Abstract
In the authors’ previous research the possible usage of the correlation clustering in rough set theory was investigated. Correlation clustering relies on a tolerance relation. Its result is a partition. From the similarity point of view singleton clusters have no information. A system of base sets can be generated from the partition, and if the singleton clusters are left out, then it is a partial approximation space. This way the approximation space focuses on the similarity (the tolerance relation) itself and it is different from the covering type approximation space relying on the tolerance relation. In this paper the authors examine how the partiality can be decreased by inserting the members of some singletons into an arbitrary base set and how this annotation affects the approximations. The authors provide software that can execute this process and also helps to select the destination base set and it can also handle missing data with the help of the annotation.
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References
Aigner, M.: Enumeration via ballot numbers. Discrete Math. 308(12), 2544–2563 (2008). http://www.sciencedirect.com/science/article/pii/S0012365X07004542
Aszalós, L., Mihálydeák, T.: Rough clustering generated by correlation clustering. In: Ciucci, D., Inuiguchi, M., Yao, Y., Ślęzak, D., Wang, G. (eds.) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. RSFDGrC 2013. LNCS, vol. 8170, pp. 315–324. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-41218-9_34
Aszalós, L., Mihálydeák, T.: Rough classification based on correlation clustering. In: Miao D., Pedrycz W., Ślęzak, D., Peters, G., Hu, Q., Wang, R. (eds.) Rough Sets and Knowledge Technology. RSKT 2014. LNCS, vol. 8818, pp. 399–410. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11740-9_37
Aszalós, L., Mihálydeák, T.: Correlation clustering by contraction. In: 2015 Federated Conference on Computer Science and Information Systems (FedCSIS), pp. 425–434. IEEE (2015)
Aszalós, L., Mihálydeák, T.: Correlation clustering by contraction, a more effective method. In: Fidanova, S. (ed.) Recent Advances in Computational Optimization. SCI, vol. 655, pp. 81–95. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40132-4_6
Bansal, N., Blum, A., Chawla, S.: Correlation clustering. Mach. Learn. 56(1–3), 89–113 (2004)
Becker, H.: A survey of correlation clustering. In: Advanced Topics in Computational Learning Theory, pp. 1–10 (2005)
Mani, A.: Choice inclusive general rough semantics. Inf. Sci. 181(6), 1097–1115 (2011)
Nagy, D., Mihálydeák, T., Aszalós, L.: Similarity based rough sets. In: Polkowski, L. (ed.) Rough Sets. LNCS, vol. 10314, pp. 94–107. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-60840-2_7
Pawlak, Z.: Rough sets. Int. J. Parallel Program. 11(5), 341–356 (1982)
Pawlak, Z., Skowron, A.: Rudiments of rough sets. Inf. Sci. 177(1), 3–27 (2007)
Pawlak, Z., et al.: Rough sets: theoretical aspects of reasoning about data. In: System Theory, Knowledge Engineering and Problem Solving, vol. 9. Kluwer Academic Publishers, Dordrecht (1991)
Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27(2), 245–253 (1996)
Zimek, A.: Correlation clustering. ACM SIGKDD Explor. Newslett. 11(1), 53–54 (2009)
Acknowledgement
This work was supported by the construction EFOP-3.6.3-VEKOP-16-2017-00002. The project was co-financed by the Hungarian Government and the European Social Fund.
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Nagy, D., Mihálydeák, T., Aszalós, L. (2018). Similarity Based Rough Sets with Annotation. In: Nguyen, H., Ha, QT., Li, T., Przybyła-Kasperek, M. (eds) Rough Sets. IJCRS 2018. Lecture Notes in Computer Science(), vol 11103. Springer, Cham. https://doi.org/10.1007/978-3-319-99368-3_7
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