Abstract
Computation of rough set approximation (RSA) is a critical step for attribute reduction and knowledge acquisition in rough set theory. Continuously improving computation efficiency of RSA is very meaningful, because it can enhance user experience of existing applications. Furthermore, it is helpful to apply rough sets to some fields with high performance requirement. Graphics processing unit (GPU) has gained a lot of attention from scientific communities for its applicability in high-performance computing. Different from existing works, this paper tries to apply GPU to accelerate a state-of-the-art serial algorithm of RSA computation, which is based on radix sorting. Three key steps of the serial algorithm are parallel designed, including object sorting, computation of equivalence classes, and computation of RSA. The experimental results show that the parallel method can accelerate the computation process efficiently.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Balamash AS, Pedrycz W, -Hmouz RA et al (2017) Granular classifiers and their design through refinement of information granules. Soft Comput 21(10):2745–2759
Chen HM, Li TR, Ruan D et al (2013) A rough-set-based incremental approach for updating approximations under dynamic maintenance environments. IEEE Trans Knowl Data Eng 25(2):274–284
Cheng Y (2011) The incremental method for fast computing the rough fuzzy approximations. Data Knowl Eng 70(1):84–100
David K, Hwu WM (2010) Programming massively parallel processors: a hand-on approach. Morgan Kaufmann Publishers Inc., San Francisco
Dean J, Ghemawat S (2008) Mapreduce: simplified data processing on large clusters. Commun ACM 51(1):107–113
Deng DY, Yan DX, Wang JY (2010) Parallel reducts based on attribute significance. In: Yu J, Greco S, Lingras P et al (eds) Rough Set and Knowledge Technology, vol 6401. Lecture Notes in Computer Science. Springer, Berlin, pp 336–343
Fan A, Zhao H, Zhu W (2016) Test-cost-sensitive attribute reduction on heterogeneous data for adaptive neighborhood model. Soft Comput 20(12):4813–4824
Harris M, Sengupta S, Owens JD (2007) Parallel prefix sum (scan) with CUDA. In: Nguyen H (ed) GPU gems 3. Addison Wesley, Reading
Hu QH, Xie ZX, Yu DR (2007) Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation. Pattern Recognit 40(22):3509–3521
Hu QH, Yu DR, Liu JF et al (2008) Neighborhood rough set based heterogeneous feature subset selection. Inf Sci 178(18):3577–3594
Jensen R, Shen Q (2004) Fuzzy-rough attribute reduction with application to web categorization. Fuzzy Sets Syst 131(3):469–485
Jing SY (2014) A hybrid genetic algorithm for feature subset selection in rough set theory. Soft Comput 18(7):1373–1382
Jing SY, Ali S, She K et al (2013) State-of-the-art research study for green cloud computing. J Supercomput 65(1):445–468
Li TR, Ruan D, Wets G et al (2007) A rough sets based characteristic relation approach for dynamic attribute generalization in data mining. Knowl Based Syst 20(5):485–494
Li SY, Li TR, Zhang ZX et al (2015) Parallel computing of approximations in dominance-based rough sets approach. Knowl Based Syst 87:202–211
Liang JY, Qian YH (2008) Information granules and entropy theory in information systems. Sci China Ser F Inf Sci 51(10):1427–1444
Liang JY, Wang F, Dang CY et al (2012) An efficient rough feature selection algorithm with a multi-granulation view. Int J Approx Reason 53:912–926
Lindholm E, Nickolls J, Oberman S (2008) Nvidia tesla: a unified graphics and computing architecture. IEEE Micro 28(2):39–55
Min F, He HP, Qian YH et al (2011) Test-cost-sensitive attribute reduction. Inf Sci 181(22):4928–4942
Min F, Hu QH, Zhu W (2014) Feature selection with test cost constraint. Int J Approx Reason 55(1):167–179
Pawlak Z (1991) Rough sets, theoretical aspects of reasoning about data. Kluwer Academic Publishers, Dordrecht
Pawlak Z, Skowron A (2007a) Rough sets and Boolean reasoning. Inf Sci 177(1):41–73
Pawlak Z, Skowron A (2007b) Rough sets: some extensions. Inf Sci 177(1):28–40
Pawlak Z, Skowron A (2007c) Rudiments of rough sets. Inf Sci 177(1):3–27
Pedrycz W (2001) Granular computing: an introduction. In: IFSA world congress & NAFIPS international conference
Pedrycz W, Al-Hmouz R, Balamash AS et al (2017) Modeling with linguistic entities and linguistic descriptors: a perspective of granular computing. Soft Comput 21(7):1833–1845
Qian YH, Liang JY, Dang CY (2010a) Incomplete multigranulation rough set. IEEE Trans Syst Man Cybern Part A 40(2):420–431
Qian YH, Liang JY, Pedrycz W et al (2010b) Positive approximation: an accelerator for attribute reduction in rough set theory. Artif Intell 174(9–10):597–618
Qian J, Miao DQ, Zhang ZH (2011) Knowledge reduction algorithms in cloud computing. Chin J Comput 34(12):2332–2342
Qian J, Miao DQ, Zhang ZH et al (2014) Parallel attribute reduction algorithms using MapReduce. Inf Sci 279:671–690
Ryoo S, Rodrigues CI, Baghsorkhi SS et al (2008) Optimization principles and application performance evaluation of a multi-threaded GPU using CUDA. In: Proceedings of the PPoPP’08, pp 73–82
Satish N, Harris M, Garland M (2009) Designing efficient sorting algorithms for manycore GPUs. In: Proceedings of the IPDPS’09, pp 1–10
Susmaga R (2004) Tree-like parallelization of reduct and construct computation. In: Tsumoto S et al (eds) RSCTC 2004, LNAI 3066, Springer, Berlin, pp 455–464
Tang JG, She K, Min F, Zhu W (2013) A matroidal approach to rough set theory. Theor Comput Sci 471:1–11
Tay FEH, Shen L (2002) Economic and financial prediction using rough sets model. Eur J Oper Res 141(3):641–659
Tsumoto S (2004) Mining diagnostic rules from clinical databases using rough sets and medical diagnostic model. Inf Sci 162(2):65–80
Wang GY, Yu H, Yang DC (2002) Decision table reduction based on conditional information entropy. Chin J Comput 25(7):759–766
Xu ZY, Liu ZP, Yang BR et al (2006) A quick attribute reduction algorithm with complexity of max(\(O|C, U|, O|C|^{2}|U/C|\)). Chi J Comput 29(3):391–399
Yu J, Yang Y (2016) Minimal attribute reduction with rough set based on compactness discernibility information tree. Soft Computing 20(6):2233–2243
Zeng K (2016) Preference mining using neighborhood rough set model on two universes. Comput Intell Neurosci (Public online)
Zhang JB, Li TR, Ruan D et al (2012) A parallel method for computing rough set approximations. Inf Sci 194:209–223
Zhang JB, Wong JS, Pan Y et al (2015) A parallel matrix-based method for computing approximations in incomplete information systems. IEEE Trans Knowl Data Eng 27(2):326–339
Zhang JB, Zhu Y, Li TR et al (2016) Efficient parallel Boolean matrix based algorithms for computing composite rough set approximations. Inf Sci 329:287–302
Zhu W (2007a) Topological approaches to covering rough sets. Inf Sci 177(6):1499–1508
Zhu W (2007b) Generalized rough sets based on relations. Inf Sci 177(22):4997–5011
Zhu XZh, Zhu W, Fan XN (2017) Rough set methods in feature selection via submodular function. Soft Comput 21(13):3699–3711
Acknowledgements
This study was funded by the National Science Foundation of China (Grand No. 61702128); the Scientific Research Fund of Sichuan Provincial Department (Grand No. 17ZA0201); the Scientific Research Fund of Leshan Normal University (Grand No. Z1325).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Additional information
Communicated by A. Di Nola.
Rights and permissions
About this article
Cite this article
Jing, SY., Li, GL., Zeng, K. et al. Efficient parallel algorithm for computing rough set approximation on GPU. Soft Comput 22, 7553–7569 (2018). https://doi.org/10.1007/s00500-018-3050-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-018-3050-z