Abstract
An important issue in clustering is how to deal with data containing missing values. A three-way decision making approach has recently been introduced for this purpose. It includes an added option of deferment which is exercised whenever it is not clear to include or exclude an object from a cluster. A critical issue in the three-way approach is how to decide the thresholds defining the three types of decisions. We examine the role of game-theoretic rough set model (GTRS) to address this issue. The GTRS model induces three-way decisions by implementing a game between multiple cooperative or competitive criteria. In particular, a game in GTRS is proposed which realizes the determination of thresholds from the viewpoint of tradeoff between accuracy and generality of clustering. Experimental results are reported for two datasets from UCI machine learning repository. The comparison of the GTRS results with another three-way model of (1, 0) suggests that the GTRS model significantly improves generality by upto 65% while maintaining similar levels of accuracy. In comparison to the (0.5, 0.5) model, the GTRS improves accuracy by upto 5% at a cost of some decrease in generality.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Azam, N., Yao, J.T.: Formulating game strategies in game-theoretic rough sets. In: Lingras, P., Wolski, M., Cornelis, C., Mitra, S., Wasilewski, P. (eds.) RSKT 2013. LNCS (LNAI), vol. 8171, pp. 145–153. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-41299-8_14
Bugnet, M., Kula, A., Niewczas, M., Botton, G.A.: Segregation and clustering of solutes at grain boundaries in mgrare earth solid solutions. Acta Mater. 79, 66–73 (2014)
Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Stat. Soc.: Ser. B (Methodol.) 39(1), 1–38 (1977)
Eye, A.V.: Statistical Methods in Longitudinal Research: Principles and Structuring Change. Statistical Modeling and Decision Science, vol. 1 (2014)
Haitovsky, V.: Missing data in regression analysis. J. Roy. Stat. Soc. 30, 67–82 (1968)
Herbert, J.P., Yao, J.T.: Game-theoretic rough sets. Fundam. Inf. 108(3–4), 267–286 (2011)
Hu, J., Li, T., Wang, H., Fujita, H.: Hierarchical cluster ensemble model based on knowledge granulation. Knowl.-Based Syst. 91, 179–188 (2016)
Iam-On, N., Boongeon, T., Garrett, S., Price, C.: A link-based cluster ensemble approach for categorical data clustering. IEEE Trans. Knowl. Data Eng. 24(3), 413–425 (2012)
Li, J.H., Song, S.J., Zhang, Y.L., Zhou, Z.: Robust k-median and k-means clustering algorithms for incomplete data. Mathe. Probl. Eng. 2016, 1–8 (2016)
Lichman, M.: UCI machine learning repository (2013). http://archive.ics.uci.edu/ml. Accessed 9 Feb 2017
Little, T.D., Lang, K.M., Wu, W., Rhemtulla, M.: Missing Data. Wiley, New York (2016)
Timm, H., Dring, C., Kruse, R.: Different approaches to fuzzy clustering of incomplete datasets. Int. J. Approximate Reasoning 35(3), 239–249 (2004)
Xu, D., Tian, Y.: A comprehensive survey of clustering algorithms. Ann. Data Sci. 2(2), 165–193 (2015)
Xu, R., Wunsch, D.: Survey of clustering algorithms. IEEE Trans. Neural Netw. 16(3), 645–678 (2005)
Yang, X., Li, T., Fujita, H., Liu, D., Yao, Y.: A unified model of sequential three-way decisions and multilevel incremental processing. Knowl.-Based Syst. 134, 172–188 (2017)
Yao, Y.: Rough sets and three-way decisions. In: Ciucci, D., Wang, G., Mitra, S., Wu, W.-Z. (eds.) RSKT 2015. LNCS (LNAI), vol. 9436, pp. 62–73. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-25754-9_6
Yu, H.: A framework of three-way cluster analysis. In: Polkowski, L., Yao, Y., Artiemjew, P., Ciucci, D., Liu, D., Ślęzak, D., Zielosko, B. (eds.) IJCRS 2017. LNCS (LNAI), vol. 10314, pp. 300–312. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-60840-2_22
Yu, H., Su, T., Zeng, X.: A three-way decisions clustering algorithm for incomplete data. In: Miao, D., Pedrycz, W., Ślȩzak, D., Peters, G., Hu, Q., Wang, R. (eds.) RSKT 2014. LNCS (LNAI), vol. 8818, pp. 765–776. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11740-9_70
Yu, H., Zhang, C., Wang, G.: A tree-based incremental overlapping clustering method using the three-way decision theory. Knowl.-Based Syst. 91, 189–203 (2016)
Acknowledgements
This work was partially supported by a Discovery Grant from NSERC Canada and Indigenous Student Scholarship from HEC Pakistan.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Azam, N., Afridi, M.K., Yao, J. (2018). A Game-Theoretic Rough Set Approach for Handling Missing Data in Clustering. In: Mouhoub, M., Sadaoui, S., Ait Mohamed, O., Ali, M. (eds) Recent Trends and Future Technology in Applied Intelligence. IEA/AIE 2018. Lecture Notes in Computer Science(), vol 10868. Springer, Cham. https://doi.org/10.1007/978-3-319-92058-0_61
Download citation
DOI: https://doi.org/10.1007/978-3-319-92058-0_61
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-92057-3
Online ISBN: 978-3-319-92058-0
eBook Packages: Computer ScienceComputer Science (R0)