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An Introduction to Symbolic Data Analysis and the Sodas Software
 Journal of Symbolic Data Analysis
, 2003
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Extracting Formal Concepts out of Relational Data
 Proceedings of the 4th Intl. Conference Journées de l’Informatique Messine (JIM’03): Knowledge Discovery and Discrete Mathematics, Metz (FR), 36 September
, 2003
"... Relational datasets, i.e., datasets in which individuals are described both by their own features and by their relations to other individuals, arise from various sources such as databases, both relational and objectoriented, or software models, e.g., UML class diagrams. When processing such complex ..."
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Cited by 7 (5 self)
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Relational datasets, i.e., datasets in which individuals are described both by their own features and by their relations to other individuals, arise from various sources such as databases, both relational and objectoriented, or software models, e.g., UML class diagrams. When processing such complex datasets, it is of prime importance for an analysis tool to hold as much as possible to the initial format so that the semantics is preserved and the interpretation of the final results eased. There have been several attempts to introduce relations into the Galois lattice and formal concept analysis fields. We propose a novel approach to this problem which relies on an enhanced version of the classical binary data descriptions based on the distinction of several mutually related formal contexts. Key Words: Galois lattices, conceptual scaling, lattice constructing algorithms, relational information. 1
Similaritybased Clustering versus Galois lattice building: Strengths and Weaknesses
 Workshop ’Objects and Classification, A Natural Convergence’. European Conference on ObjectOriented Programming
, 2000
"... In many realworld applications, designers tend towards building classes of objects such as concepts, chunks and clusters according to some similarity criteria. In this paper, we first compare two approaches to clustering: the Galois lattice approach [14] and a similaritybased clustering approac ..."
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Cited by 3 (0 self)
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In many realworld applications, designers tend towards building classes of objects such as concepts, chunks and clusters according to some similarity criteria. In this paper, we first compare two approaches to clustering: the Galois lattice approach [14] and a similaritybased clustering approach [27]. Then, we sketch the possible ways each approach can benefit from the other in refining the process of building a hierarchy of classes out of a set of instances.
A fast and general algorithm for Galois lattices building
 J. of Symbolic Data Analysis
, 2005
"... Standard Galois Lattices are effective tools for data analysis and knowledge discovery. They allow structuring data sets, by extracting concepts and rules to deduce concepts from other concepts. They focus on binary data arrays, called contexts. Several algorithms were proposed to generate concepts ..."
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Standard Galois Lattices are effective tools for data analysis and knowledge discovery. They allow structuring data sets, by extracting concepts and rules to deduce concepts from other concepts. They focus on binary data arrays, called contexts. Several algorithms were proposed to generate concepts or concept lattices on a data context. However, the mining of large databases needs more efficient algorithms. Nowadays, we need to deal with contexts which are large and not necessarily binary. In this paper, we propose a new and fast Galois latticebuilding algorithm, called ELL algorithm, for generating closed itemsets from objects having general descriptions; and a generalization of the Ganter algorithm (GGA). A comparison of performance between GGA, ELL, and another published algorithm, called Close By One, is presented. 1
Knowledge Discovery From Symbolic Data And The Sodas Software
 Conf. on Principles and Practice of Knowledge Discovery in Databases, PPKDD2000
, 2000
"... The data descriptions of the units are called "symbolic" when they are more complex than the standard ones due to the fact that they contain internal variation and are structured. Symbolic data happen from many sources, for instance in order to summarise huge Relational Data Bases by t ..."
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The data descriptions of the units are called "symbolic" when they are more complex than the standard ones due to the fact that they contain internal variation and are structured. Symbolic data happen from many sources, for instance in order to summarise huge Relational Data Bases by their underlying concepts. "Extracting knowledge" means getting explanatory results, that why, "symbolic objects" are introduced and studied in this paper. They model concepts and constitute an explanatory output for data analysis. Moreover they can be used in order to define queries of a Relational Data Base and propagate concepts between Data Bases. We define "Symbolic Data Analysis" (SDA) as the extension of standard Data Analysis to symbolic data tables as input in order to find symbolic objects as output. In this paper we give an overview on recent development on SDA. We present some tools and methods of SDA and introduce the SODAS software prototype (issued from the work of 17 teams of nine countries involved in an European project of EUROSTAT). 1
STRUCTURING PROBABILISTIC DATA BY GALOIS LATTICES
 MATH. & SCI. HUM. / MATHEMATICS AND SOCIAL SCIENCES (43 E ANNÉE, N ° 169, 2005(1), P. 77104)
, 2005
"... In this paper we address the problem of organising probabilistic data by Galois concept lattices. Two lattices are proposed, the union lattice and the intersection lattice, corresponding to two distinct semantics, by choosing accordingly the join and meet operators. A new algorithm is proposed to c ..."
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In this paper we address the problem of organising probabilistic data by Galois concept lattices. Two lattices are proposed, the union lattice and the intersection lattice, corresponding to two distinct semantics, by choosing accordingly the join and meet operators. A new algorithm is proposed to construct the concept lattice. Two real data examples illustrate the presented approach.
A Adistributed version version of the of Ganter the Ganter algorithm algorithm for general for general Galois Galois Lattices Lattices
"... Abstract. Standard Galois Lattices are effective tools for data analysis and knowledge discovery. Several algorithms were proposed to generate concepts of lattices, among which the ScalingNextClosure algorithm. In order to share the production workload between several processors when the number of c ..."
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Abstract. Standard Galois Lattices are effective tools for data analysis and knowledge discovery. Several algorithms were proposed to generate concepts of lattices, among which the ScalingNextClosure algorithm. In order to share the production workload between several processors when the number of closed itemsets to determine is very large, this algorithm leans on the sequential character of the closed itemsets determination of a Galois Lattice by the Ganter algorithm. In this paper, we prove that the parallelised version of the ScalingNextClosure can be extended to more general contexts (even some complex data) than usual binary contexts and that the partition of the workload between processors can be made with all the wished precision. 1
A fast and general algorithm to build Galois lattices
"... Standard Galois Lattices are effective tools for data analysis and knowledge discovery. Many research works in classification or association rules increase the interest of them for data mining. They allow structuring data sets, by extracting concepts and rules to deduce concepts from other concepts. ..."
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Standard Galois Lattices are effective tools for data analysis and knowledge discovery. Many research works in classification or association rules increase the interest of them for data mining. They allow structuring data sets, by extracting concepts and rules to deduce concepts from other concepts. They concern binary data arrays, called contexts. Several algorithms were proposed to generate concepts of lattices, among which Ganter algorithm is the best one for large contexts. However, it’s also hard to face the complexity of large data with Ganter algorithm. So we propose a new and fast Galois latticebuilding algorithm GL which works for objects having very general descriptions. And we propose a way to parallelise large context.
Ann Math Artif Intell (2007) 49:39–76 DOI 10.1007/s1047200790563 Relational concept discovery in structured datasets
, 2007
"... Abstract Relational datasets, i.e., datasets in which individuals are described both by their own features and by their relations to other individuals, arise from various sources such as databases, both relational and objectoriented, knowledge bases, or software models, e.g., UML class diagrams. Wh ..."
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Abstract Relational datasets, i.e., datasets in which individuals are described both by their own features and by their relations to other individuals, arise from various sources such as databases, both relational and objectoriented, knowledge bases, or software models, e.g., UML class diagrams. When processing such complex datasets, it is of prime importance for an analysis tool to hold as much as possible to the initial format so that the semantics is preserved and the interpretation of the final results eased. Therefore, several attempts have been made to introduce relations into the formal concept analysis field which otherwise generated a large number of knowledge discovery methods and tools. However, the proposed approaches invariably look at relations as an intraconcept construct, typically relating two parts of the concept description, and therefore can only lead to the discovery of coarsegrained patterns. As an approach towards the discovery of finergrain relational concepts, we propose to enhance the classical (object × attribute) data representations with a new dimension that is made out of interobject links (e.g., spouse, friend, managerof, etc.). Consequently, the discovered concepts are linked by relations which, like
Abstract Galois Connections, TCUBES & Database Mining
"... Galois connections are the bread and butter of the formal concept analysis. The universe of discourse there is the collections of objects with properties. A property corresponds typically to a singlevalued (.true or null) binary attribute of the object. Probably the most studied connections are the ..."
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Galois connections are the bread and butter of the formal concept analysis. The universe of discourse there is the collections of objects with properties. A property corresponds typically to a singlevalued (.true or null) binary attribute of the object. Probably the most studied connections are the closed sets and Galois lattices. We propose a generalization of these connections to the relational database universe with the multivalued domains. We show the database mining queries that appear from, hard or impossible to formulate with SQL at present. We further show that the groups produced by the popular CUBE operator form a type of multivalued closed sets, including the traditional binary closed sets. To deal with more types of closed sets, we generalize CUBE to a new operator we call θCUBE, writing it TCUBE. This one calculates the groups according to all the values of the θ operator popular with the relational joins, namely θ = {=, ≤, <, <>, ≥,>}. The θ = ‘= ’ defines the CUBE. The generalization applies naturally also to GROUP BY and to the other popular SQL grouping operators. We further show the utility of the aggregate function LIST and of a new one that we have named TGROUP. The couple conveniently aggregates the composition of a closed set produced by TCUBE into a single tuple. We finally discuss the algorithms for the computation of the queries involving the closed sets. Unlike perhaps for the concept analysis, the scalable distributed algorithms in P2P or grid environment appear the most useful for the database mining in practice. Our proposals should benefit to both the database mining and the concept analysis over larger collections of objects. 1