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NextClosures with Constraints
2016
International Conference on Concept Lattices and their Applications
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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
2017
Journal of the Indonesian Mathematical Society
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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]
2021
arXiv
pre-print
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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]
2006
Lecture Notes in Computer Science
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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
2017
International Journal of General Systems
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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]
2013
Lecture Notes in Computer Science
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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]
2009
Lecture Notes in Computer Science
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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
2006
IEEE International Conference on Data Mining. Proceedings
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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]
2009
Lecture Notes in Computer Science
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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
2011
Information Sciences
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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
2006
Proceedings of the 9th Joint Conference on Information Sciences (JCIS)
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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
2013
Discrete Applied Mathematics
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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
2008
Journal of Web Semantics
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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
2015
Machine Learning
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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
2013
International Conference on Concept Lattices and their Applications
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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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