Abstract
We equip our algorithm LinCbO with a pruning technique similar to that of LCM. Our experimental evaluation shows that it significantly improves the performance of the algorithm.
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- 1.
The pruning is utilized in the implementation LCM2 (available at http://research.nii.ac.jp/~uno/codes.htm). However it is not described in the related paper. An interested reader can find the description of the LCM’s pruning in [9].
- 2.
For now, ignore the argument y and line 16 as it will be explained later.
- 3.
Available at https://github.com/yazevnul/fcai.
References
Andrews, S.: In-Close, a fast algorithm for computing formal concepts. In: International Conference on Conceptual Structures (ICCS), Moscow (2009)
Andrews, S.: Making use of empty intersections to improve the performance of CbO-type algorithms. In: Bertet, K., Borchmann, D., Cellier, P., Ferré, S. (eds.) ICFCA 2017. LNCS (LNAI), vol. 10308, pp. 56–71. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59271-8_4
Andrews, S.: A new method for inheriting canonicity test failures in close-by-one type algorithms (2018)
Bazhanov, K., Obiedkov, S.A.: Optimizations in computing the Duquenne-Guigues basis of implications. Ann. Math. Artif. Intell. 70(1–2), 5–24 (2014)
Beeri, C., Bernstein, P.A.: Computational problems related to the design of normal form relational schemas. ACM Trans. Database Syst. (TODS) 4(1), 30–59 (1979)
Dua, D., Graff, C.: UCI machine learning repository (2017)
Ganter, B., Wille, R.: Formal Concept Analysis - Mathematical Foundations. Springer, Heidelberg (1999)
Guigues, J.-L., Duquenne, V.: Familles minimales d’implications informatives resultant d’un tableau de données binaires. Math. Sci. Humaines 95, 5–18 (1986)
Janostik, R., Konecny, J., Krajča, P.: LCM is well implemented CbO: study of LCM from FCA point of view. CoRR, abs/2010.06980 (2020)
Janostik, R., Konecny, J., Krajča, P.: LinCbO: fast algorithm for computation of the Duquenne-Guigues basis. CoRR, abs/2011.04928 (2020)
Konecny, J., Krajča, P.: Pruning in map-reduce style CbO algorithms. In: Alam, M., Braun, T., Yun, B. (eds.) ICCS 2020. LNCS (LNAI), vol. 12277, pp. 103–116. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-57855-8_8
Krajča, P., Outrata, J., Vychodil, V.: Advances in algorithms based on CbO. CLA 672, 325–337 (2010)
Krajča, P., Outrata, J., Vychodil, V.: Parallel algorithm for computing fixpoints of Galois connections. Ann. Math. Artif. Intell. 59(2), 257–272 (2010)
Krajca, P., Vychodil, V.: Distributed algorithm for computing formal concepts using map-reduce framework. In: Adams, N.M., Robardet, C., Siebes, A., Boulicaut, J.-F. (eds.) IDA 2009. LNCS, vol. 5772, pp. 333–344. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03915-7_29
Kuznetsov, S.O.: A fast algorithm for computing all intersections of objects from an arbitrary semilattice. Nauchno-Tekhnicheskaya Informatsiya Seriya 2-Informatsionnye Protsessy i Sistemy, (1), 17–20 (1993)
Kuznetsov, S.O.: On the intractability of computing the Duquenne-Guigues base. J. Univ. Comput. Sci. 10(8), 927–933 (2004)
Maier, D.: The Theory of Relational Databases, vol. 11. Computer Science Press, Rockville (1983)
Obiedkov, S.A., Duquenne, V.: Attribute-incremental construction of the canonical implication basis. .Ann. Math. Artif. Intell. 49(1–4), 77–99 (2007)
Outrata, J., Vychodil, V.: Fast algorithm for computing fixpoints of Galois connections induced by object-attribute relational data. Inf. Sci. 185(1), 114–127 (2012)
Uno, T., Asai, T., Uchida, Y., Hiroki A.: LCM: an efficient algorithm for enumerating frequent closed item sets. In: FIMI, vol. 90. Citeseer (2003)
Uno, T., Asai, T., Uchida, Y., Arimura, H.: An efficient algorithm for enumerating closed patterns in transaction databases. In: Suzuki, E., Arikawa, S. (eds.) DS 2004. LNCS (LNAI), vol. 3245, pp. 16–31. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30214-8_2
Uno, T., Kiyomi, M., Arimura, H.: LCM ver. 2: efficient mining algorithms for frequent/closed/maximal itemsets. In: FIMI, vol. 126 (2004)
Uno, T., Kiyomi, M., Arimura, H.: LCM ver. 3: collaboration of array, bitmap and prefix tree for frequent itemset mining. In: Proceedings of the 1st International Workshop on Open Source Data Mining: Frequent Pattern Mining Implementations, pp. 77–86. ACM (2005)
Wild, M.: Computations with finite closure systems and implications. In: Du, D.-Z., Li, M. (eds.) COCOON 1995. LNCS, vol. 959, pp. 111–120. Springer, Heidelberg (1995). https://doi.org/10.1007/BFb0030825
Acknowledgment
The authors acknowledge support by the grants
– IGA UP 2020 of Palacký University Olomouc, No. IGA_PrF_2020_019,
– JG 2019 of Palacký University Olomouc, No. JG_2019_008.
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Janostik, R., Konecny, J., Krajča, P. (2021). Pruning Techniques in LinCbO for Computation of the Duquenne-Guigues Basis. In: Braud, A., Buzmakov, A., Hanika, T., Le Ber, F. (eds) Formal Concept Analysis. ICFCA 2021. Lecture Notes in Computer Science(), vol 12733. Springer, Cham. https://doi.org/10.1007/978-3-030-77867-5_6
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