关联规则分析中兴趣度量Lift与Conviction的关系探讨及教育数据验证
Exploration of the Relationship between Interest Measures Lift and Conviction in Association Rule Analysis and Education Data Validation
摘要: 关联规则分析是数据挖掘中最常用的研究方法之一。在关联关系的发现过程中兴趣度量是关联规则发现的理论基础，它可以度量规则的重要程度，其中Lift和Conviction这两个度量在数据分析中被广泛应用于筛选关联规则。本文对这两种兴趣度量进行了研究。首先，提出并证明了当后项集固定时，Conviction取值随Lift取值单调增加，且Conviction (Lift)是一个凸函数。然后，证明了当Confidence固定时，Conviction取值随Lift取值单调增加，且Conviction (Lift)是一个凹函数。最后，综合以上两个方面，得到一个重要结论：当后项集保持不变或当Confidence固定时，根据Conviction和Lift筛选出来的规则都是相同的。最后，利用某高校数学类专业三个年级的成绩数据进行了定理及相应结论的验证。
Abstract: Association rule analysis is one of the most active research methods in data mining. In the process of finding association relationships, interest measures are the theoretical basis and can measure the significance of rules, where Lift and Conviction are widely used in data analyses to find association rules. This paper studies these two measures. First, it is proven that when the Consequent is fixed, the value of Conviction increases monotonically with the value of Lift, and Conviction is a convex function of Lift. Second, when Confidence is fixed, the value of Conviction increases monotonically with the value of Lift, and Conviction is a concave function of Lift. Then, integrating the above two aspects, we obtain an important conclusion: when the Consequent remains fixed or when the Confidence value is fixed, the rules selected by Conviction are the same as those selected by Lift. Finally, the theorems and the corresponding conclusion are verified by using the achievement data of three grades of mathematics major in a university.
文章引用：万鑫, 李梓如, 李裕梅. 关联规则分析中兴趣度量Lift与Conviction的关系探讨及教育数据验证[J]. 数据挖掘, 2024, 14(3): 189-206. https://doi.org/10.12677/hjdm.2024.143018

参考文献

[1] Rakesh, A. and Ramakrishnan, S. (1994) Fast Algorithms for Mining Association Rules in Large Databases. Morgan Kaufmann Publishers Inc., 487-499.
[2] Brin, S., Motwani, R., Ullman, J.D. and Tsur, S. (1997) Dynamic Itemset Counting and Implication Rules for Market Basket Data. ACM SIGMOD Record, 26, 255-264. [Google Scholar] [CrossRef] 
[3] Wong, M., Sze-To, H., Lo, L., Chan, T. and Leung, K. (2015) Discovering Binding Cores in Protein-DNA Binding Using Association Rule Mining with Statistical Measures. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 12, 142-154. [Google Scholar] [CrossRef] [PubMed]
[4] Xiang, Y., Shuai, C., Li, Y. and Zhang, Y. (2022) Information Reconstruction of Student Management Work Based on Association Rules Mining. Computational Intelligence and Neuroscience, 2022, Article ID: 2318515. [Google Scholar] [CrossRef] [PubMed]
[5] Shrestha, A., Zikos, D. and Fegaras, L. (2021) An Annotated Association Mining Approach for Extracting and Visualizing Interesting Clinical Events. International Journal of Medical Informatics, 148, Article ID: 104366. [Google Scholar] [CrossRef] [PubMed]
[6] Hu, K., Qiu, L., Zhang, S., Wang, Z. and Fang, N. (2023) An Animal Dynamic Migration Optimization Method for Directional Association Rule Mining. Expert Systems with Applications, 211, Article ID: 118617. [Google Scholar] [CrossRef] 
[7] Ohsaki, M., Kitaguchi, S., Okamoto, K., Yokoi, H. and Yamaguchi, T. (2004) Evaluation of Rule Interestingness Measures with a Clinical Dataset on Hepatitis. 8th European Conference on Principles and Practice of Knowledge Discovery in Databases, Pisa, 20-24 September 2004, 362-373. [Google Scholar] [CrossRef] 
[8] Brin, S., Motwani, R. and Silverstein, C. (1997) Beyond Market Baskets: Generalizing Association Rules to Correlations. ACM SIGMOD Record, 26, 265-276. [Google Scholar] [CrossRef] 
[9] Azevedo, P.J. and Jorge, A.M. (2007) Comparing Rule Measures for Predictive Association Rules. In: Machine Learning: ECML 2007, Springer, 510-517. [Google Scholar] [CrossRef] 
[10] Lenca, P., Meyer, P., Vaillant, B. and Lallich, S. (2008) On Selecting Interestingness Measures for Association Rules: User Oriented Description and Multiple Criteria Decision Aid. European Journal of Operational Research, 184, 610-626. [Google Scholar] [CrossRef] 
[11] 姜盛彬. 数据挖掘中基于兴趣度的关联规则研究[D]: [硕士学位论文]. 长沙: 湖南师范大学, 2016.
[12] Lobo, D. (2014) Association Rules: Normalizing the Lift. 9th International Conference on Digital Information Management (ICDIM 2014), Phitsanulok, 29 September-1 October 2014, 151-155. [Google Scholar] [CrossRef] 
[13] Ordonez, C. and Zhao, K. (2011) Evaluating Association Rules and Decision Trees to Predict Multiple Target Attributes. Intelligent Data Analysis, 15, 173-192. [Google Scholar] [CrossRef] 
[14] 邱均平, 崔腾腾, 陈仕吉. 基于聚类和关联规则的Altmetric TOP榜文献特征分析[J]. 现代情报, 2021, 41(9): 12-21+63.
[15] 李鑫, 史天运, 常宝, 等. 基于优化的MsEclat算法的铁路机车事故故障关联规则挖掘[J]. 中国铁道科学, 2021, 42(4): 155-165.
[16] 王枭翔. 基于相关兴趣度的关联规则挖掘[D]: [硕士学位论文]. 兰州: 兰州交通大学, 2014.
[17] Bao, F., Mao, L., Zhu, Y., Xiao, C. and Xu, C. (2021) An Improved Evaluation Methodology for Mining Association Rules. Axioms, 11, Article No. 17. [Google Scholar] [CrossRef] 
[18] McNicholas, P.D., Murphy, T.B. and O’Regan, M. (2008) Standardising the Lift of an Association Rule. Computational Statistics & Data Analysis, 52, 4712-4721. [Google Scholar] [CrossRef] 
[19] Liu, B., Hsu, W. and Ma, Y. (1998) Integrating Classification and Association Rule Mining. Proceedings of KDD, Vol. 1711, 80-86.
[20] 朱晓燕, 宋擒豹. 基于排序的关联分类算法[J]. 计算机科学, 2009, 36(7): 204-207.
[21] 宋威, 高磊, 李晋宏. 一种基于闭项集的无冗余关联规则挖掘方法[J]. 北京交通大学学报, 2009, 33(6): 91-96.
[22] Zaki, M.J., Meira Jr., W. 数据挖掘与分析概念与算法[M]. 吴诚堃, 译. 北京: 人民邮电出版社, 2017: 186-189.
[23] 李珺, 刘鹤, 朱良宽. 基于改进的K-means算法的关联规则数据挖掘研究[J]. 小型微型计算机系统, 2021, 42(1): 15-19.
[24] 李珺, 刘鹤, 朱良宽. 基于Apriori关联规则算法的草莓叶片含水状况研究[J]. 北方园艺, 2020(19): 146-151.
[25] Hussein, N., Alashqur, A. and Sowan, B. (2015) Using the Interestingness Measure Lift to Generate Association Rules. Journal of Advanced Computer Science & Technology, 4, 156-162. [Google Scholar] [CrossRef] 

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