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62
Incremental concept formation algorithms based on Galois (concept) lattices
, 1995
"... . The Galois (or concept) lattice produced from a binary relation has been proved useful for many applications. Building the Galois lattice can be considered as a conceptual clustering method since it results in a concept hierarchy. This article presents incremental algorithms for updating the Galoi ..."
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Cited by 105 (9 self)
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. The Galois (or concept) lattice produced from a binary relation has been proved useful for many applications. Building the Galois lattice can be considered as a conceptual clustering method since it results in a concept hierarchy. This article presents incremental algorithms for updating the Galois lattice and corresponding graph, resulting in an incremental concept formation method. Different strategies are considered based on a characterization of the modifications implied by such an update. Results of empirical tests are given in order to compare the performance of the incremental algorithms to three other batch algorithms. Surprisingly, when the total time for incremental generation is used, the simplest and less efficient variant of the incremental algorithms outperforms the batch algorithms in most cases. When only the incremental update time is used, the incremental algorithm outperforms all the batch algorithms. Empirical evidence shows that, on the average, the incremental u...
Experimental comparison of navigation in a Galois lattice with conventional information retrieval methods
 International Journal of Manmachine Studies
, 1998
"... A controlled experiment was conducted comparing information retrieval using a Galois lattice structure with two more conventional retrieval methods: navigating in a manually built hierarchical classification and Boolean querying with index terms. No significant performance difference was found be ..."
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Cited by 50 (5 self)
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A controlled experiment was conducted comparing information retrieval using a Galois lattice structure with two more conventional retrieval methods: navigating in a manually built hierarchical classification and Boolean querying with index terms. No significant performance difference was found between Boolean querying and the Galois lattice retrieval method for subject searching with the three measures used for the experiment: user searching time, recall and precision. However, hierarchical classification retrieval did show significantly lower recall compared to the two other methods. This experiment suggests that retrieval using a Galois lattice structure may be an attractive alternative since it combines a good performance for subject searching along with browsing potential. 11/12/98 2 1. Introduction Information retrieval is concerned with the representation, storage, organization, and accessing of information items (Salton & McGill, 1983). As opposed to the traditional f...
Formal Concept Analysis in Information Science
 ANNUAL REVIEW OF INFORMATION SCIENCE AND TECHNOLOGY
, 1996
"... ..."
Structural machine learning with Galois lattice and Graphs
 Proc. of the 1998 Int. Conf. on Machine Learning (ICML'98
, 1998
"... This paper defines a formal approach to learning from examples described by labelled graphs. We propose a formal model based upon lattice theory and in particular with the use of Galois lattice. We enlarge the domain of formal concept analysis, by the use of the Galois lattice model with structural ..."
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Cited by 26 (2 self)
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This paper defines a formal approach to learning from examples described by labelled graphs. We propose a formal model based upon lattice theory and in particular with the use of Galois lattice. We enlarge the domain of formal concept analysis, by the use of the Galois lattice model with structural description of examples and concepts. Our implementation, called "Graal" (for GRAph And Learning) constructs a Galois lattice for any description language provided that the two operations of comparison and generalization are determined for that language. We prove that these operations exist in the case of labelled graphs. 1.
Building concept (Galois) lattices from parts: Generalizing the incremental methods
 Proceedings of the ICCS’01
, 2001
"... Formal concept analysis and Galois lattices in general are increasingly used as a framework for the resolution of practical problems from software engineering, knowledge engineering and data mining. Recent applications have put the emphasis on the need for both efficient, scalable and flexible al ..."
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Cited by 16 (6 self)
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Formal concept analysis and Galois lattices in general are increasingly used as a framework for the resolution of practical problems from software engineering, knowledge engineering and data mining. Recent applications have put the emphasis on the need for both efficient, scalable and flexible algorithms to build the lattice. Such features are sought in the development of incremental algorithms. However, the major known incremental algorithm lacks clear theoretical foundations and shows some design flaws which strongly affect its practical performances. Our paper presents a general theoretical framework for the assembly of lattices sharing a same set of attributes based on existing theory on subposition of contexts. The framework underlies the design of a generic procedure for lattice assembly from parts, a new lattice building approach which is more general than the existing incremental and batch ones. As an argument for its theoretical strength, we describe the way our procedure reduces to an improved version of the major known incremental algorithm, which both corrects existing bugs and increases its overall efficiency.
Generating Frequent Itemsets Incrementally: Two Novel Approaches Based on Galois Lattice Theory
, 2002
"... Galois (concept) lattice theory has been successfully applied to the resolution of the association rule problem in data mining. In particular, structural results about lattices have been used in the design of e#cient procedures for mining the frequent patterns (itemsets) in a transaction database. ..."
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Cited by 14 (3 self)
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Galois (concept) lattice theory has been successfully applied to the resolution of the association rule problem in data mining. In particular, structural results about lattices have been used in the design of e#cient procedures for mining the frequent patterns (itemsets) in a transaction database.
Galicia: An Open Platform for Lattices
 In Using Conceptual Structures: Contributions to the 11th Intl. Conference on Conceptual Structures (ICCS'03
, 2003
"... Formal concept analysis (FCA) has proved helpful in the resolution of practical problems from fields such software engineering, knowledge engineering and data mining. Recently, a substantial push has been done toward the design of e#cient procedures for lattice construction, with a variety of no ..."
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Cited by 14 (1 self)
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Formal concept analysis (FCA) has proved helpful in the resolution of practical problems from fields such software engineering, knowledge engineering and data mining. Recently, a substantial push has been done toward the design of e#cient procedures for lattice construction, with a variety of novel algorithms proposed in the literature.
Incremental Structuring of Knowledge Bases
, 1995
"... An important structuring mechanism for knowledge bases is building an inheritance hierarchy of classes based on the content of their knowledge objects. The hierarchy can be used to handle several query processing tasks more efficiently. Building and maintaining this hierarchy is a difficult task for ..."
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Cited by 12 (4 self)
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An important structuring mechanism for knowledge bases is building an inheritance hierarchy of classes based on the content of their knowledge objects. The hierarchy can be used to handle several query processing tasks more efficiently. Building and maintaining this hierarchy is a difficult task for the knowledge engineer. The notion of knowledge space has been previously proposed to help automate such a task. In this paper an incremental algorithm for building the knowledge space is proposed and tested on a sample knowledge base. The empirical behavior shows that after a point the knowledge space can be updated in close to constant time on the average. The knowledge space structure is presented in the framework of the theory of concept lattices. The presentation suggests that the notion of a complete knowledge lattice might be a worthwhile alternative because of the additional richness of the structure. However, this richness induces a large amount of additional processing and storage...
A PartitionBased Approach towards Constructing Galois (Concept) Lattices
 Discrete Mathematics
, 2002
"... Galois lattices and formal concept analysis of binary relations have proved useful in the resolution of many problems of theoretical or practical interest. Recent studies of practical applications in data mining and software engineering have put the emphasis on the need for both efficient and fle ..."
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Cited by 11 (3 self)
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Galois lattices and formal concept analysis of binary relations have proved useful in the resolution of many problems of theoretical or practical interest. Recent studies of practical applications in data mining and software engineering have put the emphasis on the need for both efficient and flexible algorithms to construct the lattice. Our paper presents a novel approach for lattice construction based on the apposition of binary relation fragments. We extend the existing theory to a complete characterization of the global Galois (concept) lattice as a substructure of the direct product of the lattices related to fragments. The structural properties underlie a procedure for extracting the global lattice from the direct product, which is the basis for a fullscale lattice construction algorithm implementing a divideandconquer strategy. The paper provides a complexity analysis of the algorithm together with some results about its practical performance and describes a class of binary relations for which the algorithm outperforms the most efficient latticeconstructing methods.
Weighted lattice polynomials
 Discrete Mathematics
"... We define the concept of weighted lattice polynomial functions as lattice polynomial functions constructed from both variables and parameters. We provide equivalent forms of these functions in an arbitrary bounded distributive lattice. We also show that these functions include the class of discrete ..."
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Cited by 8 (8 self)
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We define the concept of weighted lattice polynomial functions as lattice polynomial functions constructed from both variables and parameters. We provide equivalent forms of these functions in an arbitrary bounded distributive lattice. We also show that these functions include the class of discrete Sugeno integrals and that they are characterized by a remarkable median based decomposition formula. Key words: weighted lattice polynomial, lattice polynomial, bounded distributive lattice, discrete Sugeno integral. 1