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NextClosures with Constraints

Francesco Kriegel
2016 International Conference on Concept Lattices and their Applications  
is not compatible with the data-set.  ...  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.  ...  Next, Section 4 generalizes the parallel NextClosures algorithm from [20] to the case of closure operators (with constraints) in complete lattices.  ... 
dblp:conf/cla/Kriegel16 fatcat:vgbn3cxstnbhnmmo2gzp5qrwri

Formal Concept Analysis with Constraints by EM Operators

Hua Mao
2017 Journal of the Indonesian Mathematical Society  
Particularly, only concepts which are compatible with the constraint are extracted from data. Therefore, the number of extracted concepts becomes smaller since we leave out non-interesting concepts.  ...  The type of background knowledge we deal with relates to relative importance of attributes in the input data. We introduce EM operators which constrain in attributes of formal concept analysis.  ...  with constraints by other operators.  ... 
doi:10.22342/jims.23.1.197.13-26 fatcat:eoqulufsa5dkvlzrgrj6zjaxmi

LinCbO: fast algorithm for computation of the Duquenne-Guigues basis [article]

Radek Janostik, Jan Konecny, Petr Krajča
2021 arXiv   pre-print
Experimental Comparison We compare LinCbO with other algorithms, namely: • NextClosure with naïve closure (NC1), LinClosure (NC2), and Wild's closure (NC3). • NextClosure`, which is NextClosure with the  ...  return D 8 return Y NextClosure can be seen as an iterative version of CbO with the right depth-first sweep through the tree of all subsets.  ... 
arXiv:2011.04928v2 fatcat:hmliwwjk2fctfjph4zal4jwcya

Formal Concept Analysis with Constraints by Closure Operators [chapter]

Radim Bělohlávek, Vilém Vychodil
2006 Lecture Notes in Computer Science  
The constraints represent a user-defined requirements which are supplied along with the input data table.  ...  The main effect is to filterout outputs of the analysis (conceptual clusters and if-then rules) which are not compatible with the constraint, in a computationally efficient way (polynomial time delay algorithm  ...  Still, the number of C-interesting concepts is usually much smaller than the number of all concepts, thus, NextClosure with C is in most situations considerably faster than NextClosure with ↓↑ .  ... 
doi:10.1007/11787181_10 fatcat:hhuhrow7pre25m6fqplz6br3oa

NextClosures: parallel computation of the canonical base with background knowledge

Francesco Kriegel, Daniel Borchmann
2017 International Journal of General Systems  
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.  ...  Acknowledgements The authors gratefully thank Bernhard Ganter for his helpful hints on optimal formal contexts for his NextClosure algorithm.  ...  Finally, we compared our two implementations of NextClosure and NextClosures when only one CPU core is utilized.  ... 
doi:10.1080/03081079.2017.1349570 fatcat:gnrogf6kizdgtga4r3szeagkzi

Formal Concept Analysis via Atomic Priming [chapter]

Ruairí de Fréin
2013 Lecture Notes in Computer Science  
To address this, we prime NextClosure with multiple starting-intents by taking reduced rank approximations of the binary relation using Nonnegative Matrix Factorization (NMF) [18] .  ...  Aside from sparsity, the main bottlenecks are memory and processing constraints.  ...  Adding the closure F 6 does not: this closure overlaps with existing closures in F l . Fig. 1 illustrates the order closures are mined by NextClosure.  ... 
doi:10.1007/978-3-642-38317-5_6 fatcat:qfphjxbpxbemlgwouvsczzquyi

Comparison of Data Structures for Computing Formal Concepts [chapter]

Petr Krajca, Vilem Vychodil
2009 Lecture Notes in Computer Science  
Memory consumption , presenting computation time of NextClosure algorithm with data tables consisting of 100 objects, various numbers of attributes and 15 % density of 1's.  ...  From the computational point of view, these applications of FCA depend on algorithms for computing all formal concepts (possibly satisfying additional constraints) given an input data set.  ... 
doi:10.1007/978-3-642-04820-3_11 fatcat:ma24uhkunrcztaqomdmplxnbv4

TRIAS--An Algorithm for Mining Iceberg Tri-Lattices

Robert Jaschke, Andreas Hotho, Christoph Schmitz, Bernhard Ganter, Gerd Stumme
2006 IEEE International Conference on Data Mining. Proceedings  
NEXTCLOSURE computes concepts in lectic order.  ...  The lighter version with only two constraints is then just a special case (e. g., by letting r-minsupp:= 0).  ... 
doi:10.1109/icdm.2006.162 dblp:conf/icdm/JaschkeHSGS06 fatcat:4xnq4zzolvdr7drtqyeq5tno3q

Two FCA-Based Methods for Mining Gene Expression Data [chapter]

Mehdi Kaytoue, Sébastien Duplessis, Sergei O. Kuznetsov, Amedeo Napoli
2009 Lecture Notes in Computer Science  
Experiments with gene expression data are discussed.  ...  The second method is based on pattern structures and needs adaptations of standard algorithms to computing with interval algebra. The two methods are described in details and discussed.  ...  In terms of computation, using any of these constraints means that only some lower part of the pattern lattice is computed, with patterns satisfying the constraints.  ... 
doi:10.1007/978-3-642-01815-2_19 fatcat:wbma4fxsuvav5nxp66266wr6mu

Mining gene expression data with pattern structures in formal concept analysis

Mehdi Kaytoue, Sergei O. Kuznetsov, Amedeo Napoli, Sébastien Duplessis
2011 Information Sciences  
This paper addresses the important problem of efficiently mining numerical data with formal concept analysis (FCA).  ...  Experiments with real-world gene expression data are discussed and give a practical basis for the comparison and evaluation of the methods.  ...  In terms of computation, this means that only some lower part of the pattern lattice is computed, with patterns satisfying the constraints.  ... 
doi:10.1016/j.ins.2010.07.007 fatcat:gqxivxkecnbtfohxfagsuzqas4

Semantic entailment of attribute-dependency formulas and their non-redundant bases

Radim Belohlavek, Vilem Vychodil
2006 Proceedings of the 9th Joint Conference on Information Sciences (JCIS)  
Namely, we first associate with any T a closure operator C, then use Ganter's NEXTCLOSURE algorithm [4] to compute a minimal basis (of attribute implications) related to C, and then use the set to determine  ...  The main benefits are the following: B T (X,Y, I) is smaller and thus better comprehensible for a user than B(X,Y,I); B T (X,Y, I) contains only those concepts which respect the constraints represented  ... 
doi:10.2991/jcis.2006.234 dblp:conf/jcis/BelohlavekV06b fatcat:xhc5djmbkbbhln4u2nhxx67bte

Closure-based constraints in formal concept analysis

Radim Belohlavek, Vilem Vychodil
2013 Discrete Applied Mathematics  
The idea is to consider relevant and thus to extract only these itemsets that are compatible with the background knowledge.  ...  The constraints are represented by closure operators and their purpose is to mimic background knowledge a user may have of the data.  ...  This provides us with a way to determine a Cbase: we can use the NextClosure [9] algorithm to compute fix(cl T ) and then single out the C-pseudo-intents according to P C (X, Y, I) = {P ∈ fix(cl T )  ... 
doi:10.1016/j.dam.2013.02.029 fatcat:3osrlm34fjd6lhpb3jjtbn6w3i

Discovering shared conceptualizations in folksonomies

Robert Jäschke, Andreas Hotho, Christoph Schmitz, Bernhard Ganter, Gerd Stumme
2008 Journal of Web Semantics  
We present a new data mining task, the \emph{mining of all frequent tri-concepts}, together with an efficient algorithm, for discovering these implicit shared conceptualisations.  ...  We present a new data mining task, the mining of all frequent tri-concepts, together with an efficient algorithm, for discovering these implicit shared conceptualisations.  ...  NEXTCLOSURE computes the concepts of a dyadic formal context (G, M, I) in a particular order, starting with the concept (∅ I , ∅ II ).  ... 
doi:10.1016/j.websem.2007.11.004 fatcat:iok6wta5mbcrjbvrabpedy6e3i

Triadic Formal Concept Analysis and triclustering: searching for optimal patterns

Dmitry I. Ignatov, Dmitry V. Gnatyshak, Sergei O. Kuznetsov, Boris G. Mirkin
2015 Machine Learning  
Relaxations of this notion under consideration are: OAC-triclusters; triclusters optimal with respect to the leastsquare criterion; and graph partitions obtained by using spectral clustering.  ...  In Trias this approach is extended to the triadic case and minimal support constraints are added (triclusters with too small extent, intent or modus are skipped).  ...  Also, some minimum size constraint can be used to avoid too deep partitioning.  ... 
doi:10.1007/s10994-015-5487-y fatcat:qpedyeugvzgmbaidv3izlhcvja

From Triadic FCA to Triclustering: Experimental Comparison of Some Triclustering Algorithms

Dmitry Gnatyshak, Dmitry I. Ignatov, Sergei O. Kuznetsov
2013 International Conference on Concept Lattices and their Applications  
In Trias this approach is extended to the triadic case and minimal support constraints are added (triclusters with too small extent, intent or modus are skipped).  ...  Also, some minimum size constraint can be used to avoid too deep partitioning.  ... 
dblp:conf/cla/GnatyshakIK13 fatcat:psszgieh2ndnrifctffe6czkdi
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