Abstract
Formal concept analysis (FCA) is a well-founded method for data analysis and has many applications in data mining. Pattern structures is an extension of FCA for dealing with complex data such as sequences or graphs. However the computational complexity of computing with pattern structures is high and projections of pattern structures were introduced for simplifying computation. In this paper we introduce o-projections of pattern structures, a generalization of projections which defines a wider class of projections preserving the properties of the original approach. Moreover, we show that o-projections form a semilattice and we discuss the correspondence between o-projections and the representation contexts of o-projected pattern structures.
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
Similar content being viewed by others
Notes
- 1.
We use the expression “a projected pattern structure” instead of “a projection of a pattern structure” to distinguish between projection as an operator \(\psi \) and as the result of applying the operator to a pattern structure.
References
Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations, 1st edn. Springer, Heidelberg (1999)
Ganter, B., Kuznetsov, S.O.: Pattern structures and their projections. In: Delugach, H.S., Stumme, G. (eds.) ICCS 2001. LNCS (LNAI), vol. 2120, pp. 129–142. Springer, Heidelberg (2001)
Ganter, B., Grigoriev, P.A., Kuznetsov, S.O., Samokhin, M.V.: Concept-based data mining with scaled labeled graphs. In: Wolff, K.E., Pfeiffer, H.D., Delugach, H.S. (eds.) ICCS 2004. LNCS (LNAI), vol. 3127, pp. 94–108. Springer, Heidelberg (2004)
Kuznetsov, S.O., Samokhin, M.V.: Learning closed sets of labeled graphs for chemical applications. In: Kramer, S., Pfahringer, B. (eds.) ILP 2005. LNCS (LNAI), vol. 3625, pp. 190–208. Springer, Heidelberg (2005)
Buzmakov, A., Egho, E., Jay, N., Kuznetsov, S.O., Napoli, A., Raïssi, C.: On projections of sequential pattern structures (with an application on care trajectories). In: Proceeding of the 10th International Conference on Concept Lattices Their Application, pp. 199–208 (2013)
Kaytoue, M., Kuznetsov, S.O., Napoli, A., Duplessis, S.: Mining gene expression data with pattern structures in formal concept analysis. Inf. Sci. (Ny) 181(10), 1989–2001 (2011)
Kuznetsov, S.O.: A fast algorithm for computing all intersections of objects from an arbitrary semilattice. Nauchno-Tekhnicheskaya Informatsiya Seriya 2 (Autom. Doc. Mathem. Ling.) (1), 17–20 (1993)
Kaiser, T.B., Schmidt, S.E.: Some remarks on the relation between annotated ordered sets and pattern structures. In: Kuznetsov, S.O., Mandal, D.P., Kundu, M.K., Pal, S.K. (eds.) PReMI 2011. LNCS, vol. 6744, pp. 43–48. Springer, Heidelberg (2011)
Acknowledgments
This research was supported by the Basic Research Program at the National Research University Higher School of Economics (Moscow, Russia) and by the BioIntelligence project (France). The second author was also supported by a grant from Russian Foundation for Basic Research, grant no. 13-0700504.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Buzmakov, A., Kuznetsov, S.O., Napoli, A. (2015). Revisiting Pattern Structure Projections. In: Baixeries, J., Sacarea, C., Ojeda-Aciego, M. (eds) Formal Concept Analysis. ICFCA 2015. Lecture Notes in Computer Science(), vol 9113. Springer, Cham. https://doi.org/10.1007/978-3-319-19545-2_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-19545-2_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19544-5
Online ISBN: 978-3-319-19545-2
eBook Packages: Computer ScienceComputer Science (R0)