A proposal for extending formal concept analysis to knowledge graphs. (English) Zbl 1312.68187
Baixeries, Jaume (ed.) et al., Formal concept analysis. 13th international conference, ICFCA 2015, Nerja, Spain, June 23–26, 2015. Proceedings. Cham: Springer (ISBN 978-3-319-19544-5/pbk; 978-3-319-19545-2/ebook). Lecture Notes in Computer Science 9113. Lecture Notes in Artificial Intelligence, 271-286 (2015).
Summary: Knowledge graphs offer a versatile knowledge representation, and have been studied under different forms, such as conceptual graphs or Datalog databases. With the rise of the Semantic Web, more and more data are available as knowledge graphs. FCA has been successful for analyzing, mining, learning, and exploring tabular data, and our aim is to help transpose those results to graph-based data. Previous FCA approaches have already addressed relational data, hence graphs, but with various limits. We propose G-FCA as an extension of FCA where the formal context is a knowledge graph based on \(n\)-ary relationships. The main contributions is the introduction of “\(n\)-ary concepts”, i.e. concepts whose extents are \(n\)-ary relations of objects. Their intents, “projected graph patterns”, mix relationships of different arities, objects, and variables. In this paper, we lay first theoretical results, in particular the existence of a concept lattice for each concept arity, and the role of relational projections to connect those different lattices.
For the entire collection see [Zbl 1312.68004].
For the entire collection see [Zbl 1312.68004].
MSC:
| 68T30 | Knowledge representation |
| 68R10 | Graph theory (including graph drawing) in computer science |
| 68T05 | Learning and adaptive systems in artificial intelligence |
Keywords:
formal concept analysis; knowledge graph; semantic web; graph pattern; relation; projectionSoftware:
SPARQLReferences:
| [1] | Allard, P.; Ferré, S.; Ridoux, O.; Kryszkiewicz, M.; Obiedkov, S., Discovering functional dependencies and association rules by navigating in a lattice of OLAP views, Concept Lattices and Their Applications, 199-210 (2010), Sevilla: CEUR-WS, Sevilla |
| [2] | Baader, F.; Calvanese, D.; McGuinness, DL; Nardi, D.; Patel-Schneider, PF, The Description Logic Handbook: Theory, Implementation, and Applications (2003), Cambridge: Cambridge University Press, Cambridge · Zbl 1058.68107 |
| [3] | Baader, F.; Distel, F.; Medina, R.; Obiedkov, S., A finite basis for the set of EL-implications holding in a finite model, Formal Concept Analysis, 46-61 (2008), Heidelberg: Springer, Heidelberg · Zbl 1132.68056 · doi:10.1007/978-3-540-78137-0_4 |
| [4] | Ceri, S.; Gottlob, G.; Tanca, L., What you always wanted to know about datalog (and never dared to ask), IEEE Trans. Knowl. Data Eng., 1, 1, 146-166 (1989) · doi:10.1109/69.43410 |
| [5] | Chein, M.; Mugnier, ML, Graph-Based Knowledge Representation: Computational Foundations of Conceptual Graphs (2008), London: Springer, London |
| [6] | Ferré, S.; Kwuida, L.; Sertkaya, B., Conceptual navigation in RDF graphs with SPARQL-like queries, Formal Concept Analysis, 193-208 (2010), Heidelberg: Springer, Heidelberg · Zbl 1274.68110 · doi:10.1007/978-3-642-11928-6_14 |
| [7] | Ferré, S.; Ridoux, O.; Ganter, B.; Mineau, GW, A logical generalizationof formal concept analysis, Conceptual Structures: Logical, Linguistic, and Computational Issues, 371-384 (2000), Heidelberg: Springer, Heidelberg · Zbl 0973.68219 · doi:10.1007/10722280_26 |
| [8] | Ferré, S.; Ridoux, O.; Priss, U.; Corbett, DR; Angelova, G., The use of associative concepts in the incremental building of a logical context, Conceptual Structures: Integration and Interfaces, 299 (2002), Heidelberg: Springer, Heidelberg · Zbl 1067.68688 · doi:10.1007/3-540-45483-7_23 |
| [9] | Ganter, B.; Kuznetsov, SO; Delugach, HS; Stumme, G., Pattern structures and their projections, Conceptual Structures: Broadening the Base, 129 (2001), Heidelberg: Springer, Heidelberg · Zbl 0994.68147 · doi:10.1007/3-540-44583-8_10 |
| [10] | Ganter, B.; Wille, R., Formal Concept Analysis - Mathematical Foundations (1999), Heidelberg: Springer, Heidelberg · Zbl 0909.06001 · doi:10.1007/978-3-642-59830-2 |
| [11] | Hitzler, P.; Krötzsch, M.; Rudolph, S., Foundations of Semantic Web Technologies (2009), London: Chapman & Hall/CRC, London |
| [12] | Kötters, J.; Pfeiffer, HD; Ignatov, DI; Poelmans, J.; Gadiraju, N., Concept lattices of a relational structure, Conceptual Structures for STEM Research and Education, 301-310 (2013), Heidelberg: Springer, Heidelberg · Zbl 1351.68277 · doi:10.1007/978-3-642-35786-2_23 |
| [13] | Kuznetsov, SO; Samokhin, MV; Kramer, S.; Pfahringer, B., Learning closed sets of labeled graphs for chemical applications, Inductive Logic Programming, 190-208 (2005), Heidelberg: Springer, Heidelberg · Zbl 1134.68476 · doi:10.1007/11536314_12 |
| [14] | Kuznetsov, SO; Cellier, P.; Distel, F.; Ganter, B., Fitting pattern structures to knowledge discovery in big data, Formal Concept Analysis, 254-266 (2013), Heidelberg: Springer, Heidelberg · Zbl 1397.68173 · doi:10.1007/978-3-642-38317-5_17 |
| [15] | Muggleton, S.; Raedt, LD, Inductive logic programming: theory and methods, J. Logic Program., 19, 20, 629-679 (1994) · Zbl 0816.68043 · doi:10.1016/0743-1066(94)90035-3 |
| [16] | Rouane-Hacene, M.; Huchard, M.; Napoli, A.; Valtchev, P., Relational concept analysis: mining concept lattices from multi-relational data, Annals Math. Artif. Intell., 67, 1, 81-108 (2013) · Zbl 1297.68220 · doi:10.1007/s10472-012-9329-3 |
| [17] | Schmachtenberg, M.; Bizer, C.; Paulheim, H.; Mika, P.; Tudorache, T.; Bernstein, A.; Welty, C.; Knoblock, C.; Vrandečić, D.; Groth, P.; Noy, N.; Janowicz, K.; Goble, C., Adoption of the linked data best practices in different topical domains, The Semantic Web - ISWC 2014, 245-260 (2014), Heidelberg: Springer, Heidelberg · doi:10.1007/978-3-319-11964-9_16 |
| [18] | Wille, R.; Lukose, D.; Delugach, H.; Keeler, M.; Searle, L.; Sowa, J., Conceptual graphs and formal concept analysis, Conceptual Structures: Fulfilling Peirce’s Dream, 290-303 (1997), Springer: Springer, Springer · doi:10.1007/BFb0027878 |
| [19] | Yan, X., Han, J.: Closegraph: mining closed frequent graph patterns. In: ACM International Conference on Knowledge Discovery and Data Mining (SIGKDD). pp. 286-295. ACM (2003) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
