# Attribute reduction on real-valued data in rough set theory using hybrid artificial bee colony: extended FTSBPSD algorithm

## Abstract

Discretization and attribute reduction are two preprocessing steps for most of the induction algorithms. Discretization before attribute reduction will result in high computation cost as many irrelevant and redundant attributes need to be discretized. Attribute reduction before discretization may result in over-fitting of the data leading to low performance of the induction algorithm. In this paper, we have proposed a hybrid algorithm using artificial bee colony (ABC) algorithm and extended forward tentative selection with backward propagation of selection decision (EFTSBPSD) algorithm for attribute reduction on *real*-*valued* data in rough set theory (RST). Based on the principle of indiscernibility, the hybrid ABC–EFTSBPSD algorithm performs discretization and attribute reduction together. The hybrid ABC–EFTSBPSD algorithm takes as input the decision system consisting of real-valued attributes and determines a near optimal set of irreducible cuts. Here, optimality of the set of irreducible cuts is defined in terms of the cardinality of the set of irreducible cuts. Reduct is obtained from the determined approximate optimal set of irreducible cuts by extracting the attributes corresponding to the cuts in the obtained set of irreducible cuts. The proposed hybrid algorithm is tested on various data sets from University of California Machine Learning Repository. Experimental results obtained by the proposed hybrid algorithm are compared with those obtained by the Q-MDRA, ACO-RST and IMCVR algorithms described in the literature and found to give better classification accuracy when tested using (1) C4.5 classifier and (2) SVM classifier. The proposed hybrid algorithm has also shown reduced length of the reduct in comparison with the results obtained by Q-MDRA, ACO-RST and IMCVR algorithms.

## Keywords

Rough set theory Indiscernibility Boolean reasoning Discretization Attribute reduction Artificial bee colony algorithm FTSBPSD algorithm## Notes

### Acknowledgments

This work is supported by Tata Consultancy Services, under TCS Research Scholar Program.

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

## References

- Alcalá-Fdez J, Fernández A, Luengo J, Derrac J, García S, Sánchez L, Herrera F (2011) KEEL data-mining software tool: data set repository, integration of algorithms and experimental analysis framework. Mult Valued Logic Soft Comput 17:255–287Google Scholar
- Bhatt RB, Gopal M (2005) On fuzzy-rough sets approach to feature selection. Pattern Recognit Lett 26(7):965–975CrossRefGoogle Scholar
- Chebrolu S, Sanjeevi SG (2015) Attribute reduction on continuous data in rough set theory using ant colony optimization metaheuristic. In: Proceedings of the third international symposium on women in computing and informatics, WCI ’15, pp 17–24, ACM, New York, 2015Google Scholar
- Chebrolu S, Sanjeevi SG (2015) Forward tentative selection with backward propagation of selection decision algorithm for attribute reduction in rough set theory. Int J Reason Based Intell Syst 7(3/4):221–243Google Scholar
- Cornelis C, Jensen R, Hurtado G, Ślȩzak D (2010) Attribute selection with fuzzy decision reducts. Inf Sci 180(2):209–224CrossRefzbMATHMathSciNetGoogle Scholar
- Cristianini N, Shawe-Taylor J (2000) An introduction to support vector machines: and other kernel-based learning methods. Cambridge University Press, New YorkCrossRefzbMATHGoogle Scholar
- Dai J, Xu Q (2013) Attribute selection based on information gain ratio in fuzzy rough set theory with application to tumor classification. Appl Soft Comput 13(1):211–221CrossRefGoogle Scholar
- Friedman M (1940) A comparison of alternative tests of significance for the problem of \(m\) rankings. Ann Math Stat 11(1):86–92CrossRefzbMATHMathSciNetGoogle Scholar
- Gao KZ, Suganthan PN, Chua TJ, Chong CS, Cai TX, Pan QK (2015) A two-stage artificial bee colony algorithm scheduling flexible job-shop scheduling problem with new job insertion. Expert Syst Appl 42(21):7652–7663CrossRefGoogle Scholar
- Guan Y-Y, Wang H-K, Wang Y, Yang F (2009) Attribute reduction and optimal decision rules acquisition for continuous valued information systems. Inf Sci 179(17):2974–2984CrossRefzbMATHMathSciNetGoogle Scholar
- Hu Q, Liu J, Yu D (2008) Mixed feature selection based on granulation and approximation. Knowl Based Syst 21(4):294–304CrossRefGoogle Scholar
- Hu Q, Yu D, Liu J, Wu C (2008) Neighborhood rough set based heterogeneous feature subset selection. Inf Sci 178(18):3577–3594CrossRefzbMATHMathSciNetGoogle Scholar
- IBM Corp (2013) IBM SPSS Statistics for Windows, Version 22.0. IBM Corp, ArmonkGoogle Scholar
- Jensen R, Shen Q (2004) Fuzzy-rough attribute reduction with application to web categorization. Fuzzy Sets Syst 141(3):469–485CrossRefzbMATHMathSciNetGoogle Scholar
- Jia X, Liao W, Tang Z, Shang L (2013) Minimum cost attribute reduction in decision-theoretic rough set models. Inf Sci 219:151–167CrossRefzbMATHMathSciNetGoogle Scholar
- Jiang F, Sui Y (2015) A novel approach for discretization of continuous attributes in rough set theory. Knowl Based Syst 73:324–334CrossRefGoogle Scholar
- Jun Z, Zhou Y (2009) New heuristic method for data discretization based on rough set theory. J China Univ Posts Telecommun 16(6):113–120CrossRefGoogle Scholar
- Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical Report TR06, Erciyes University, October 2005Google Scholar
- Karaboga D (2010) Artificial bee colony algorithm. Scholarpedia 5(3):6915CrossRefGoogle Scholar
- Karaboga D, Akay B (2009) A comparative study of artificial bee colony algorithm. Appl Math Comput 214(1):108–132zbMATHMathSciNetGoogle Scholar
- Karaboga D, Basturk B (2008) On the performance of artificial bee colony (ABC) algorithm. Appl Soft Comput 8(1):687–697CrossRefGoogle Scholar
- Karaboga D, Akay B, Ozturk C (2007) Artificial bee colony (ABC) optimization algorithm for training feed-forward neural networks. In: Torra V, Narukawa Y, Yoshida Y (eds) Modeling decisions for artificial intelligence: 4th international conference, MDAI 2007, Kitakyushu, Japan, August 16–18, 2007. Proceedings, pp 318–329Google Scholar
- Kent ridge bio-medical data set repository. http://sdmc.lit.org.sg/gedatasets/datasets.html
- Komorowski J, Pawlak Z, Polkowski L, Skowron A (1999) Rough sets: a tutorial. In: Pal SK, Skowron A (eds) Rough fuzzy hybridization: a new trend in decision-making. Springer, Singapore, pp 3–98Google Scholar
- Li M, Deng SB, Feng S, Fan J (2011) An effective discretization based on class-attribute coherence maximization. Pattern Recognit Lett 32(15):1962–1973CrossRefGoogle Scholar
- Li M, Shang C, Feng S, Fan J (2014) Quick attribute reduction in inconsistent decision tables. Inf Sci 254:155–180CrossRefzbMATHMathSciNetGoogle Scholar
- Lichman M (2013) UCI machine learning repository. School of Information and Computer Sciences, University of California, Irvine. http://archive.ics.uci.edu/ml
- Mac Parthaláin N, Jensen R (2013) Unsupervised fuzzy-rough set-based dimensionality reduction. Inf Sci 229:106–121CrossRefzbMATHMathSciNetGoogle Scholar
- Mac Parthaláin N, Shen Q (2009) Exploring the boundary region of tolerance rough sets for feature selection. Pattern Recognit 42(5):655–667CrossRefzbMATHGoogle Scholar
- Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11:341–356CrossRefzbMATHGoogle Scholar
- Pawlak Z (2002) Rough set theory and its applications. J Telecommun Inf Technol 3:7–10Google Scholar
- Pawlak Z, Skowron A (2007a) Rough sets and boolean reasoning. Inf Sci 177(1):41–73CrossRefzbMATHMathSciNetGoogle Scholar
- Pawlak Z, Skowron A (2007b) Rough sets: some extensions. Inf Sci 177(1):28–40CrossRefzbMATHMathSciNetGoogle Scholar
- Pawlak Z, Skowron A (2007c) Rudiments of rough sets. Inf Sci 177(1):3–27Google Scholar
- Pawlak Z, Grzymala-Busse J, Slowinski R, Ziarko W (1995) Rough sets. Commun ACM 38(11):88–95CrossRefGoogle Scholar
- Quinlan JR (1993) C4.5: programs for machine learning. Morgan Kaufmann Publishers Inc, San FranciscoGoogle Scholar
- Roy A, Pal SK (2003) Fuzzy discretization of feature space for a rough set classifier. Pattern Recognit Lett 24(6):895–902CrossRefzbMATHGoogle Scholar
- Singh A (2009) An artificial bee colony algorithm for the leaf-constrained minimum spanning tree problem. Appl Soft Comput 9(2):625–631CrossRefGoogle Scholar
- Skowron A, Rauszer C (1992) The discernibility matrices and functions in information systems. In: Słowiński R (ed) Intelligent decision support: handbook of applications and advance of the rough sets theory, volume 11 of theory and decision library. Springer, Dordrecht, pp 331–362CrossRefGoogle Scholar
- Sun B, Ma W, Chen D (2014) Rough approximation of a fuzzy concept on a hybrid attribute information system and its uncertainty measure. Inf Sci 284:60–80CrossRefzbMATHMathSciNetGoogle Scholar
- Wang C, Shao M, Sun B, Qinghua H (2015) An improved attribute reduction scheme with covering based rough sets. Appl Soft Comput 26:235–243CrossRefGoogle Scholar
- Yao Y-Q, Mi J-S, Li Z-J (2011) Attribute reduction based on generalized fuzzy evidence theory in fuzzy decision systems. Fuzzy Sets Syst 170(1):64–75CrossRefzbMATHMathSciNetGoogle Scholar
- Ye D, Chen Z (2015) A new approach to minimum attribute reduction based on discrete artificial bee colony. Soft Comput 19(7):1893–1903CrossRefGoogle Scholar
- Ye D, Chen Z, Ma S (2013) A novel and better fitness evaluation for rough set based minimum attribute reduction problem. Inf Sci 222:413–423CrossRefzbMATHMathSciNetGoogle Scholar
- Yong L, Wenliang H, Yunliang J, Zhiyong Z (2014) Quick attribute reduct algorithm for neighborhood rough set model. Inf Sci 271:65–81CrossRefzbMATHMathSciNetGoogle Scholar
- Zheng K, Jie H, Zhan Z, Ma J, Qi J (2014) An enhancement for heuristic attribute reduction algorithm in rough set. Expert Syst Appl 41(15):6748–6754CrossRefGoogle Scholar