Abstract
The article introduces a representation of a formal context by an undirected graph called a context graph with the formal objects being the nodes of the graph. We use as a defining property for this graph that it contains every concept extent as a connected subgraph. The graph is not uniquely defined by this property — we focus on those graphs that are edge-minimal and present a result with respect to the number of their edges. We then study how the structure of an edge-minimal context graph can be updated to adjust to the subsequent addition of an object to the context. This leads to an incremental construction algorithm that does not require the explicit computation of formal concepts.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ganter, B., Wille, R.: Formal concept analysis: mathematical foundations. Springer, Berlin (1999)
Wille, R.: Concept lattices and conceptual knowledge systems. Computers and Mathematics with Applications 23(6–9), 493–515 (1992)
Davis, A., Gardner, B.B., Gardner, M.R.: Deep South. Univ. Chicago Press, Chicago (1941)
Kuznetsov, S.O., Obiedkov, S.A.: Comparing performance of algorithms for generating concept lattices. Journal of Experimental and Theoretical Artificial Intelligence 14, 189–216 (2002)
Priss, U.: Lattice-based information retrieval. Knowledge Organization 27(3), 132–142 (2000)
Carpineto, C.: Conceptual structures in modern information retrieval. In: [16], p. 1
Delteil, A., Faron, C., Dieng, R.: Building concept lattices by learning concepts from RDF graphs annotating web documents. In: [16], pp. 191–204
Duquenne, V., Chabert, C., Cherfouh, A., Delabar, J.M., Doyen, A.L., Pickering, D.: Structuration of phenotypes/genotypes through Galois lattices and implications. In: The 2001 International Workshop on Concept Lattice-based theory, methods and tools for Knowledge Discovery in Databases, Stanford University, CA, USA, July 30 (2001)
Godin, R., Mili, H.: Building and maintaining analysis-level class hierarchies using Galois lattices. In: Paepcke, A. (ed.) The Conference on Object-oriented Programming Systems, Languages and Applications, Washington, DC, pp. 394–410 (1993)
Carpineto, C., Romano, G.: Information retrieval through hybrid navigation of lattice representations. International Journal of Human-Computer Studies 45(5), 553–578 (1996)
ter Hofstede, A.H.M., Proper, H.A., van der Weide, T.P.: Query formulation as an information retrieval problem. The Computer Journal 39(4), 255–274 (1996)
Ferré, S.: CAMELIS: Organizing and browsing a personal photo collection with a logical information system. In: Diatta, J., Eklund, P., Liquière, M. (eds.) The International Conference on Concept Lattices and Their Applications. CEUR Workshop Proceedings, vol. 331, pp. 112–123 (2007)
Lindig, C.: Fast concept analysis. In: Working with Conceptual Structures - Contributions to ICCS 2000, pp. 152–161. Shaker Verlag (2000)
Breiger, R.L.: The duality of persons and groups. In: Wellman, B., Berkowitz, S.D. (eds.) Social Structures: A Network Approach, pp. 83–98. Cambridge University Press, Cambridge (1988)
Sowa, J.F.: Conceptual Structures: Information Processing in Mind and Machine. Addison-Wesley, Reading (1984)
Priss, U., Corbett, D.R., Angelova, G. (eds.): ICCS 2002. LNCS, vol. 2393. Springer, Heidelberg (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kötters, J., Schmidt, H., Squire, D.M. (2009). Context Graphs — Representing Formal Concepts by Connected Subgraphs. In: Ferré, S., Rudolph, S. (eds) Formal Concept Analysis. ICFCA 2009. Lecture Notes in Computer Science(), vol 5548. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01815-2_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-01815-2_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01814-5
Online ISBN: 978-3-642-01815-2
eBook Packages: Computer ScienceComputer Science (R0)