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In this paper, an efficient hybrid algorithm is proposed with the strategy of two-stage searches. For first-stage search, it firstly determines the local search space based on Maximal Information Coefficient by introducing penalty factors p1, p2, then searches the local space by Binary Particle Swarm Optimization. For second-stage search, an efficient ADR (the abbreviation of Add, Delete, Reverse) algorithm based on three basic operators is designed to extend the local space to the whole space. Experiment results show that the proposed algorithm can obtain better performance of BN structure learning.<\/jats:p>","DOI":"10.3233\/ida-194844","type":"journal-article","created":{"date-parts":[[2020,10,2]],"date-time":"2020-10-02T13:35:11Z","timestamp":1601645711000},"page":"1087-1106","source":"Crossref","is-referenced-by-count":10,"title":["An efficient Bayesian network structure learning algorithm using the strategy of two-stage searches"],"prefix":"10.1177","volume":"24","author":[{"given":"Huiping","family":"Guo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongru","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"key":"10.3233\/IDA-194844_ref1","first-page":"1","article-title":"A novel method for Bayesian networks structure learning based on Breeding Swarm algorithm","volume":"13","author":"Khanteymoori","year":"2017","journal-title":"Soft Computing"},{"key":"10.3233\/IDA-194844_ref2","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/S0141-9331(02)00053-4","article-title":"Particle swarm optimization for task assignment problem","volume":"26","author":"Salman","year":"2002","journal-title":"Microprocessors and Microsystems"},{"key":"10.3233\/IDA-194844_ref3","doi-asserted-by":"crossref","first-page":"3383","DOI":"10.12733\/jics20105969","article-title":"Learning Bayesian Network Structure Based on Topological Potential","volume":"12","author":"Wang","year":"2015","journal-title":"Journal of Information & Computational Science"},{"key":"10.3233\/IDA-194844_ref4","first-page":"121","article-title":"Learning bayesian networks is np-complete","volume":"112","author":"Chickering","year":"1996","journal-title":"Networks"},{"key":"10.3233\/IDA-194844_ref5","first-page":"507","article-title":"Optimal Structure Identification With Greedy Search","volume":"3","author":"Chickering","year":"2002","journal-title":"Journal of Machine Learning Research"},{"key":"10.3233\/IDA-194844_ref6","doi-asserted-by":"crossref","first-page":"1518","DOI":"10.1126\/science.1205438","article-title":"Detecting novel associations in large data sets","volume":"334","author":"Reshef","year":"2011","journal-title":"Science"},{"key":"10.3233\/IDA-194844_ref7","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1007\/s10489-015-0686-6","article-title":"Intelligent control of photovoltaic system using BPSO-GSA-optimized neural network and fuzzy-based PID for maximum power point tracking","volume":"44","author":"Azali","year":"2016","journal-title":"Applied Intelligence"},{"key":"10.3233\/IDA-194844_ref8","first-page":"151","article-title":"Bayesian network learning with discrete case-control data","author":"Borboudakis","year":"2015","journal-title":"Uncertainty in Artificial Intelligence"},{"key":"10.3233\/IDA-194844_ref9","unstructured":"G.L. Li, X.G. Gao and R.H. Di, DBN structure learning based on mi-bpso algorithm, in: Ieee\/acis International Conference on Computer and Information Science, 2014, pp. 245\u2013250."},{"key":"10.3233\/IDA-194844_ref10","doi-asserted-by":"crossref","unstructured":"H. Guo, R. Zhang, J. Yong and B. 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Li, Fault detection for medical body sensor networks under bayesian network model, in: International Conference on Mobile Ad-Hoc and Sensor Networks, 2016, pp. 37\u201342.","DOI":"10.1109\/MSN.2015.21"},{"key":"10.3233\/IDA-194844_ref14","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s10994-006-6889-7","article-title":"The max-min hill-climbing Bayesian network structure learning algorithm","volume":"65","author":"Tsamardinos","year":"2006","journal-title":"Machine Learning"},{"key":"10.3233\/IDA-194844_ref15","doi-asserted-by":"crossref","unstructured":"J.B. Kinney and G.S. 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Li and Y.X. Zhang, A Method for Learning Bayesian Network Structure, in: Sixth International Conference on Intelligent Human-Machine Systems and Cybernetics, 2014, pp. 222\u2013225."},{"key":"10.3233\/IDA-194844_ref20","first-page":"331","article-title":"The bayes net toolbox for matlab","volume":"33","author":"Murphy","year":"2001","journal-title":"Comput Sci Stat"},{"key":"10.3233\/IDA-194844_ref21","doi-asserted-by":"crossref","unstructured":"K.X. Huang, C.J. Zhou, Y.C. Tian, W. Tu and Y. Peng, Application of Bayesian network to data-driven cyber-security risk assessment in SCADA networks, in: 2017 27th International Telecommunication Networks and Applications Conference (ITNAC), 2017, pp.\u00a01\u20136.","DOI":"10.1109\/ATNAC.2017.8215355"},{"key":"10.3233\/IDA-194844_ref22","doi-asserted-by":"crossref","first-page":"12699","DOI":"10.1016\/j.eswa.2011.04.057","article-title":"Improved binary particle swarm optimization using catfish effect for feature selection","volume":"38","author":"Chuang","year":"2011","journal-title":"Expert Systems with Applications"},{"key":"10.3233\/IDA-194844_ref23","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.ijar.2006.06.009","article-title":"Bayesian network learning algorithms using structural restrictions","volume":"45","author":"Campos","year":"2007","journal-title":"International Journal of Approximate Reasoning"},{"key":"10.3233\/IDA-194844_ref24","unstructured":"L. Zhang, A bayesian network based structure learning algorithm, in: International Conference on Robots and Intelligent System, 2016, pp. 12\u201315."},{"key":"10.3233\/IDA-194844_ref25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4018\/IJRSDA.2018040101","article-title":"Particle Swarm Optimization from Theory to Applications","volume":"5","author":"El-Shorbagy","year":"2018","journal-title":"International Journal of Rough Sets and Data Analysis"},{"key":"10.3233\/IDA-194844_ref26","doi-asserted-by":"crossref","first-page":"6755","DOI":"10.1016\/j.eswa.2014.04.032","article-title":"A hybrid algorithm for Bayesian network structure learning with application to multi-label learning","volume":"41","author":"Gasse","year":"2014","journal-title":"Expert Systems with Applications"},{"key":"10.3233\/IDA-194844_ref27","first-page":"889","article-title":"Learning bayesian networks in the space of structures by a hybrid optimization algorithm","volume":"11","author":"Zhu","year":"2016","journal-title":"International Journal of Intelligent Systems"},{"key":"10.3233\/IDA-194844_ref28","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1109\/TEVC.2009.2024142","article-title":"Using a local discovery ant algorithm for bayesian network structure learning","volume":"13","author":"Pinto","year":"2009","journal-title":"IEEE Transactions on Evolutionary Computation"},{"key":"10.3233\/IDA-194844_ref29","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.ifacol.2016.11.006","article-title":"Object Oriented Bayesian Network for complex system risk assessment","volume":"49","author":"Liu","year":"2017","journal-title":"IFAC-PapersOnLine"},{"key":"10.3233\/IDA-194844_ref30","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1007\/978-3-319-91189-2_21","article-title":"MIC-KMeans: A Maximum Information Coefficient Based High-Dimensional Clustering Algorithm","author":"Wang","year":"2019","journal-title":"Artificial Intelligence and Algorithms in Intelligent Systems"},{"key":"10.3233\/IDA-194844_ref31","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1007\/BFb0069178","article-title":"Counting unlabeled acyclic digraphs","volume":"622","author":"Robinson","year":"1977","journal-title":"Combinatorial Mathematics V"},{"key":"10.3233\/IDA-194844_ref32","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1007\/978-3-319-07593-8_58","article-title":"Learning Bayesian Networks Using Probability Vectors","volume":"290","author":"Fukuda","year":"2014","journal-title":"Advances in Intelligent Systems and Computing"},{"key":"10.3233\/IDA-194844_ref33","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1016\/j.ins.2016.01.090","article-title":"BNC-PSO: structure learning of Bayesian networks by Particle Swarm Optimization","volume":"348","author":"Gheisari","year":"2016","journal-title":"Information Sciences"},{"key":"10.3233\/IDA-194844_ref34","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.patrec.2013.12.021","article-title":"An efficient node ordering method using the conditional frequency for the K2 algorithm","volume":"40","author":"Ko","year":"2014","journal-title":"Pattern Recognition Letters"},{"key":"10.3233\/IDA-194844_ref35","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.swevo.2012.09.002","article-title":"S-shaped versus V-shaped transfer functions for binary Particle Swarm Optimization","volume":"9","author":"Mirjalili","year":"2013","journal-title":"Swarm & Evolutionary Computation"},{"key":"10.3233\/IDA-194844_ref36","unstructured":"T. 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