Abstract
In this paper, a Modified variant of Particle Swarm Optimization named MPSOPR is proposed. The velocity update in MPSOPR follows a neighbourhood-based learning strategy based on PageRank (PR) algorithm and a scale-free network is proposed for the interaction among particles in the population. This is in contrast to the basic PSO which has a fully connected topology or regular topology. The inclusion of these two modifications helps in enhancing the diversity and the information dissemination ability of the algorithm. Performance of MPSOPR is validated on a set of 17 benchmark problems divided into 3 groups, on basis of level of difficulties. Comparative analysis of the results obtained through MPSOPR with 9 other variants of PSO, indicate that the proposed scheme can help in improving the performance of PSO significantly. The performance of MPSOPR is further validated by employing it for solving problems related to recommender system.
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References
Adomavicius G, Tuzhilin A (2005) Toward the next generation of recommender systems: a survey of the state-of-the-art and possible extensions. IEEE Trans Knowl Data Eng 17(6):734–749. https://doi.org/10.1109/TKDE.2005.99
Ahn HJ (2008) A new similarity measure for collaborative filtering to alleviate the new user cold-starting problem. Inf Sci 178(1):37–51. https://doi.org/10.1016/j.ins.2007.07.024
Barabasi, & Albert. (1999). Emergence of scaling in random networks. Science (New York, N.Y.), 286(5439), 509–512. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/10521342
Birtolo C, Ronca D (2013) Advances in Clustering Collaborative Filtering by means of Fuzzy C-means and trust. Expert Syst Appl 40(17):6997–7009. https://doi.org/10.1016/j.eswa.2013.06.022
Birtolo C, Ronca D, Armenise R (2011) Improving accuracy of recommendation system by means of Item-based Fuzzy Clustering Collaborative Filtering. In 2011 11th International Conference on Intelligent Systems Design and Applications (pp. 100–106). IEEE. https://doi.org/10.1109/ISDA.2011.6121638
Celebi ME, Kingravi HA, Vela PA (2013) A comparative study of efficient initialization methods for the k-means clustering algorithm. Expert Syst Appl 40(1):200–210. https://doi.org/10.1016/j.eswa.2012.07.021
Chen C-Y, Ye F (2004). Particle swarm optimization algorithm and its application to clustering analysis. 2004 IEEE Conference on Networking, Sensing and Control, (1), 789–794. Retrieved from http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1297047
Chen WN, Zhang J, Lin Y, Chen N, Zhan ZH, Chung HSH, Shi YH (2013) Particle swarm optimization with an aging leader and challengers. IEEE Trans Evol Comput 17(2):241–258. https://doi.org/10.1109/TEVC.2011.2173577
Dowlatshahi MB, Nezamabadi-Pour H (2014) GGSA: A Grou** Gravitational Search Algorithm for data clustering. Eng Appl Artif Intell 36:114–121. https://doi.org/10.1016/j.engappai.2014.07.016
Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. MHS’95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science, 39–43. https://doi.org/10.1109/MHS.1995.494215
Ferman AM, Errico JH, van Beek P, Sezan MI (2002). Content-based filtering and personalization using structured metadata. In Proceedings of the second ACM/IEEE-CS joint conference on Digital libraries - JCDL ‘02 (p. 393). New York, New York, USA: ACM Press. https://doi.org/10.1145/544220.544341
Funk S (2006) Netflix update: Try this at home. http://sifter.org/simon/journal/20061211.html. Accessed 4 Nov 2017
Hanjalic A, Lienhart R, Ma W-Y, Smith JR (2008) The Holy Grail of Multimedia Information Retrieval: So Close or Yet So Far Away? Proc IEEE 96(4):541–547. https://doi.org/10.1109/JPROC.2008.916338
Herlocker J, Konstan JA, Riedl J (2002) An Empirical Analysis of Design Choices in Neighborhood-Based Collaborative Filtering Algorithms. Inf Retr 5(4):287–310. https://doi.org/10.1023/A:1020443909834
Herlocker JL, Konstan JA, Terveen LG, Riedl JT (2004) Evaluating collaborative filtering recommender systems. ACM Trans Inf Syst 22(1):5–53. https://doi.org/10.1145/963770.963772
Hruschka ER, Campello RJGB, Freitas AA, de Carvalho ACPLF (2009) A survey of evolutionary algorithms for clustering. IEEE Trans Syst Man Cybern Part C Appl Rev 39(2):133–155. https://doi.org/10.1109/TSMCC.2008.2007252
Janson S, Middendorf M (2003) A hierarchical particle swarm optimizer. The 2003 Congress on Evolutionary Computation, 2003. CEC ‘03., 2(6), 770–776. https://doi.org/10.1109/CEC.2003.1299745
Katarya R, Verma OP (2016) A collaborative recommender system enhanced with particle swarm optimization technique. Multimedia Tools and Applications 75(15):9225–9239 https://doi.org/10.1007/s11042-016-3481-4
Kennedy J, Mendes R (2002) Population structure and particle swarm performance. In Evolutionary Computation, 2002. CEC'02. Proceedings of the 2002 Congress on (Vol. 2, pp. 1671–1676). IEEE.
Kennedy J (1999) Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance. In Evolutionary Computation, 1999. CEC 99. Proceedings of the 1999 Congress on (Vol. 3)
Kennedy J, Mendes R (2003) Neighborhood topologies in fully-informed and best-of-neighborhood particle swarms. SMCia 2003 - Proceedings of the 2003 IEEE International Workshop on Soft Computing in Industrial Applications, (August 2006), 45–50. https://doi.org/10.1109/SMCIA.2003.1231342
Kiran MS (2017) Particle swarm optimization with a new update mechanism. Appl Soft Comput 60:670–678. https://doi.org/10.1016/j.asoc.2017.07.050
Koohi H, Kiani K (2016) User based Collaborative Filtering using fuzzy C-means. Measurement 91:134–139. https://doi.org/10.1016/j.measurement.2016.05.058
Koren Y (2008) Factorization meets the neighborhood. In Proceeding of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD 08 (p. 426). New York, New York, USA: ACM Press. https://doi.org/10.1145/1401890.1401944
Koren Y (2010) Factor in the neighbors. ACM Trans Knowl Discov Data 4(1):1–24. https://doi.org/10.1145/1644873.1644874
Liang J, Suganthan P (2005) Dynamic multi-swarm particle swarm optimizer with local search. 2005 IEEE Congress On. Retrieved from http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1554727
Liang JJ, Qin AK, Member S, Suganthan PN, Member S, Baskar S (2006) Comprehensive Learning Particle Swarm Optimizer for Global Optimization of Multimodal Functions, 10(3), 281–295. https://doi.org/10.1109/TEVC.2005.857610
Liu Y, Qin Z, Shi Z, Lu J (2007) Center particle swarm optimization. Neurocomputing 70(4–6):672–679. https://doi.org/10.1016/j.neucom.2006.10.002
Liu Q, Chen E, **ong H, Ding CHQ, Chen J (2012) Enhancing collaborative filtering by user interest expansion via personalized ranking. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 42(1):218–233. https://doi.org/10.1109/TSMCB.2011.2163711
Liu C, Du WB, Wang WX (2014a) Particle swarm optimization with scale-free interactions. PLoS One 9(5):1–8. https://doi.org/10.1371/journal.pone.0097822
Liu H, Hu Z, Mian A, Tian H, Zhu X (2014b) A new user similarity model to improve the accuracy of collaborative filtering. Knowl-Based Syst 56:156–166. https://doi.org/10.1016/j.knosys.2013.11.006
Ma C-C (2008) A guide to singular value decomposition for collaborative filtering. Computer (Long Beach, CA), 1–14
Maulik U, Bandyopadhyay S (2000) Genetic algorithm-based clustering technique. Pattern Recogn 33:1455–1465. https://doi.org/10.1016/S0031-3203(99)00137-5
Mendes R, Kennedy J, Neves J (2004) The fully informed particle swarm: Simpler, maybe better. IEEE Trans Evol Comput 8(3):204–210. https://doi.org/10.1109/TEVC.2004.826074
Ozturk C, Hancer E, Karaboga D (2015) Dynamic clustering with improved binary artificial bee colony algorithm. Applied Soft Computing Journal 28:69–80. https://doi.org/10.1016/j.asoc.2014.11.040
Page L, Brin S, Motwani R, Winograd T (1998) The PageRank Citation Ranking: Bringing Order to the Web. World Wide Web Internet And Web Information Systems 54(1999–66):1–17.
Parsopoulos KE, Vrahatis MN (2004) UPSO: A unified particle swarm optimization scheme. Lecture Series on Computer and Computational Sciences 1(5):868–873
Patra BK, Launonen R, Ollikainen V, Nandi S (2015) A new similarity measure using Bhattacharyya coefficient for collaborative filtering in sparse data. Knowl-Based Syst 82:163–177. https://doi.org/10.1016/j.knosys.2015.03.001
Peña J, Lozano J, Larrañaga P (1999) An empirical comparison of four initialization methods for the K-Means algorithm. Pattern Recogn Lett 20(10):1027–1040. https://doi.org/10.1016/S0167-8655(99)00069-0
Peram T, Veeramachaneni K, Mohan CK (2003) Fitness-distance-ratio based particle swarm optimization. Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS’03, (2), 174–181. https://doi.org/10.1109/SIS.2003.1202264
Pitsilis G, Zhang X, Wang W (2011) Clustering Recommenders in Collaborative Filtering Using Explicit Trust Information. Springer, Berlin, pp 82–97. https://doi.org/10.1007/978-3-642-22200-9_9
Ratnaweera A, Halgamuge SK, Watson HC (2004) Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients. IEEE Trans Evol Comput 8(3):240–255 https://doi.org/10.1109/TEVC.2004.826071
Resnick P, Iacovou N, Suchak M, Bergstrom P, Riedl J (1994) GroupLens. In Proceedings of the 1994 ACM conference on Computer supported cooperative work - CSCW ‘94 (pp. 175–186). New York: ACM Press. https://doi.org/10.1145/192844.192905
Salomon R (1996) Re-evaluating Genetic Algorithm Performane under Coordinate Rotatation of Benchmark Functions. BioSystems 39(3):263–278
Sarwar B, Karypis G, Konstan J, Reidl J (2001). Item-based collaborative filtering recommendation algorithms. In Proceedings of the tenth international conference on World Wide Web - WWW ‘01 (pp. 285–295). New York: ACM Press. https://doi.org/10.1145/371920.372071
Sarwar BM, Karypis G, Konstan J, Riedl J (2002) Recommender Systems for large-scale e-commerce: scalable neighborhood formation using clustering. Communications, 50(12), 158–167. 10.1114.6985
Selim SZ, Alsultan K (1991) A simulated annealing algorithm for the clustering problem. Pattern Recogn 24(10):1003–1008. https://doi.org/10.1016/0031-3203(91)90097-O
Shardanand U, Maes P (1995) Social information filtering. In Proceedings of the SIGCHI conference on Human factors in computing systems - CHI ‘95 (pp. 210–217). New York: ACM Press. https://doi.org/10.1145/223904.223931
Shelokar P., Jayaraman V., Kulkarni B. (2004) An ant colony approach for clustering. Anal Chim Acta 509:187–195. https://doi.org/10.1016/J.ACA.2003.12.032
Tian D, Shi Z (2018) MPSO: Modified particle swarm optimization and its applications. Swarm Evol Comput 1–20. https://doi.org/10.1016/j.swevo.2018.01.011
Tzortzis G, Likas A (2014) The MinMax k-Means clustering algorithm. Pattern Recogn 47(7):2505–2516. https://doi.org/10.1016/j.patcog.2014.01.015
van der Merwe DW, Engelbrecht AP (2003) Data clustering using particle swarm optimization. The 2003 Congress on Evolutionary Computation, 2003. CEC ‘03., 215–220. https://doi.org/10.1109/CEC.2003.1299577
vandenBergh F, Engelbrecht AP (2004) A Cooperative Approach to Particle Swarm Optimization. IEEE Trans Evol Comput 8(3):225–239. https://doi.org/10.1109/TEVC.2004.826069
Wang J, de Vries AP, Reinders MJT (2006) Unifying user-based and item-based collaborative filtering approaches by similarity fusion. In Proceedings of the 29th annual international ACM SIGIR conference on Research and development in information retrieval - SIGIR ‘06 (p. 501). New York: ACM Press. https://doi.org/10.1145/1148170.1148257
Wang H, Sun H, Li C, Rahnamayan S, Pan J-S (2013) Diversity enhanced particle swarm optimization with neighborhood search. Inf Sci 223:119–135. https://doi.org/10.1016/j.ins.2012.10.012
Xu X, Tang Y, Li J, Hua C, Guan X (2015) Dynamic multi-swarm particle swarm optimizer with cooperative learning strategy. Appl Soft Comput 29:169–183. https://doi.org/10.1016/j.asoc.2014.12.026
Zhan Z-H, Zhang J, Li Y, Chung HS-H (2009) Adaptive particle swarm optimization. IEEE Transactions on Systems, Man, and Cybernetics Part B, Cybernetics: A Publication of the IEEE Systems, Man, and Cybernetics Society 39(6):1362–1381. https://doi.org/10.1109/TSMCB.2009.2015956
Zhang C, Yi Z (2011) Scale-free fully informed particle swarm optimization algorithm. Inf Sci 181(20):4550–4568. https://doi.org/10.1016/j.ins.2011.02.026
Zhao ZL, Wang CD, Lai JH (2016a) AUI&GIV: Recommendation with asymmetric user influence and global importance value
Zhao ZL, Wang CD, Lai JH (2016b) AUI&GIV: Recommendation with Asymmetric User Influence and Global Importance Value. PLoS One 11(2):1–21. https://doi.org/10.1371/journal.pone.0147944
Zhou, R., Khemmarat, S., & Gao, L. (2010). The impact of YouTube recommendation system on video views. In Proceedings of the 10th annual conference on Internet measurement - IMC ‘10 (p. 404). New York: ACM Press. https://doi.org/10.1145/1879141.1879193
Zhou R, Khemmarat S, Gao L, Wan J, Zhang J (2016) How YouTube videos are discovered and its impact on video views. Multimedia Tools and Applications 75(10):6035–6058. https://doi.org/10.1007/s11042-015-3206-0
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Kushwaha, N., Pant, M. Modified particle swarm optimization for multimodal functions and its application. Multimed Tools Appl 78, 23917–23947 (2019). https://doi.org/10.1007/s11042-018-6324-7
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DOI: https://doi.org/10.1007/s11042-018-6324-7