{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,11]],"date-time":"2026-07-11T16:45:54Z","timestamp":1783788354725,"version":"3.55.0"},"reference-count":36,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,7,23]],"date-time":"2020-07-23T00:00:00Z","timestamp":1595462400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61906104"],"award-info":[{"award-number":["61906104"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Natural Science Foundation of Shandong Province, China","award":["ZR2019BF018"],"award-info":[{"award-number":["ZR2019BF018"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>As an important technology in computer science, data mining aims to mine hidden, previously unknown, and potentially valuable patterns from databases.High utility negative sequential rule (HUNSR) mining can provide more comprehensive decision-making information than high utility sequential rule (HUSR) mining by taking non-occurring events into account. HUNSR mining is much more difficult than HUSR mining because of two key intrinsic complexities. One is how to define the HUNSR mining problem and the other is how to calculate the antecedent\u2019s local utility value in a HUNSR, a key issue in calculating the utility-confidence of the HUNSR. To address the intrinsic complexities, we propose a comprehensive algorithm called e-HUNSR and the contributions are as follows. (1) We formalize the problem of HUNSR mining by proposing a series of concepts. (2) We propose a novel data structure to store the related information of HUNSR candidate (HUNSRC) and a method to efficiently calculate the local utility value and utility of HUNSRC\u2019s antecedent. (3) We propose an efficient method to generate HUNSRC based on high utility negative sequential pattern (HUNSP) and a pruning strategy to prune meaningless HUNSRC. To the best of our knowledge, e-HUNSR is the first algorithm to efficiently mine HUNSR. The experimental results on two real-life and 12 synthetic datasets show that e-HUNSR is very efficient.<\/jats:p>","DOI":"10.3390\/sym12081211","type":"journal-article","created":{"date-parts":[[2020,7,23]],"date-time":"2020-07-23T11:26:01Z","timestamp":1595503561000},"page":"1211","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["e-HUNSR: An Efficient Algorithm for Mining High Utility Negative Sequential Rules"],"prefix":"10.3390","volume":"12","author":[{"given":"Mengjiao","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tiantian","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhao","family":"Li","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China"},{"name":"Shandong Computer Science Center (National Supercomputer Center in Jinan), Shandong Provincial Key Laboratory of Computer Networks, Jinan 250014, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiqing","family":"Han","sequence":"additional","affiliation":[{"name":"Shandong Institute of Commerce and Technology, Jinan 250103, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiangjun","family":"Dong","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,23]]},"reference":[{"key":"ref_1","unstructured":"(2020, May 20). 2nd International Workshop on Utility-Driven Mining and Learning [EB\/OL]. Available online: http:\/\/www.philippe-fournier-viger.com\/utility_mining_workshop_2019\/."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"676","DOI":"10.4218\/etrij.10.1510.0066","article-title":"A Novel Approach for Mining High-Utility Sequential Patterns in Sequence Databases","volume":"32","author":"Ahmed","year":"2010","journal-title":"Etri J."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Yin, J., Zheng, Z., and Cao, L. (2012, January 12\u201316). USpan: An efficient algorithm for mining high utility sequential patterns. Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Beijing, China.","DOI":"10.1145\/2339530.2339636"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.eswa.2018.03.019","article-title":"A pure array structure and parallel strategy for high-utility sequential pattern mining","volume":"104","author":"Le","year":"2018","journal-title":"Expert Syst. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.knosys.2017.03.016","article-title":"An efficient algorithm for mining high utility patterns from incremental databases with one database scan","volume":"124","author":"Yun","year":"2017","journal-title":"Knowl.-Based Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1007\/s10994-016-5617-1","article-title":"Memory-adaptive high utility sequential pattern mining over data streams","volume":"106","author":"Zihayat","year":"2017","journal-title":"Mach. Learn."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1142\/S0218001418590176","article-title":"Mining High Utility Sequential Patterns Using Multiple Minimum Utility","volume":"32","author":"Xu","year":"2018","journal-title":"Int. J. Pattern Recogn. Artif. Intell."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Xu, T., Dong, X., Xu, J., and Dong, X. (2017). Mining High Utility Sequential Patterns with Negative Item Values. Int. J. Pattern Recogn. Artif. Intell., 31.","DOI":"10.1142\/S0218001417500355"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"40714","DOI":"10.1109\/ACCESS.2020.2976662","article-title":"Efficient Chain Structure for High-Utility Sequential Pattern Mining","volume":"8","author":"Lin","year":"2020","journal-title":"IEEE Access"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1195","DOI":"10.1109\/TCYB.2019.2896267","article-title":"HUOPM: High-Utility Occupancy Pattern Mining","volume":"50","author":"Gan","year":"2020","journal-title":"IEEE Trans. Cybern."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.ins.2019.05.006","article-title":"An efficient method for mining high utility closed itemsets","volume":"495","author":"Nguyen","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"e12296.1","DOI":"10.1111\/exsy.12296","article-title":"Mining of high-utility itemsets with negative utility","volume":"35","author":"Singh","year":"2018","journal-title":"Expert Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.knosys.2017.12.035","article-title":"Efficiently mining high utility itemsets with negative unit profits","volume":"145","author":"Krishnamoorthy","year":"2018","journal-title":"Knowl.-Based Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"23839","DOI":"10.1109\/ACCESS.2018.2827167","article-title":"Efficient High Utility Negative Sequential Patterns Mining in Smart Campus","volume":"6","author":"Xu","year":"2018","journal-title":"IEEE Access"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Zida, S., Fournier-Viger, P., and Wu, C.-W. (2015). Efficient Mining of High-Utility Sequential Rules. International Workshop on Machine Learning and Data Mining in Pattern Recognition, Springer.","DOI":"10.1007\/978-3-319-21024-7_11"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.neucom.2018.09.108","article-title":"An efficient method for pruning redundant negative and positive association rules","volume":"393","author":"Dong","year":"2020","journal-title":"Neurocomputing"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"576","DOI":"10.3390\/sym10110576","article-title":"Efficient Association Rules Hiding Using Genetic Algorithms","volume":"10","author":"Bux","year":"2018","journal-title":"Symmetry"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Xu, J.Y., Liu, T., and Yang, L.T. (2019). Finding College Student Social Networks by Mining the Records of Student ID Transactions. Symmetry, 11.","DOI":"10.3390\/sym11030307"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5754","DOI":"10.1016\/j.eswa.2015.02.051","article-title":"An efficient approach for mining association rules from high utility itemsets","volume":"42","author":"Sahoo","year":"2015","journal-title":"Expert Syst. Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.artint.2016.03.001","article-title":"e-NSP: Efficient negative sequential pattern mining","volume":"235","author":"Cao","year":"2016","journal-title":"Artif. Intell."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2764","DOI":"10.1109\/TNNLS.2018.2886199","article-title":"Mining Top-k Useful Negative Sequential Patterns via Learning","volume":"30","author":"Dong","year":"2019","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2084","DOI":"10.1109\/TCYB.2018.2869907","article-title":"e-RNSP: An Efficient Method for Mining Repetition Negative Sequential Patterns","volume":"50","author":"Dong","year":"2018","journal-title":"IEEE Trans. Cybern."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.patcog.2018.06.016","article-title":"F-NSP+: A fast negative sequential patterns mining method with self-adaptive data storage","volume":"84","author":"Dong","year":"2018","journal-title":"Pattern Recogn."},{"key":"ref_24","unstructured":"Nguyen, L.T.T., Mai, T., and Vo, B. (2018, January 3\u20137). High Utility Association Rule Mining. Proceedings of the 17th International Conference (ICAISC 2018), Zakopane, Poland."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.ins.2017.02.058","article-title":"A lattice-based approach for mining high utility association rules","volume":"399","author":"Mai","year":"2017","journal-title":"Inf. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2715","DOI":"10.1016\/j.eswa.2012.11.021","article-title":"Utility-based association rule mining: A marketing solution for cross-selling","volume":"40","author":"Lee","year":"2013","journal-title":"Expert Syst. Appl."},{"key":"ref_27","unstructured":"Agrawal, R., and Srikant, R. (1995, January 6\u201310). Mining sequential patterns. Proceedings of the Eleventh International Conference on Data Engineering, Taipei, Taiwan."},{"key":"ref_28","unstructured":"Yin, J. (2015). Mining High Utility Sequential Patterns, University of Technology Sydney."},{"key":"ref_29","unstructured":"(2019, September 05). Kdd Cup 2000: Online Retailer Website Clickstream Analysis [EB\/OL]. Available online: http:www.sigkdd.org\/kdd-cup-2000-online-retailer-websiteclickstream-analysis."},{"key":"ref_30","unstructured":"(2019, October 15). SPMF: An Open-Source Data Mining Library [EB\/OL]. Available online: http:\/\/www.philippe-fournier-viger.com\/spmf\/."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1177\/1362168816662290","article-title":"Chunk use and development in advanced Chinese L2 learners of English","volume":"22","author":"Hou","year":"2018","journal-title":"Lang. Teach. Res."},{"key":"ref_32","first-page":"131","article-title":"Research on the Teaching of Spoken English Based on the Theory of Prefabricated Chunks","volume":"2","author":"Wen","year":"2011","journal-title":"J. Mudanjiang Coll. Educ."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"115","DOI":"10.17507\/jltr.0801.14","article-title":"Promoting Interpreter Competence through Input Enhancement of Prefabricated Lexical Chunks","volume":"8","author":"Meng","year":"2017","journal-title":"J. Lang. Teach. Res."},{"key":"ref_34","first-page":"194","article-title":"Prefabricated Chunks and Second Language Listening Comprehension","volume":"16","author":"Guan","year":"2014","journal-title":"J. Dalian Natl. Univ."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"666","DOI":"10.1016\/j.knosys.2018.09.026","article-title":"Finding tendencies in streaming data using Big Data frequent itemset mining","volume":"163","author":"Fernandezbasso","year":"2019","journal-title":"Knowl.-Based syst."},{"key":"ref_36","unstructured":"Yen, S.J., and Lee, Y.S. (2007, January 3\u20137). Mining high utility quantitative association rules. Proceedings of the International Conference on Data Warehousing and Knowledge Discovery, Regensburg, Germany."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/8\/1211\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:51:14Z","timestamp":1760176274000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/8\/1211"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,23]]},"references-count":36,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2020,8]]}},"alternative-id":["sym12081211"],"URL":"https:\/\/doi.org\/10.3390\/sym12081211","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,7,23]]}}}