattice merge upon context subposition.  ...  Acknowledgments This research was supported by the authors' individual NSERC grants as well as by the FQRNT team grant.  ... 
doi:10.1007/11524564_12 fatcat:a2xvhllunbgqldkrdav2h5ocwq

The joy of implications, aka pure Horn formulas: Mainly a survey

Marcel Wild
2017 Theoretical Computer Science  
Some keywords: The Duquenne-Guiges (implicational) base, the canonical direct base, prime implicates, the consensus method, implications and meet irreducible closed sets, optimum bases for certain lattices  ...  It is mainly a survey of results obtained in the last thirty years, but features a few novelties as well.  ...  Another popular application of NextClosure is attribute exploration [GW, p.85 ]. This particular kind of Query Learning strives to compute the canonical base Σ GD of some hidden closure system F.  ... 
doi:10.1016/j.tcs.2016.03.018 fatcat:hrz2vsn66rdt3obw42or57h7pa

Extracting concepts from triadic contexts using Binary Decision Diagram

Julio Cesar Vale Neves, Luiz Enrique Zarate, Mark Alan Junho Song
2022 Journal of universal computer science (Online)  
Moreover, to reduce the computational resources needed to manipulate a high-volume of data, the usage of BDD was implemented to simplify and represent data.  ...  Due to the high complexity of real problems, a considerable amount of research that deals with high volumes of information has emerged.  ...  Acknowledgements The authors acknowledge the financial support of FAPEMIG, CNPq, and CAPES.  ... 
doi:10.3897/jucs.67953 fatcat:czbp3tfqvzffpnashpw7ucctnu

Axiomatisation of general concept inclusions from finite interpretations

D. Borchmann, F. Distel, F. Kriegel
2016 Journal of Applied Non-Classical Logics  
However, the tasks of constructing knowledge bases itself, often performed by human experts, is difficult, timeconsuming and expensive.  ...  As such graphs appear naturally within the scope of the Semantic Web in the form of sets of RDF triples, the presented approach opens up another possibility to extract terminological knowledge from the  ...  Franz Baader for helpful discussions during the research on this paper. We also express our thanks to the anonymous reviewers who greatly helped to improve the presentation of our work.  ... 
doi:10.1080/11663081.2016.1168230 fatcat:22qcez3ldndibktp3f2l5bxonu

Extracting ALEQR Self-Knowledge Bases from Graphs

Francesco Kriegel
2015 International Conference on Formal Concept Analysis  
Furthermore, also sublogics may be chosen to express the axioms in the knowledge base.  ...  The extracted knowledge base entails exactly all those statements that can be expressed in the chosen description logic and are encoded in the input graph.  ...  -for example the standard NextClosure algorithm from Ganter [10] , or the parallel algorithm that has been introduced in [15] and implemented in [14] .  ... 
dblp:conf/icfca/Kriegel15 fatcat:sblgxv3khjeuhjxklerzvw3vpy

Concept Learning from Triadic Data

Roman Zhuk, Dmitry I. Ignatov, Natalia Konstantinova
2014 Procedia Computer Science  
We propose extensions of the classical JSM-method and the Naïve Bayesian classifier for the case of triadic relational data.  ...  In addition to classification precision and recall we also evaluated the time performance of the proposed methods.  ...  Acknowledgments The study was conducted in the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE) in 2013 and 2014 and in the Laboratory of Intelligent  ... 
doi:10.1016/j.procs.2014.05.345 fatcat:at3y5tuyxbag7mvapmmw6rvqom

Exploring different paradigms to extract proper implications from high dimensional formal contexts

Julio C. V. Neves, Pedro Henrique B. Ruas, Rokia Missaoui, Sergio M. Dias, Luis E. Zarate, Mark A. J. Song
2020 IEEE Access  
In addition, we implemented a parallel computing model for generating and obtaining different implications.  ...  This article explores different approaches to extract proper implications from high dimensional contexts based on constraints to obtain the set of implications rules.  ...  ACKNOWLEDGMENT The authors would also like to warmly thank PUC-MG researchers for raising important questions and making relevant suggestions that helped improve the quality of the article.  ... 
doi:10.1109/access.2020.3010482 fatcat:tkcyewl4yzgxja6vk2beavfcya
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