Uncovering and Reducing Hidden Combinatorics in Guigues-Duquenne Bases

Gély, Alain; Medina, Raoul; Nourine, Lhouari; Renaud, Yoan

doi:10.1007/978-3-540-32262-7_16

Cited by 13 publications

(12 citation statements)

References 3 publications

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“…In [18] Gély et al have investigated possible reasons why the number of pseudo-intents can be exponential in the size of the given context. They have shown that in some cases the exponential blow-up arises from the so-called P-clone attributes, which are attributes that can be exchanged to give new pseudo-intents.…”

Section: Related Work and Previous Resultsmentioning

confidence: 99%

On the complexity of enumerating pseudo-intents

Distel

Sertkaya²

2011

Discrete Applied Mathematics

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a b s t r a c tWe investigate whether the pseudo-intents of a given formal context can efficiently be enumerated. We show that they cannot be enumerated in a specified lexicographic order with polynomial delay unless P = NP. Furthermore we show that if the restriction on the order of enumeration is removed, then the problem becomes at least as hard as enumerating minimal transversals of a given hypergraph. We introduce the notion of minimal pseudo-intents and show that recognizing minimal pseudo-intents is polynomial. Despite their less complicated nature, surprisingly it turns out that minimal pseudo-intents cannot be enumerated in output-polynomial time unless P = NP.

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Section: Related Work and Previous Resultsmentioning

confidence: 99%

On the complexity of enumerating pseudo-intents

Distel

Sertkaya²

2011

Discrete Applied Mathematics

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“…Next, we describe for such contexts how clones can be identified directly from the context's table. [7] already found it is sufficient to check join-irreducible intents to check the clone property. The respective result there (Proposition 1) is formulated for the dual version of formal contexts, i. e., where G and M are interchanged.…”

Section: Theoretical Observationsmentioning

confidence: 99%

“…The notion of clones was initially proposed 5 in "Clone items: a pre-processing information for knowledge discovery" by R. Medina and L. Nourine. Subsequently, a plethora of desirable properties of clone items has been shown, such as, "hidden combinatorics" [7] that allow factorizations of data structures containing clones, computational properties investigations, like [14], or the use of clones in association rule mining [13]. Finally, the question of semantics was addressed by [11], who investigated clones in three well-known data sets (Mushroom, Adults, and Anonymous from the UCI Machine Learning Repository [9]).…”

Section: Introductionmentioning

confidence: 99%

Clones in Graphs

Doerfel¹,

Hanika²,

Stumme³

2018

Lecture Notes in Computer Science

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Finding structural similarities in graph data, like social networks, is a far-ranging task in data mining and knowledge discovery. A (conceptually) simple reduction would be to compute the automorphism group of a graph. However, this approach is ineffective in data mining since real world data does not exhibit enough structural regularity. Here we step in with a novel approach based on mappings that preserve the maximal cliques. For this we exploit the well known correspondence between bipartite graphs and the data structure formal context (G, M, I) from Formal Concept Analysis. From there we utilize the notion of clone items. The investigation of these is still an open problem to which we add new insights with this work. Furthermore, we produce a substantial experimental investigation of real world data. We conclude with demonstrating the generalization of clone items to permutations.

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“…There is an enormous interest in the community to present efficient solutions, since this restriction is closely related to an open problem in FCA: handling dense and highly dimensional contexts. [8,9] To address this situation techniques capable of reducing the complexity of constructing lattices, [10] selecting specific concepts [11,12] or even acting directly on the input context, [13,14] have recently been addressed. However, even with the aid of these techniques, obtaining the lattice can be infeasible.…”

Section: Introductionmentioning

confidence: 99%

Parallelization of the next Closure algorithm for generating the minimum set of implication rules

Moraes

Dias²,

Freitas

et al. 2016

AIR

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This paper addresses the problem of handling dense contexts of high dimensionality in the number of objects, which is still an open problem in formal concept analysis. The generation of minimal implication basis in contexts with such characteristics is investigated, where the NextClosure algorithm is employed in obtaining the rules. Therefore, this work makes use of parallel computing as a means to reduce the prohibitive times observed in scenarios where the input context has high density and high dimensionality. The sequential and parallel versions of the NextClosure algorithm applied to generating implications are employed. The experiments show a reduction of approximately 75% in execution time in the contexts of greater size and density, which attests to the viability of the strategy presented in this work.

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Uncovering and Reducing Hidden Combinatorics in Guigues-Duquenne Bases

Abstract: Abstract. Mannila and Räihä [5] have shown that minimum implicational bases can have an exponential number of implications. Aim of our paper is to understand how and why this combinatorial explosion arises and to propose mechanisms which reduce it.

Cited by 13 publications

References 3 publications

On the complexity of enumerating pseudo-intents

On the complexity of enumerating pseudo-intents

Clones in Graphs

Parallelization of the next Closure algorithm for generating the minimum set of implication rules

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