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Peter W. Eklund - One of the best experts on this subject based on the ideXlab platform.
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Using Formal Concept analysis to create pathways through museum collections
2014Co-Authors: Tim Wray, Peter W. EklundAbstract:This paper presents A Place for Art – an iPad app that allows users to explore an art collection via semantically linked pathways that are generated using Formal Concept Analysis. The app embraces the information seeking approach of exploration and is based on the idea that showing context and relationships among objects in a museum collection augments an interpretive experience. The fundamental interaction metaphor inherent in A Place for Art relies on Formal Concept Analysis so the interface has embedded within it the semantic clustering features of machine learning in artificial intelligence.
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Concept similarity and related categories in information retrieval using Formal Concept analysis
International Journal of General Systems, 2012Co-Authors: Peter W. Eklund, Jon Ducrou, Frithjof DauAbstract:The application of Formal Concept analysis to the problem of information retrieval has been shown useful but has lacked any real analysis of the idea of relevance ranking of search results. SearchSleuth is a program developed to experiment with the automated local analysis of Web search using Formal Concept analysis. SearchSleuth extends a standard search interface to include a Conceptual neighbourhood centred on a Formal Concept derived from the initial query. This neighbourhood of the Concept derived from the search terms is decorated with its upper and lower neighbours representing more general and special Concepts, respectively. SearchSleuth is in many ways an archetype of search engines based on Formal Concept analysis with some novel features. In SearchSleuth, the notion of related categories – which are themselves Formal Concepts – is also introduced. This allows the retrieval focus to shift to a new Formal Concept called a sibling. This movement across the Concept lattice needs to relate one forma...
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PKAW - Navigation and Annotation with Formal Concept Analysis
Knowledge Acquisition: Approaches Algorithms and Applications, 2009Co-Authors: Peter W. Eklund, Jon DucrouAbstract:AnnotationSleuth is software to experiment with knowledge acquisition using Formal Concept Analysis (FCA). The system extends a standard search and browsing interface to feature a Conceptual neighborhood centered on a Formal Concept derived from curatorial tags in a museum management system. The neighborhood of a Concept is decorated with upper and lower neighbors in a Concept lattice. Movement through the information space is achieved by the addition and removal of attributes resulting in more general and specialized Formal Concepts respectively. AnnotationSleuth employs several search methods: attribute search based on a control vocabulary, query refinement and query-by-example. A number of management interfaces are included to enable content to be added and tagged, the control vocabulary to be extended or Conceptual scales to be defined. AnnotationSleuth, is an extensible environment for the creation of attribute lists and Conceptual scales and can subsequently be used to flexibly navigate a collection of digital objects based on any user-defined semantic theme.
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Dynamic schema navigation using Formal Concept analysis
Lecture Notes in Computer Science, 2005Co-Authors: Jon Ducrou, Bastian Wormuth, Peter W. EklundAbstract:This paper introduces a framework for relational schema navigation via a Web-based browser application that uses Formal Concept Analysis as the metaphor for analysis and interaction. Formal Concept Analysis is a rich framework for data analysis based on applied lattice and order theory. The application we develop, D-SIFT, is intended to provide users untrained in Formal Concept Analysis with practical and intuitive access to the core functionality of Formal Concept Analysis for the purpose of exploring relational database schema. D-SIFT is a Web-based information systems architecture that supports natural search processes over a preexisting database schema and its content.
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DaWaK - Dynamic schema navigation using Formal Concept analysis
Data Warehousing and Knowledge Discovery, 2005Co-Authors: Jon Ducrou, Bastian Wormuth, Peter W. EklundAbstract:This paper introduces a framework for relational schema navigation via a Web-based browser application that uses Formal Concept Analysis as the metaphor for analysis and interaction. Formal Concept Analysis is a rich framework for data analysis based on applied lattice and order theory. The application we develop, D-SIFT, is intended to provide users untrained in Formal Concept Analysis with practical and intuitive access to the core functionality of Formal Concept Analysis for the purpose of exploring relational database schema. D-SIFT is a Web-based information systems architecture that supports natural search processes over a preexisting database schema and its content.
Rudolf Wille - One of the best experts on this subject based on the ideXlab platform.
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Formal Concept analysis foundations and applications
2005Co-Authors: Bernhard Ganter, Gerd Stumme, Rudolf WilleAbstract:Foundations.- Formal Concept Analysis as Mathematical Theory of Concepts and Concept Hierarchies.- SemiConcept and ProtoConcept Algebras: The Basic Theorems.- Features of Interaction Between Formal Concept Analysis and Algebraic Geometry.- From Formal Concept Analysis to Contextual Logic.- Contextual Attribute Logic of Many-Valued Attributes.- Treating Incomplete Knowledge in Formal Concept Analysis.- States, Transitions, and Life Tracks in Temporal Concept Analysis.- Applications.- Linguistic Applications of Formal Concept Analysis.- Using Concept Lattices for Text Retrieval and Mining.- Efficient Mining of Association Rules Based on Formal Concept Analysis.- Galois Connections in Data Analysis: Contributions from the Soviet Era and Modern Russian Research.- Conceptual Knowledge Processing in the Field of Economics.- Software Engineering.- A Survey of Formal Concept Analysis Support for Software Engineering Activities.- Concept Lattices in Software Analysis.- Formal Concept Analysis Used for Software Analysis and Modelling.- Formal Concept Analysis-Based Class Hierarchy Design in Object-Oriented Software Development.- The ToscanaJ Suite for Implementing Conceptual Information Systems.
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Formal Concept Analysis - Formal Concept analysis as mathematical theory of Concepts and Concept hierarchies
Formal Concept Analysis, 2005Co-Authors: Rudolf WilleAbstract:Formal Concept Analysis has been originally developed as a subfield of Applied Mathematics based on the mathematization of Concept and Concept hierarchy. Only after more than a decade of development, the connections to the philosophical logic of human thought became clearer and even later the connections to Piaget's cognitive structuralism which Thomas Bernhard Seiler convincingly elaborated to a comprehensive theory of Concepts in his recent book [Se01]. It is the main concern of this paper to show the surprisingly rich correspondences between Seiler's multifarious aspects of Concepts in the human mind and the structural properties and relationships of Formal Concepts in Formal Concept Analysis. These correspondences make understandable, what has been experienced in a great multitude of applications, that Formal Concept Analysis may function in the sense of transdisciplinary mathematics, i.e., it allows mathematical thought to aggregate with other ways of thinking and thereby to support human thought and action.
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Formal Concept analysis as mathematical theory of Concepts and Concept hierarchies
Formal Concept Analysis, 2005Co-Authors: Rudolf WilleAbstract:Formal Concept Analysis has been originally developed as a subfield of Applied Mathematics based on the mathematization of Concept and Concept hierarchy. Only after more than a decade of development, the connections to the philosophical logic of human thought became clearer and even later the connections to Piaget's cognitive structuralism which Thomas Bernhard Seiler convincingly elaborated to a comprehensive theory of Concepts in his recent book [Se01]. It is the main concern of this paper to show the surprisingly rich correspondences between Seiler's multifarious aspects of Concepts in the human mind and the structural properties and relationships of Formal Concepts in Formal Concept Analysis. These correspondences make understandable, what has been experienced in a great multitude of applications, that Formal Concept Analysis may function in the sense of transdisciplinary mathematics, i.e., it allows mathematical thought to aggregate with other ways of thinking and thereby to support human thought and action.
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Formal Concept analysis mathematical foundations
1998Co-Authors: Bernhard Ganter, Rudolf Wille, C FranzkeAbstract:From the Publisher: This is the first textbook on Formal Concept analysis. It gives a systematic presentation of the mathematical foundations and their relation to applications in computer science, especially in data analysis and knowledge processing. Above all, it presents graphical methods for representing Conceptual systems that have proved themselves in communicating knowledge. Theory and graphical representation are thus closely coupled together. The mathematical foundations are treated thoroughly and illuminated by means of numerous examples.
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Conceptual graphs and Formal Concept analysis
International Conference on Conceptual Structures, 1997Co-Authors: Rudolf WilleAbstract:It is shown how Conceptual Graphs and Formal Concept Analysis may be combined to obtain a Formalization of Elementary Logic which is useful for knowledge representation and processing. For this, a translation of Conceptual graphs to Formal contexts and Concept lattices is described through an example. Using a suitable mathematization of Conceptual graphs, basics of a unified mathematical theory for Elementary Logic are proposed.
Jon Ducrou - One of the best experts on this subject based on the ideXlab platform.
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Concept similarity and related categories in information retrieval using Formal Concept analysis
International Journal of General Systems, 2012Co-Authors: Peter W. Eklund, Jon Ducrou, Frithjof DauAbstract:The application of Formal Concept analysis to the problem of information retrieval has been shown useful but has lacked any real analysis of the idea of relevance ranking of search results. SearchSleuth is a program developed to experiment with the automated local analysis of Web search using Formal Concept analysis. SearchSleuth extends a standard search interface to include a Conceptual neighbourhood centred on a Formal Concept derived from the initial query. This neighbourhood of the Concept derived from the search terms is decorated with its upper and lower neighbours representing more general and special Concepts, respectively. SearchSleuth is in many ways an archetype of search engines based on Formal Concept analysis with some novel features. In SearchSleuth, the notion of related categories – which are themselves Formal Concepts – is also introduced. This allows the retrieval focus to shift to a new Formal Concept called a sibling. This movement across the Concept lattice needs to relate one forma...
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PKAW - Navigation and Annotation with Formal Concept Analysis
Knowledge Acquisition: Approaches Algorithms and Applications, 2009Co-Authors: Peter W. Eklund, Jon DucrouAbstract:AnnotationSleuth is software to experiment with knowledge acquisition using Formal Concept Analysis (FCA). The system extends a standard search and browsing interface to feature a Conceptual neighborhood centered on a Formal Concept derived from curatorial tags in a museum management system. The neighborhood of a Concept is decorated with upper and lower neighbors in a Concept lattice. Movement through the information space is achieved by the addition and removal of attributes resulting in more general and specialized Formal Concepts respectively. AnnotationSleuth employs several search methods: attribute search based on a control vocabulary, query refinement and query-by-example. A number of management interfaces are included to enable content to be added and tagged, the control vocabulary to be extended or Conceptual scales to be defined. AnnotationSleuth, is an extensible environment for the creation of attribute lists and Conceptual scales and can subsequently be used to flexibly navigate a collection of digital objects based on any user-defined semantic theme.
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Dynamic schema navigation using Formal Concept analysis
Lecture Notes in Computer Science, 2005Co-Authors: Jon Ducrou, Bastian Wormuth, Peter W. EklundAbstract:This paper introduces a framework for relational schema navigation via a Web-based browser application that uses Formal Concept Analysis as the metaphor for analysis and interaction. Formal Concept Analysis is a rich framework for data analysis based on applied lattice and order theory. The application we develop, D-SIFT, is intended to provide users untrained in Formal Concept Analysis with practical and intuitive access to the core functionality of Formal Concept Analysis for the purpose of exploring relational database schema. D-SIFT is a Web-based information systems architecture that supports natural search processes over a preexisting database schema and its content.
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DaWaK - Dynamic schema navigation using Formal Concept analysis
Data Warehousing and Knowledge Discovery, 2005Co-Authors: Jon Ducrou, Bastian Wormuth, Peter W. EklundAbstract:This paper introduces a framework for relational schema navigation via a Web-based browser application that uses Formal Concept Analysis as the metaphor for analysis and interaction. Formal Concept Analysis is a rich framework for data analysis based on applied lattice and order theory. The application we develop, D-SIFT, is intended to provide users untrained in Formal Concept Analysis with practical and intuitive access to the core functionality of Formal Concept Analysis for the purpose of exploring relational database schema. D-SIFT is a Web-based information systems architecture that supports natural search processes over a preexisting database schema and its content.
Henri Prade - One of the best experts on this subject based on the ideXlab platform.
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possibility theory and Formal Concept analysis characterizing independent sub contexts
Fuzzy Sets and Systems, 2012Co-Authors: Didier Dubois, Henri PradeAbstract:Formal Concept analysis is a lattice-theoretic framework devised for the extraction of knowledge from Boolean data tables. A possibility-theoretic view of Formal Concept analysis has been recently introduced, and in particular set-valued counterparts of the four set-functions, respectively, evaluating potential or actual, possibility or necessity, that underlie bipolar possibility theory. It enables us to retrieve an enlarged perspective for Formal Concept analysis, already laid bare by some researchers like Dunsch and Gediga, or Georgescu and Popescu. The usual (Galois) connection that defines the notion of a Formal Concept as the pair of its extent and its intent is based on the actual (or guaranteed) possibility function, where each object in a Concept has all properties of its intent, and each property is possessed by all objects of its extent. Noticing the Formal similarity between the operator underlying classical Formal Concept analysis and the notion of division in relational algebra, we briefly indicate how to define approximate Concepts by relaxing the universal quantifier in the definition of intent and extent as already done for relational divisions. The main thrust of the paper is the detailed study of another connection based on the counterpart to necessity measures. We show that it leads to partition a Formal context into disjoint subsets of objects having distinct properties, and to split a data table into independent sub-tables.
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possibility theory and Formal Concept analysis context decomposition and uncertainty handling
Information Processing and Management of Uncertainty, 2010Co-Authors: Yassine Djouadi, Didier Dubois, Henri PradeAbstract:Formal Concept Analysis uses a simple representation framework called 'Formal context'. In the classical setting, a Formal context specifies existing Boolean relationships between a set of objects and their corresponding properties. Formal Concepts are then defined as pairs consisting of a set of objects and a set of properties that mutually characterize each other through a Galois connection. Another Galois connection is also introduced in this setting on the basis of operators induced by a recent possibility theory reading of Formal Concept Analysis. It is shown that this second Galois connection enables us to characterize independent sub-contexts inside the Formal context. The second part of the paper discusses an extension of Formal Concept Analysis that has not been much studied, namely the situation where one may be uncertain on the fact that an object possesses or not a Boolean property. Uncertainty is here represented in the possibilistic representation framework.
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A Parallel between Extended Formal Concept Analysis and Bipartite Graphs Analysis
2010Co-Authors: Bruno Gaume, Emmanuel Navarro, Henri PradeAbstract:The paper offers a parallel between two approaches to con- ceptual clustering, namely Formal Concept analysis (augmented with the introduction of new operators) and bipartite graph analysis. It is shown that a Formal Concept (as defined in Formal Concept analysis) corresponds to the idea of a maximal bi-clique, while a “Conceptual world” (defined through a Galois connection associated of the new operators) is a dis- connected sub-graph in a bipartite graph. The parallel between Formal Concept analysis and bipartite graph analysis is further exploited by con- sidering “approximation” methods on both sides. It leads to suggests new ideas for providing simplified views of datasets.
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A Possibility-Theoretic View of Formal Concept Analysis
Fundamenta Informaticae, 2007Co-Authors: Didier Dubois, Florence Dupin De Saint-cyr, Henri PradeAbstract:The paper starts from the standard relational view linking objects and properties in Formal Concept analysis, here augmented with four modal-style operators (known as sufficiency, dual sufficiency, necessity and possibility operators). Formal Concept analysis is mainly based on the first operator, while the others come from qualitative data analysis and can be also related to rough set theory. A possibility-theoretic reading of Formal Concept analysis with these four operators is proposed. First, it is shown that four and only four operators are indeed needed in order to describe the nine situations that can occur when comparing a statement (or its negation) with a state of information. The parallel between possibility theory and Formal Concept analysis suggests the introduction of new notions such as normalization and conditioning in the latter framework, also leading to point out some meaningful properties. Moreover, the graded setting of possibility theory allows us to suggest the extension of Formal Concept analysis to situations with incomplete or uncertain information.
Yaohua Chen - One of the best experts on this subject based on the ideXlab platform.
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rough set approximations in Formal Concept analysis
Lecture Notes in Computer Science, 2006Co-Authors: Yiyu Yao, Yaohua ChenAbstract:A basic notion shared by rough set analysis and Formal Concept analysis is the definability of a set of objects based on a set of properties. The two theories can be compared, combined and applied to each other based on definability. In this paper, the notion of rough set approximations is introduced into Formal Concept analysis. Rough set approximations are defined by using a system of definable sets. The similar idea can be used in Formal Concept analysis. The families of the sets of objects and the sets of properties established in Formal Concept analysis are viewed as two systems of definable sets. The approximation operators are then formulated with respect to the systems. Two types of approximation operators, with respect to lattice-theoretic and set-theoretic interpretations, are studied. The results provide a better understanding of data analysis using rough set analysis and Formal Concept analysis.
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Trans. Rough Sets - Rough set approximations in Formal Concept analysis
Lecture Notes in Computer Science, 2006Co-Authors: Yiyu Yao, Yaohua ChenAbstract:A basic notion shared by rough set analysis and Formal Concept analysis is the definability of a set of objects based on a set of properties. The two theories can be compared, combined and applied to each other based on definability. In this paper, the notion of rough set approximations is introduced into Formal Concept analysis. Rough set approximations are defined by using a system of definable sets. The similar idea can be used in Formal Concept analysis. The families of the sets of objects and the sets of properties established in Formal Concept analysis are viewed as two systems of definable sets. The approximation operators are then formulated with respect to the systems. Two types of approximation operators, with respect to lattice-theoretic and set-theoretic interpretations, are studied. The results provide a better understanding of data analysis using rough set analysis and Formal Concept analysis.
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rough set approximations in Formal Concept analysis
North American Fuzzy Information Processing Society, 2004Co-Authors: Yiyu Yao, Yaohua ChenAbstract:An important topic of rough set theory is the approximation of undefinable sets or Concepts through definable sets. It involves the construction of a system of definable sets and the definition of approximation operators. In this paper, the notion of rough set approximations is introduced into Formal Concept analysis. Approximation operators are defined based on both lattice-theoretic and set-theoretic operators. The results provide a better understanding of data analysis using rough set theory and Formal Concept analysis.
