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Representing a Concept Lattice By a Graph
 Proceedings of Discrete Maths and Data Mining Workshop, 2nd SIAM Conference on Data Mining (SDM'02
, 2004
"... Concept lattices (also called Galois lattices) are an ordering of the maximal rectangles dened by a binary relation. In this paper, we present a new relationship between lattices and graphs: given a binary relation R, we dene an underlying graph GR , and establish a onetoone correspondence between ..."
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Cited by 20 (14 self)
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Concept lattices (also called Galois lattices) are an ordering of the maximal rectangles dened by a binary relation. In this paper, we present a new relationship between lattices and graphs: given a binary relation R, we dene an underlying graph GR , and establish a onetoone correspondence between the set of elements of the concept lattice of R and the set of minimal separators of GR .
On Horn axiomatizations for sequential data
 Computer Science
, 2005
"... Abstract. We propose a notion of deterministic association rules for ordered data. We prove that our proposed rules can be formally justified by a purely logical characterization, namely, a natural notion of empirical Horn approximation for ordered data which involves background Horn conditions; the ..."
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Cited by 16 (10 self)
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Abstract. We propose a notion of deterministic association rules for ordered data. We prove that our proposed rules can be formally justified by a purely logical characterization, namely, a natural notion of empirical Horn approximation for ordered data which involves background Horn conditions; these ensure the consistency of the propositional theory obtained with the ordered context. The main proof resorts to a concept lattice model in the framework of Formal Concept Analysis, but adapted to ordered contexts. We also discuss a general method to mine these rules that can be easily incorporated into any algorithm for mining closed sequences, of which there are already some in the literature. 1
Closed Sets for Labeled Data ⋆
"... Abstract. Closed sets are being successfully applied in the context of compacted data representation for association rule learning. However, their use is mainly descriptive. This paper shows that, when considering labeled data, closed sets can be adapted for prediction and discrimination purposes by ..."
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Cited by 13 (0 self)
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Abstract. Closed sets are being successfully applied in the context of compacted data representation for association rule learning. However, their use is mainly descriptive. This paper shows that, when considering labeled data, closed sets can be adapted for prediction and discrimination purposes by conveniently contrasting covering properties on positive and negative examples. We formally justify that these sets characterize the space of relevant combinations of features for discriminating the target class. In practice, identifying relevant/irrelevant combinations of features through closed sets is useful in many applications. Here we apply it to compacting emerging patterns and essential rules and to learn descriptions for subgroup discovery. 1
G.: Approximable concepts, Chu spaces, and information systems. Theory and Applications of Categories (200x
"... ABSTRACT. This paper serves to bring three independent but important areas of computer science to a common meeting point: Formal Concept Analysis (FCA), Chu Spaces, and Domain Theory (DT). Each area is given a perspective or reformulation that is conducive to the flow of ideas and to the exploration ..."
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Cited by 12 (8 self)
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ABSTRACT. This paper serves to bring three independent but important areas of computer science to a common meeting point: Formal Concept Analysis (FCA), Chu Spaces, and Domain Theory (DT). Each area is given a perspective or reformulation that is conducive to the flow of ideas and to the exploration of crossdisciplinary connections. Among other results, we show that the notion of state in Scott’s information system corresponds precisely to that of formal concepts in FCA with respect to all finite Chu spaces, and the entailment relation corresponds to “association rules”. We introduce, moreover, the notion of approximable concept and show that approximable concepts represent algebraic lattices which are identical to Scott domains except the inclusion of a top element. This notion serves as a stepping stone in the recent work [Hitzler and Zhang, 2004] in which a new notion of morphism on formal contexts results in a category equivalent to (a) the category of complete algebraic lattices and Scott continuous functions, and (b) a category of information systems and approximable mappings. 1.
Obtaining and Maintaining PolynomialSized Concept Lattices
, 2002
"... We use our definition of an underlying cobipartite graph which encodes a given binary relation to propose a new approach to defining a subrelation or incrementally maintaining a relation which will define only a polynomial number of concepts. ..."
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Cited by 5 (3 self)
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We use our definition of an underlying cobipartite graph which encodes a given binary relation to propose a new approach to defining a subrelation or incrementally maintaining a relation which will define only a polynomial number of concepts.
Maintaining Class Membership Information
 Proceedings Workshop MASPEGHI (MAnaging of SPEcialization/Generalization HIerarchies) LNCS proceedings of OOIS 02 (ObjectOriented Information Systems
, 2002
"... Galois lattices (or concept lattices), which are lattices built on a binary relation, are now used in many fields, such as Data Mining and hierarchy organization, but may be of exponential size. In this paper, we propose a decomposition of a Galois subhierarchy which is of small size but contains u ..."
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Cited by 5 (4 self)
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Galois lattices (or concept lattices), which are lattices built on a binary relation, are now used in many fields, such as Data Mining and hierarchy organization, but may be of exponential size. In this paper, we propose a decomposition of a Galois subhierarchy which is of small size but contains useful inheritance information. We show how to efficiently maintain this information when an element is added to or removed from the relation, using a dynamic domination table which describes the underlying graph with which we encode the lattice.
Mining Implications from Lattices of Closed Trees
"... Abstract. We propose a way of extracting highconfidence association rules from datasets consisting of unlabeled trees. The antecedents are obtained through a computation akin to a hypergraph transversal, whereas the consequents follow from an application of the closure operators on unlabeled trees ..."
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Cited by 2 (2 self)
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Abstract. We propose a way of extracting highconfidence association rules from datasets consisting of unlabeled trees. The antecedents are obtained through a computation akin to a hypergraph transversal, whereas the consequents follow from an application of the closure operators on unlabeled trees developed in previous recent works of the authors. We discuss in more detail the case of rules that always hold, independently of the dataset, since these are more complex than in itemsets due to the fact that we are no longer working on a lattice. 1