Abstract
Because of the increasing size and complexity of available graph structures in experimental sciences like molecular biology, techniques of graph visualization tend to reach their limit. To assist experimental scientists into the understanding of the underlying phenomena, most visualization methods are based on the organization of edges and nodes in clusters. Among recent ones, Power Graph Analysis is a lossless compression of the graph based on the search of cliques and bicliques, improving the readability of the overall structure. Royer et al. introduced a heuristic approach providing approximate solutions to this NP-complete problem. Later, Bourneuf et al. formalized the heuristic using Formal Concept Analysis. This paper proposes to extend this work by a formalization of the graph compression search space. It shows that (1) the heuristic cannot always achieve an optimal compression, and (2) the concept lattice associated to a graph enables a more complete exploration of the search space. Our conclusion is that the search for graph compression can be usefully associated with the search for patterns in the concept lattice and that, conversely, confusing sets of objects and attributes brings new interesting problems for FCA.
Keywords
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ahnert, S.E.: Generalised power graph compression reveals dominant relationship patterns in complex networks. Sci. Rep. 4, 4385 (2014)
Bourneuf, L., Nicolas, J.: FCA in a logical programming setting for visualization-oriented graph compression. In: Bertet, K., Borchmann, D., Cellier, P., Ferré, S. (eds.) ICFCA 2017. LNCS (LNAI), vol. 10308, pp. 89–105. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59271-8_6
Chiaselotti, G., Ciucci, D., Gentile, T.: Simple undirected graphs as formal contexts. In: Baixeries, J., Sacarea, C., Ojeda-Aciego, M. (eds.) ICFCA 2015. LNCS (LNAI), vol. 9113, pp. 287–302. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-19545-2_18
Dwyer, T., Riche, N.H., Marriott, K., Mears, C.: Edge compression techniques for visualization of dense directed graphs. IEEE Trans. Vis. Comput. Graph. 19(12), 2596–2605 (2013)
Dwyer, T., Mears, C., Morgan, K., Niven, T., Marriott, K., Wallace, M.: Improved optimal and approximate power graph compression for clearer visualisation of dense graphs. CoRR, abs/1311.6996 (2013)
Gagneur, J., Krause, R., Bouwmeester, T., Casari, G.: Modular decomposition of protein-protein interaction networks. Genome Biol. 5(8), R57 (2004)
Habib, M., Paul, C.: A survey of the algorithmic aspects of modular decomposition. Comput. Sci. Rev. 4(1), 41–59 (2010)
Bernard, J., Seba, H.: Solving the maximal clique problem on compressed graphs. In: Ceci, M., Japkowicz, N., Liu, J., Papadopoulos, G.A., Raś, Z.W. (eds.) ISMIS 2018. LNCS (LNAI), vol. 11177, pp. 45–55. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-01851-1_5
King, A.D., Pržulj, N., Jurisica, I.: Protein complex prediction via cost-based clustering. Bioinformatics 20(17), 3013–3020 (2004)
Navlakha, S., Schatz, M.C., Kingsford, C.: Revealing biological modules via graph summarization. J. Comput. Biol. 16(2), 253–264 (2009)
Ogata, H., Fujibuchi, W., Goto, S., Kanehisa, M.: A heuristic graph comparison algorithm and its application to detect functionally related enzyme clusters. Nucleic Acids Res. 28(20), 4021–4028 (2000)
Papadopoulos, C., Voglis, C.: Drawing graphs using modular decomposition. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 343–354. Springer, Heidelberg (2006). https://doi.org/10.1007/11618058_31
Royer, L., Reimann, M., Andreopoulos, B., Schroeder, M.: Unraveling protein networks with power graph analysis. PLoS Comput. Biol. 4(7), e1000108 (2008)
Serafino, P.: Speeding up graph clustering via modular decomposition based compression. In: Proceedings of the 28th Annual ACM Symposium on Applied Computing, SAC 2013, pp. 156–163. ACM, New York (2013)
Tsatsaronis, G., Reimann, M., Varlamis, I., Gkorgkas, O., Nørvåg, K.: Efficient community detection using power graph analysis. In: Proceedings of the 9th Workshop on Large-scale and Distributed Informational Retrieval, LSDS-IR 2011, pp. 21–26. ACM, New York (2011)
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Bourneuf, L., Nicolas, J. (2019). Concept Lattices as a Search Space for Graph Compression. In: Cristea, D., Le Ber, F., Sertkaya, B. (eds) Formal Concept Analysis. ICFCA 2019. Lecture Notes in Computer Science(), vol 11511. Springer, Cham. https://doi.org/10.1007/978-3-030-21462-3_18
Download citation
DOI: https://doi.org/10.1007/978-3-030-21462-3_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-21461-6
Online ISBN: 978-3-030-21462-3
eBook Packages: Computer ScienceComputer Science (R0)