Abstract
In information systems, there may exist multiple different types of attributes like categorical attributes, numerical attributes, set-valued attributes, interval-valued attributes, missing attributes, etc. Such information systems are called as composite information systems. To process such attributes with rough set theory, composite rough set model and corresponding matrix methods were introduced in our previous research. Rough set approximations of a concept are the basis for rule acquisition and attribute reduction in rough set based methods. To accelerate the computation process of rough set approximations, this paper first presents the boolean matrix representation of the lower and upper approximations in the composite information system, then designs a parallel method based on matrix, and implements it on GPUs. The experiments on data sets from UCI and user-defined data sets show that the proposed method can accelerate the computation process efficiently.
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References
NVIDIA GPUs (2013), https://developer.nvidia.com/cuda-gpus
NVIDIA CUDA (2013), http://www.nvidia.com/object/cuda_home_new.html
Grzymała-Busse, J.W.: Characteristic relations for incomplete data: A generalization of the indiscernibility relation. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 244–253. Springer, Heidelberg (2004)
Grzymała-Busse, J.W.: Characteristic relations for incomplete data: A generalization of the indiscernibility relation. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets IV. LNCS, vol. 3700, pp. 58–68. Springer, Heidelberg (2005)
Guan, Y., Wang, H.: Set-valued information systems. Information Sciences 176(17), 2507–2525 (2006)
Hu, Q., Xie, Z., Yu, D.: Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation. Pattern Recognition 40, 3509–3521 (2007)
Hu, Q., Yu, D., Liu, J., Wu, C.: Neighborhood rough set based heterogeneous feature subset selection. Information Sciences 178(18), 3577–3594 (2008)
Kryszkiewicz, M.: Rough set approach to incomplete information systems. Information Sciences 112(1-4), 39–49 (1998)
Leung, Y., Fischer, M.M., Wu, W.Z., Mi, J.S.: A rough set approach for the discovery of classification rules in interval-valued information systems. International Journal of Approximate Reasoning 47(2), 233–246 (2008)
Li, T., Ruan, D., Geert, W., Song, J., Xu, Y.: A rough sets based characteristic relation approach for dynamic attribute generalization in data mining. Knowledge-Based Systems 20(5), 485–494 (2007)
Liu, G.: The axiomatization of the rough set upper approximation operations. Fundamenta Informaticae 69(3), 331–342 (2006)
Mi, J.S., Zhang, W.X.: An axiomatic characterization of a fuzzy generalization of rough sets. Information Sciences 160(1–4), 235–249 (2004)
Newman, D., Hettich, S., Blake, C., Merz, C.: UCI Repository of Machine Learning Databases. University of California, Department of Information and Computer Science, Irvine, CA (1998), http://archive.ics.uci.edu/ml/
Owens, J.D., Luebke, D., Govindaraju, N., Harris, M., Krüger, J., Lefohn, A.E., Purcell, T.: A survey of general-purpose computation on graphics hardware (2007)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data, System Theory, Knowledge Engineering and Problem Solving, vol. 9. Kluwer Academic Publishers, Dordrecht (1991)
Pawlak, Z., Skowron, A.: Rough sets: Some extensions. Information Sciences 177(1), 28–40 (2007)
Qian, Y., Dang, C., Liang, J., Tang, D.: Set-valued ordered information systems. Information Sciences 179(16), 2809–2832 (2009)
Qian, Y., Liang, J., Pedrycz, W., Dang, C.: Positive approximation: An accelerator for attribute reduction in rough set theory. Artificial Intelligence 174(9-10), 597–618 (2010)
Stefanowski, J., Tsoukiàs, A.: On the extension of rough sets under incomplete information. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 73–82. Springer, Heidelberg (1999)
Yao, Y.: Relational interpretations of neighborhood operators and rough set approximation operators. Information Sciences 111(1-4), 239–259 (1998)
Zhang, J., Li, T., Ruan, D., Gao, Z., Zhao, C.: A parallel method for computing rough set approximations. Information Sciences (2012)
Zhang, J., Li, T., Ruan, D., Liu, D.: Neighborhood rough sets for dynamic data mining. International Journal of Intelligent Systems 27(4), 317–342 (2012)
Zhang, J., Li, T., Chen, H.: Composite rough sets. In: Lei, J., Wang, F.L., Deng, H., Miao, D. (eds.) AICI 2012. LNCS, vol. 7530, pp. 150–159. Springer, Heidelberg (2012)
Zhang, J., Li, T., Ruan, D., Liu, D.: Rough sets based matrix approaches with dynamic attribute variation in set-valued information systems. International Journal of Approximate Reasoning 53(4), 620–635 (2012)
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Zhang, J., Zhu, Y., Pan, Y., Li, T. (2013). A Parallel Implementation of Computing Composite Rough Set Approximations on GPUs. In: Lingras, P., Wolski, M., Cornelis, C., Mitra, S., Wasilewski, P. (eds) Rough Sets and Knowledge Technology. RSKT 2013. Lecture Notes in Computer Science(), vol 8171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41299-8_23
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DOI: https://doi.org/10.1007/978-3-642-41299-8_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-41298-1
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