Modified genetic algorithm-based clustering for probability density functions

References

• Wu X, Zhu X, Wu G-Q, et al. Data mining with big data. IEEE Trans Knowl Data Eng. 2014;26:97–107. doi: 10.1109/TKDE.2013.2297923
   Web of Science ®Google Scholar
• George G, Haas MR, Pentland A. Big data and management. Acad Manag J. 2014;57:321–326. doi: 10.5465/amj.2014.4002
   Web of Science ®Google Scholar
• Rand WM. Objective criteria for the evaluation of clustering methods. J Am Stat Assoc. 1971;66:846–850. doi: 10.1080/01621459.1971.10482356
   Web of Science ®Google Scholar
• MacQueen J. Some methods for classification and analysis of multivariate observations. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability; Oakland, CA, USA; 1967. p. 281–297.
   Google Scholar
• Xie XL, Beni G. A validity measure for fuzzy clustering. IEEE Trans Pattern Anal Mach Intell. 1991;13:841–847. doi: 10.1109/34.85677
   Web of Science ®Google Scholar
• Dunn JC. A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters. J Cybern. 1973;3:32–57.
   Google Scholar
• Davies DL, Bouldin DW. A cluster separation measure. IEEE Trans Pattern Anal Mach Intell. 1979;PAMI-1:224–227. doi: 10.1109/TPAMI.1979.4766909
   Web of Science ®Google Scholar
• Rousseeuw PJ. Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J Comput Appl Math. 1987;20:53–65. doi: 10.1016/0377-0427(87)90125-7
   Web of Science ®Google Scholar
• Caliński T, Harabasz J. A dendrite method for cluster analysis. Commun Stat Theory Methods. 1974;3:1–27. doi: 10.1080/03610927408827101
   Google Scholar
• Falkenauer E. The grouping genetic algorithms: widening the scope of the GAs. Belg J Oper Res. 1992;33:79–102.
   Google Scholar
• Jain AK, Murty MN, Flynn PJ. Data clustering: a review. ACM Comput Surv. 1999;31:264–323. doi: 10.1145/331499.331504
   Web of Science ®Google Scholar
• Hruschka ER. A genetic algorithm for cluster analysis. Intelligent Data Anal. 2003;7:15–25.
   Google Scholar
• Agustín-Blas LE, Salcedo-Sanz S, Jiménez-Fernández S, et al. A new grouping genetic algorithm for clustering problems. Exp Syst Appl. 2012;39:9695–9703. Available from: http://linkinghub.elsevier.com/retrieve/pii/S0957417412004125. doi: 10.1016/j.eswa.2012.02.149
   Web of Science ®Google Scholar
• Das S, Abraham A, Konar A. Automatic kernel clustering with a multi-elitist particle swarm optimization algorithm. Pattern Recognit Lett. 2008;29:688–699. doi: 10.1016/j.patrec.2007.12.002
   Web of Science ®Google Scholar
• Jiang H, Yi S, Li J, et al. Ant clustering algorithm with K-harmonic means clustering. Exp Syst Appl. 2010;37:8679–8684. doi: 10.1016/j.eswa.2010.06.061
   Web of Science ®Google Scholar
• Zhang C, Ouyang D, Ning J. An artificial bee colony approach for clustering. Exp Syst Appl. 2010;37:4761–4767. doi: 10.1016/j.eswa.2009.11.003
   Web of Science ®Google Scholar
• Matusita K. On the notion of affinity of several distributions and some of its applications. Ann Inst Stat Math. 1967;19:181–192. doi: 10.1007/BF02911675
   Web of Science ®Google Scholar
• Glick N. Sample-based classification procedures derived from density estimators. J Am Stat Assoc. 1972;67:116–122. doi: 10.1080/01621459.1972.10481213
   Web of Science ®Google Scholar
• Vo Van T, Pham-Gia T. Clustering probability distributions. J Appl Stat. 2010;37:1891–1910. doi: 10.1080/02664760903186049
   Web of Science ®Google Scholar
• Goh A, Vidal R. Unsupervised Riemannian clustering of probability density functions. ECML PKDD, Part I, LNAI 5211; 2008. p. 377–392.
   Google Scholar
• Montanari A, Calò DG. Model-based clustering of probability density functions. Adv Data Anal Classif. 2013;7:301–319.
   Google Scholar
• Chen J-H, Hung W-L. An automatic clustering algorithm for probability density functions. J Stat Comput Simul. 2015;85:3047–3063. doi: 10.1080/00949655.2014.949715
   Web of Science ®Google Scholar
• Van Craenendonck T, Blockeel H. Using internal validity measures to compare clustering algorithms. AutoML Workshop at ICML 2015; 2015. p. 1–8.
   Google Scholar
• Deep K, Singh KP, Kansal ML, et al. A real coded genetic algorithm for solving integer and mixed integer optimization problems. Appl Math Comput. 2009;212:505–518; [cited 2015 Oct 18]. Available from: http://www.sciencedirect.com/science/article/pii/S0096300309001830
   Web of Science ®Google Scholar
• Back T, Hammel U, Schwefel H-P. Evolutionary computation: comments on the history and current state. IEEE Trans Evol Comput. 1997;1:3–17. doi: 10.1109/4235.585888
   Google Scholar
• Davis TE, Principe JC. A Markov chain framework for the simple genetic algorithm. Evol Comput. 1993;1:269–288. doi: 10.1162/evco.1993.1.3.269
   Web of Science ®Google Scholar
• Greenhalgh D, Marshall S. Convergence criteria for genetic algorithms. SIAM J Comput. 2000;30:269–282. doi: 10.1137/S009753979732565X
   Web of Science ®Google Scholar
• Nix AE, Vose MD. Modeling genetic algorithms with Markov chains. Ann Math Artif Intell. 1992;5:79–88. doi: 10.1007/BF01530781
   Google Scholar
• Rudolph G. Convergence analysis of canonical genetic algorithms. IEEE Trans Neural Netw. 1994;5:96–101. doi: 10.1109/72.265964
   PubMed Web of Science ®Google Scholar
• Safe M, Carballido J, Ponzoni I, et al. On stopping criteria for genetic algorithms. Braz Symp Artif Intell. 2004:405–413.
   Google Scholar
• Cinlar E. Introduction to stochastic processes. New York: Courier Corporation; 2013.
   Google Scholar
• Aytug H, Koehler GJ. Stopping criteria for finite length genetic algorithms. INFORMS J Comput. 1996;8:183–191. doi: 10.1287/ijoc.8.2.183
   Google Scholar
• Aytug H, Koehler GJ. New stopping criterion for genetic algorithms. Eur J Oper Res. 2000;126:662–674. doi: 10.1016/S0377-2217(99)00321-5
   Web of Science ®Google Scholar
• De Jong KA, Spears WM, Gordon DF. Using Markov chains to analyze GAFOs. Found Genet Algor. 1995;3:115–137. doi: 10.1016/B978-1-55860-356-1.50011-X
   Google Scholar
• Martinez WL, Martinez AR. Computational statistics handbook with MATLAB. Boca Raton: CRC Press; 2007.
   Google Scholar
• Silverman BW. Density estimation for statistics and data analysis. London: CRC Press; 1986.
   Google Scholar
• Scott DW. Multivariate density estimation. New York: Wiley; 1992.
   Google Scholar