Clustering bipartite graphs in terms of approximate formal concepts and sub-contexts

Gaume, Bruno; Navarro, Emmanuel; Prade, Henri

doi:10.1080/18756891.2013.819179

Cited by 14 publications

(8 citation statements)

References 47 publications

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“…In practice, it is important to introduce some tolerance in the evaluation of the similarity between the members of a cluster and in the separatedness of the clusters, leading to a more permissive and approximate view of granules or clusters; see, e.g., [32].…”

Section: The Invariance Of Property 4 With Respect To Complementationmentioning

confidence: 99%

“…-The parallel of FCA with PoTh leading to the introduction of new operators extends to conceptual pattern structures [28,29], where the description ∂(x) of an object x, may, e.g., be a possibilistic knowledge base [2]; -Applications of FCA to the fusion of conflicting pieces of information issued from multiple sources using pattern structures for labeling sets of possible values in terms of sources supporting them [3]; -The clustering of sets of objects on the basis of approximate concepts [24,32], with labeling of the clusters [38]; -The building of conceptual analogical proportions [37] on the basis of the formal definition of analogical proportions in non-distributive lattices [34], conceptualization and analogical reasoning being two basic cognitive activities [4].…”

Section: More Lines For Further Researchmentioning

confidence: 99%

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Formal Concept Analysis from the Standpoint of Possibility Theory

Dubois

Prade

2015

Formal Concept Analysis

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 15496The contribution was presented at : http://www.matap.uma.es/icfca2015/files/a61b70b0124cd72ef5b1442c0223db4a-0.html Abstract. Formal concept analysis (FCA) and possibility theory (PoTh) have been developed independently. They address different concerns in information processing: while FCA exploits relations linking objects and properties, and has applications in data mining and clustering, PoTh deals with the modeling of (graded) epistemic uncertainty. However, making a formal parallel between FCA and PoTh is fruitful. The four set-functions at work in PoTh have meaningful counterparts in FCA; this leads to consider operators neglected in FCA, and thus new fixed point equations. One of these pairs of equations, paralleling the one defining formal concepts in FCA, defines independent sub-contexts of objects and properties that have nothing in common. The similarity of the structures underlying FCA and PoTh is still more striking, using a cube of opposition (a device extending the traditional square of opposition in logic). Beyond the parallel between FCA and PoTh, this invited contribution, which largely relies on several past publications by the authors, also addresses issues pertaining to the possible meanings, degree of satisfaction vs. degree of certainty, of graded object-property links, which calls for distinct manners of handling the degrees. Other lines of interest for further research are briefly mentioned.

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Section: The Invariance Of Property 4 With Respect To Complementationmentioning

confidence: 99%

Section: More Lines For Further Researchmentioning

confidence: 99%

Formal Concept Analysis from the Standpoint of Possibility Theory

Dubois

Prade

2015

Formal Concept Analysis

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“…The objects (sequences) share numerous attributes (blocks) and frequently, it is the way they are combined which allow to distinguish different clusters. The issue of object clustering from a formal context is treated in paper [12]. Authors propose a two-step procedures where formal concepts are enlarged to approximate concepts during the first step and then merged in a second step when they overlap sufficiently.…”

Section: Unsupervised Classificationmentioning

confidence: 99%

Automated Enzyme Classification by Formal Concept Analysis

Coste

Garet

Groisillier

et al. 2014

Formal Concept Analysis

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Abstract. Enzymes are molecules with a catalytic activity that make them essential for any biochemical reaction. High throughput genomic technics give access to the protein sequence of new enzymes found in living organisms. Guessing the enzyme functional activity from its sequence is a crucial task that can be approached by comparing the new sequences with those of already known enzymes labeled by a family class. This task is difficult because the activity is based on a combination of small sequence patterns and sequences greatly evolved over time. This paper presents a classifier based on the identification of common subsequence blocks between known and new enzymes and the search of formal concepts built on the cross product of blocks and sequences for each class. Since new enzyme families may emerge, it is important to propose a first classification of enzymes that cannot be assigned to a known family. FCA offer a nice framework to set the task as an optimization problem on the set of concepts. The classifier has been tested with success on a particular set of enzymes present in a large variety of species, the haloacid dehalogenase superfamily.

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“…Such approaches include ice-berg lattices [1], nesting lattices [2], creating sub-contexts [3], fault-tolerance [4,5], expandable concept trees [6], rough concepts [7] and approximation [8]. However, there will always be the need for faster performance of the fundamental operations in FCA, such as the computation of formal concepts.…”

Section: Introductionmentioning

confidence: 99%

Making Use of Empty Intersections to Improve the Performance of CbO-Type Algorithms

Andrews

2017

Lecture Notes in Computer Science

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Abstract. This paper describes how improvements in the performance of Close-by-One type algorithms can be achieved by making use of empty intersections in the computation of formal concepts. During the computation, if the intersection between the current concept extent and the next attribute-extent is empty, this fact can be simply inherited by subsequent children of the current concept. Thus subsequent intersections with the same attribute-extent can be skipped. Because these intersections require the testing of each object in the current extent, significant time savings can be made by avoiding them. The paper also shows how further time savings can be made by forgoing the traditional canonicity test for new extents, if the intersection is empty. Finally, the paper describes how, because of typical optimizations made in the implementation of CbO-type algorithms, even more time can be saved by amalgamating inherited attributes with inherited empty intersections into a single, simple test.

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Clustering bipartite graphs in terms of approximate formal concepts and sub-contexts

Cited by 14 publications

References 47 publications

Formal Concept Analysis from the Standpoint of Possibility Theory

Formal Concept Analysis from the Standpoint of Possibility Theory

Automated Enzyme Classification by Formal Concept Analysis

Making Use of Empty Intersections to Improve the Performance of CbO-Type Algorithms

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