Análise Formal de Conceitos Triádicos através da utilização de Diagramas Binários de Decisão

  • Kaio H. A. Ananias PUC-MG
  • Julio C. V. Neves PUC-MG
  • Luis E. Zárate PUC-MG
  • Mark A. J. Song PUC-MG

Resumo


Formal Concept Analysis (FCA) is an approach based on the mathematization and hierarchy of formal concepts. Nowadays, with the increasing of social network for personal and professional usage, more and more applications of data analysis on environments with high dimensionality (Big Data) have been discussed in the literature. Through the Formal Concept Analysis and Triadic Concept Analysis, it is possible to extract database knowledge in a hierarchical and systematized respresentation. It is common that the data set transforms the extraction of this knowledge into a problem of high computational cost. Therefore, this work has an objective to evaluate the behavior of the algorithm for extraction in order to extract triadic concepts using TRIAS with high dimensional contexts. It was used a synthetic generator known as SCGaz (Synthetic Context Generator a-z). After the analisys, it was proposed a representation of triadic contexts using a structure known as Binary Decision Diagram (BDD).

Palavras-chave: Formal Concept Analysis, Triadic Concept Analisys, Data Mining, Binary Decision Diagram

Referências

Akers, S. B. (1978). Binary decision diagrams. IEEE Transactions on Computers, C-27(6):509–516.

Bryant, R. E. (1986). Graph-based algorithms for boolean function manipulation. Computers, IEEE Transactions on, 100(8):677–691.

Cerf, L. and Besson, J.and Robardet, C. B. J. (2009). Closed patterns meet n-ary relations. pages 1–36.

Ganter, B. and Wille, R. (1999). Formal concept analysis: mathematical foundations.

Jaschke, R., Hotho, A., Schmitz, C., Ganter, B., and Stumme, G. (2006). Trias–an algorithm for mining iceberg tri-lattices. In Data Mining, 2006. ICDM’06. Sixth International Conference on, pages 907–911. IEEE.

Lehmann, F. and Wille, R. (1995). A triadic approach to formal concept analysis. Conceptual structures: applications, implementation and theory, pages 32–43.

Missaoui, R. and Kwuida, L. (2011). Mining triadic association rules from ternary relations. Formal Concept Analysis, pages 204–218.

Neto, S. M., Zárate, L. E., and Song, M. A. (2018). Handling high dimensionality contexts in formal concept analysis via binary decision diagrams. Information Sciences, 429:361–376.

Old, J. and Priss, U. (2006). Some open problems in formal concept analysis. problems presented at international conference on formal concept analysis (icfca).

Pei, J., Han, J., Mao, R., et al. (2000). Closet: An efficient algorithm for mining frequent closed itemsets. In ACM SIGMOD workshop on research issues in data mining and knowledge discovery, volume 4, pages 21–30.

Rimsa, A., Song, M. A., and Zárate, L. E. (2013). Scgaz-a synthetic formal context generator with density control for test and evaluation of fca algorithms. In Systems, Man, and Cybernetics (SMC), 2013 IEEE International Conference on, pages 3464–3470. IEEE.

Salleb, A., Maazouzi, Z., and Vrain, C. (2002). Mining maximal frequent itemsets by a boolean based approach. In European Conf. on Artificial Intelligence, Lyon France (July 2002), pages 285–289.

Santos, P., Neves, J., Silva, P., Dias, S. M., Zárate, L., and Song, M. (2018). An approach to extract proper implications set from high-dimension formal contexts using binary decision diagram.

Trabelsi, C., Jelassi, N., and Yahia, S. B. (2012). Scalable mining of frequent tri-concepts from folksonomies. In Pacific-Asia Conference on Knowledge Discovery and Data Mining, pages 231–242. Springer.

Wille, R. (1982). Restructuring lattice thoery: An approach based on hierarchies of concepts. pages 445–470.

Wille, R. (1995). The basic theorem of triadic concept analysis. Order, 12(2):149–158.
Publicado
22/10/2018
ANANIAS, Kaio H. A.; NEVES, Julio C. V.; ZÁRATE, Luis E.; SONG, Mark A. J.. Análise Formal de Conceitos Triádicos através da utilização de Diagramas Binários de Decisão. In: SYMPOSIUM ON KNOWLEDGE DISCOVERY, MINING AND LEARNING (KDMILE), 6. , 2018, São Paulo/SP. Anais [...]. Porto Alegre: Sociedade Brasileira de Computação, 2018 . p. 9-16. ISSN 2763-8944. DOI: https://doi.org/10.5753/kdmile.2018.27379.