Abstract
In this work we have proposed a new technique of granulation in the family of methods inspired by Polkowski standard granulation algorithm. The new method is called epsilon homogenous granulation. The idea is to create the epsilon granules around the training objects lowering the r-indiscernibility ratio until the group of objects is homogenous in the sense of their belongingness to decision class of central object. We use epsilon granules, which means that during granulation process of numerical data we consider indiscernibility ratio of descriptors. The main advantage of this method in addition to reduction in the number of training objects is that there is no need to estimate the optimal granulation radii. The process of granulation is run only once, and the radii for particular objects are formed in automatic way - dependent on indiscernibility ratio of data and their homogeneity in decision concepts. Next step is to cover the original decision system with formed granules and get the final granular decision system by \(\varepsilon \)-majority voting method. We have performed preliminary experiments with use of multiple cross validation methods. We have used selected data sets from University of California, Irvine machine learning repository for our research. To verify the quality of approximation we used k-NN classifier designed for our granulation method. The method seems to be comparable with the ones of previous algorithms, with satisfying effectiveness in classification and significant reduction in number of training data.
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References
Artiemjew, P.: Classifiers from granulated data sets: concept dependent and layered granulation. In: Proceedings of RSKD 2007, the Workshops at ECML/PKDD 2007, pp. 1–9. Warsaw University Press, Warsaw (2007)
Artiemjew, P.: Natural versus granular computing: classifiers from granular structures. In: Proceedings of 6th International Conference on Rough Sets and Current Trends in Computing RSCTC 2008, Akron OH, USA (2008)
Artiemjew, P.: A review of the knowledge granulation methods: discrete vs. continuous algorithms. In: Skowron, A., Suraj, Z. (eds.) Rough Sets and Intelligent Systems - Professor Zdzisław Pawlak in Memoriam. Intelligent Systems Reference Library, vol. 43, pp. 41–59. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-30341-8_4
Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982)
Polap, D., Wozniak, M., Wei, W., Damasevicius, R.: Multi-threaded Learning Control Mechanism for Neural Networks. Future Generation Computer Systems. Elsevier (2018)
Polkowski, L.: Rough Sets. Mathematical Foundations. Physica Verlag, Heidelberg (2002)
Polkowski, L.: A rough set paradigm for unifying rough set theory and fuzzy set theory. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) RSFDGrC 2003. LNCS (LNAI), vol. 2639, pp. 70–77. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-39205-X_9
Polkowski, L.: Toward rough set foundations. Mereological approach. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 8–25. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-25929-9_2
Polkowski, L.: Granulation of knowledge in decision systems: the approach based on rough inclusions. The method and its applications. In: Kryszkiewicz, M., Peters, J.F., Rybinski, H., Skowron, A. (eds.) RSEISP 2007. LNCS (LNAI), vol. 4585, pp. 69–79. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73451-2_9
Polkowski, L.: Formal granular calculi based on rough inclusions. In: Proceedings of IEEE 2005 Conference on Granular Computing GrC05, Beijing, China, pp. 57–62. IEEE Press (2005)
Polkowski, L.: A model of granular computing with applications. In: Proceedings of IEEE 2006 Conference on Granular Computing GrC06, Atlanta, USA, pp. 9–16. IEEE Press (2006)
Polkowski, L.: The paradigm of granular rough computing. In: Proceedings ICCI 2007, Lake Tahoe NV, pp. 145–163. IEEE Computer Society, Los Alamitos (2007)
Polkowski, L.: A unified approach to granulation of knowledge and granular computing based on rough mereology: a survey. In: Pedrycz, W., Skowron, A., Kreinovich, V. (eds.) Handbook of Granular Computing, pp. 375–401. Wiley, New York (2008)
Polkowski, L.: Granulation of knowledge: similarity based approach in information and decision systems. In: Meyers, R.A. (ed.) Encyclopedia of Complexity and System Sciences. Springer, Heidelberg (2009). https://doi.org/10.1007/978-1-4614-1800-9_94. article 00788
Polkowski, L.: Approximate Reasoning by Parts. An Introduction to Rough Mereology. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22279-5
Polkowski, L., Artiemjew, P.: On granular rough computing with missing values. In: Kryszkiewicz, M., Peters, J.F., Rybinski, H., Skowron, A. (eds.) RSEISP 2007. LNCS (LNAI), vol. 4585, pp. 271–279. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73451-2_29
Polkowski, L., Artiemjew, P.: On granular rough computing: factoring classifiers through granulated decision systems. In: Kryszkiewicz, M., Peters, J.F., Rybinski, H., Skowron, A. (eds.) RSEISP 2007. LNCS (LNAI), vol. 4585, pp. 280–289. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73451-2_30
Polkowski, L., Artiemjew, P.: Towards granular computing: classifiers induced from granular structures. In: Proceedings RSKD 2007, the Workshops at ECML/PKDD 2007, pp. 43–53. Warsaw University Press, Warsaw (2007)
Polkowski, L., Artiemjew, P.: Classifiers based on granular structures from rough inclusions. In: Proceedings of 12th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems IPMU 2008, Torremolinos, Malaga, Spain, pp. 1786–1794 (2008)
Polkowski, L., Artiemjew, P.: Rough sets in data analysis: foundations and applications. In: Smoliński, T.G., Milanova, M., Hassanien, A.-E. (eds.) Applications of Computional Intelligence in Biology: Current Trends and open Problems, SCI, vol. 122, pp. 33–54. Springer, Heidelberg (2008)
Polkowski, L., Artiemjew, P.: Rough mereology in classification of data: voting by means of residual rough inclusions. In: Chan, C.-C., Grzymala-Busse, J.W., Ziarko, W.P. (eds.) RSCTC 2008. LNCS (LNAI), vol. 5306, pp. 113–120. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-88425-5_12
Polkowski, L., Artiemjew, P.: A study in granular computing: on classifiers induced from granular reflections of data. In: Peters, J.F., Skowron, A., Rybiński, H. (eds.) Transactions on Rough Sets IX. LNCS, vol. 5390, pp. 230–263. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-89876-4_14
Polkowski, L., Artiemjew, P.: On classifying mappings induced by granular structures. In: Peters, J.F., Skowron, A., Rybiński, H. (eds.) Transactions on Rough Sets IX. LNCS, vol. 5390, pp. 264–286. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-89876-4_15
Polkowski, L., Artiemjew, P.: Granular computing in decision approximation - an application of rough mereology. In: Intelligent Systems Reference Library, vol. 77, pp. 1–422. Springer, Heidelberg (2015). ISBN 978-3-319-12879-5. https://doi.org/10.1007/978-3-319-12880-1
Ohno-Machado, L.: Cross-validation and bootstrap ensembles, bagging, boosting, Harvard-MIT division of health sciences and technology (2005). http://ocw.mit.edu/courses/health-sciences-and-technology/hst-951j-medical-decision-support-fall-2005/lecture-notes/hst951_6.pdf HST.951J: Medical Decision Support, Fall
University of California, Irvine Machine Learning Repository. https://archive.ics.uci.edu/ml/index.php
Zadeh, L.A.: Fuzzy sets and information granularity. In: Gupta, M., Ragade, R., Yager, R.R. (eds.) Advances in Fuzzy Set Theory and Applications, North-Holland, Amsterdam, pp. 3–18 (1979)
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The research has been supported by grant 23:610:007-300 from Ministry of Science and Higher Education of the Republic of Poland.
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Ropiak, K., Artiemjew, P. (2018). On Granular Rough Computing: Epsilon Homogenous Granulation. 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_43
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