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An improved decision tree algorithm based on boundary mixed attribute dependency

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Abstract

As an effective extension of rough set theory, the variable precision neighborhood rough set model has been applied to the attribute dependency-based improvement of decision tree algorithm of the solution concerning continuous data. However, the boundary region, as an effective description of the uncertainty of knowledge, has not been taken into account in the existing algorithms. In this paper, we define a novel decision rule based on boundary region and attribute dependency, and construct a decision tree algorithm via this decision rule. First, we define a measure called boundary coefficient based on the boundary region, which can be used for comparative quantitative analysis. Second, we define the boundary mixed attribute dependency by combining the boundary coefficient and the attribute dependency, which can consider both the boundary case of the target set and the attribute dependency. Finally, a novel decision tree algorithm is proposed by using the boundary mixed attribute dependency as the decision rule. The experimental results show that with a slight increase in leaf nodes, the total running time decreases and the maximum accuracy increases to 0.9518, which indicates the effectiveness of the proposed algorithm.

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References

  1. Breiman L (2017) Classification and regression trees. Routledge

    Book  Google Scholar 

  2. Broelemann K, Kasneci G (2019) A gradient-based split criterion for highly accurate and transparent model trees. In: Proceedings of the twenty-eighth international joint conference on artificial intelligence. International Joint Conferences on Artificial Intelligence Organization, IJCAI-2019, pp 2030–2037. https://doi.org/10.24963/ijcai.2019/281

  3. Gao C, Zhou J, Miao D et al (2021) Granular-conditional-entropy-based attribute reduction for partially labeled data with proxy labels. Inf Sci 580:111–128. https://doi.org/10.1016/j.ins.2021.08.067

    Article  MathSciNet  Google Scholar 

  4. Gao C, Li Y, Zhou J et al (2022) Global structure-guided neighborhood preserving embedding for dimensionality reduction. Int J Mach Learn Cybern 13(7):2013–2032. https://doi.org/10.1007/s13042-021-01502-6

    Article  Google Scholar 

  5. Gao C, Wang Z, Zhou J (2022) Three-way approximate reduct based on information-theoretic measure. Int J Approx Reason 142:324–337. https://doi.org/10.1016/j.ijar.2021.12.008

    Article  MathSciNet  Google Scholar 

  6. Han X, Zhu X, Pedrycz W et al (2023) A three-way classification with fuzzy decision trees. Appl Soft Comput 132:109788. https://doi.org/10.1016/j.asoc.2022.109788

    Article  Google Scholar 

  7. Hu Q, Yu D, Liu J et al (2008) Neighborhood rough set based heterogeneous feature subset selection. Inf Sci 178(18):3577–3594. https://doi.org/10.1016/j.ins.2008.05.024

    Article  MathSciNet  Google Scholar 

  8. Hu Q, Yu D, Xie Z (2008) Neighborhood classifiers. Expert Syst Appl 34(2):866–876. https://doi.org/10.1016/j.eswa.2006.10.043

    Article  Google Scholar 

  9. Jiang F, Sui Y, Cao C (2013) An incremental decision tree algorithm based on rough sets and its application in intrusion detection. Artif Intell Rev 40(4):517–530. https://doi.org/10.1007/s10462-011-9293-z

    Article  Google Scholar 

  10. Kang Y, Dai J (2023) Attribute reduction in inconsistent grey decision systems based on variable precision grey multigranulation rough set model. Appl Soft Comput 133:109928. https://doi.org/10.1016/j.asoc.2022.109928

    Article  Google Scholar 

  11. Laber E, Murtinho L, Oliveira F (2023) Shallow decision trees for explainable k-means clustering. Pattern Recogn 137:109239. https://doi.org/10.1016/j.patcog.2022.109239

    Article  Google Scholar 

  12. Lin T (1997) Neighborhood systems-a qualitative theory for fuzzy and rough sets. Adv Mach Intell Soft Comput 4:132–155

    Google Scholar 

  13. Lin TY (2003) Neighborhood systems: mathematical models of information granulations. In: SMC’03 Conference proceedings. 2003 IEEE international conference on systems, man and cybernetics. conference theme - system security and assurance (Cat. No.03CH37483), pp 3188–3193 vol.4. https://doi.org/10.1109/ICSMC.2003.1244381

  14. Liu C, Lin B, Lai J et al (2022) An improved decision tree algorithm based on variable precision neighborhood similarity. Inf Sci 615:152–166. https://doi.org/10.1016/j.ins.2022.10.043

    Article  Google Scholar 

  15. Liu C, Lai J, Lin B et al (2023) An improved id3 algorithm based on variable precision neighborhood rough sets. Appl Intell 53:23641–23654. https://doi.org/10.1007/s10489-023-04779-y

    Article  Google Scholar 

  16. Luo C, Cao Q, Li T et al (2023) Mapreduce accelerated attribute reduction based on neighborhood entropy with apache spark. Expert Syst Appl 211:118554. https://doi.org/10.1016/j.eswa.2022.118554

    Article  Google Scholar 

  17. Luo C, Wang S, Li T et al (2023) Rhdofs: a distributed online algorithm towards scalable streaming feature selection. IEEE Trans Parallel and Distrib Syst 34(6):1830–1847. https://doi.org/10.1109/TPDS.2023.3265974

    Article  Google Scholar 

  18. Ma Z, Mi J (2016) Boundary region-based rough sets and uncertainty measures in the approximation space. Inf Sci 370–371:239–255. https://doi.org/10.1016/j.ins.2016.07.040

    Article  Google Scholar 

  19. Mani A (2018) Algebraic methods for granular rough sets. Springer International Publishing, Cham, pp 157–335. https://doi.org/10.1007/978-3-030-01162-8_3

  20. Mani A (2022) Granularity and rational approximation: rethinking graded rough sets. Springer Berlin Heidelberg, Berlin, Heidelberg, pp 33–59. https://doi.org/10.1007/978-3-662-66544-2_4

  21. Miao D, Wang J (1997) Rough sets based approach for multivariate decision tree construction. Chin J Softw 8(6):26–32(In Chinese with English Abstract)

  22. Parthaláin N, Shen Q, Jensen R (2010) A distance measure approach to exploring the rough set boundary region for attribute reduction. IEEE Trans Knowl Data Eng 22(3):305–317. https://doi.org/10.1109/TKDE.2009.119

    Article  Google Scholar 

  23. Pawlak Z (1982) Rough sets. Int J Comput Inform Sci 11(5):341–356. https://doi.org/10.1007/BF01001956

    Article  Google Scholar 

  24. Quinlan JR (1986) Induction of decision trees. Mach Learn 1:81–106

    Article  Google Scholar 

  25. Quinlan JR (2014) C4. 5: programs for machine learning. Elsevier

  26. Ren Y, Zhu X, Bai K et al (2023) A new random forest ensemble of intuitionistic fuzzy decision trees. IEEE Trans Fuzzy Syst 31(5):1729–1741. https://doi.org/10.1109/TFUZZ.2022.3215725

    Article  Google Scholar 

  27. Wang J, Qian Y, Li F et al (2020) Fusing fuzzy monotonic decision trees. IEEE Trans Fuzzy Syst 28(5):887–900. https://doi.org/10.1109/TFUZZ.2019.2953024

    Article  Google Scholar 

  28. Xie X, Xianyong Z, Wuanye W et al (2021) Neighborhood decision tree construction algorithm based on variable precision neighborhood equivalent granules. Chin J Comput Appl 42(2):382–388 (In Chinese with English Abstract)

  29. Xu B, Zhang X, Feng S (2018) Weighted denpendence of neighborhood rough sets and its heuristic reduction algorithm. Chin Pattern Recognit Artif Intell 31(3):256–264 (In Chinese with English Abstract)

  30. Xu W, Yuan Z, Liu Z (2023) Feature selection for unbalanced distribution hybrid data based on k-nearest neighborhood rough set. IEEE Trans Artif Intell pp 1–15. https://doi.org/10.1109/TAI.2023.3237203

  31. Yang X, Chen Y, Fujita H et al (2022) Mixed data-driven sequential three-way decision via subjective-objective dynamic fusion. Knowl Based Syst 237:107728. https://doi.org/10.1016/j.knosys.2021.107728

    Article  Google Scholar 

  32. Yang X, Li M, Fujita H et al (2022) Incremental rough reduction with stable attribute group. Inf Sci 589:283–299. https://doi.org/10.1016/j.ins.2021.12.119

    Article  Google Scholar 

  33. Yao Y, Zhang X, Chen S et al (2021) Decision-tree induction algorithm based on attribute purity degree. Chinese Comput Eng Des 42(1):142–149 (In Chinese with English Abstract)

  34. Zhai J, Wang X, Zhang S et al (2018) Tolerance rough fuzzy decision tree. Inf Sci 465:425–438. https://doi.org/10.1016/j.ins.2018.07.006

    Article  ADS  MathSciNet  Google Scholar 

  35. Zhang X, Yao Y (2022) Tri-level attribute reduction in rough set theory. Expert Syst Appl 190:116187. https://doi.org/10.1016/j.eswa.2021.116187

    Article  Google Scholar 

  36. Zhang X, Yuan Z, Miao D (2023) Outlier detection using three-way neighborhood characteristic regions and corresponding fusion measurement. IEEE Trans Knowl Data Eng 1–14. https://doi.org/10.1109/TKDE.2023.3312108

  37. Ziarko W (1993) Variable precision rough set model. J Comput Syst Sci 46(1):39–59. https://doi.org/10.1016/0022-0000(93)90048-2

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This research is supported by the National Natural Science Foundation of China under Grant Nos. 62166001, Graduate Innovation Funding Program of Gannan Normal University, China under Grant No. YCX22A025.

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Contributions

Bowen Lin: Conceptualization, Methodology, Writing - original draft, Software, Validation, Data-curation. Caihui Liu: Conceptualization, Methodology, Writing - review & editing, Validation, Supervision. Duoqian Miao: Writing - review & editing.

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Correspondence to Caihui Liu.

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Lin, B., Liu, C. & Miao, D. An improved decision tree algorithm based on boundary mixed attribute dependency. Appl Intell 54, 2136–2153 (2024). https://doi.org/10.1007/s10489-023-05238-4

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