Abstract
Cluster analysis, which is the subject of active research in several fields, such as statistics, pattern recognition, machine learning, and data mining, is to partition a given set of data or objects into clusters. K-means is used as a popular clustering method due to its simplicity and high speed in clustering large datasets. However, K-means has two shortcomings. First, dependency on the initial state and convergence to local optima. The second is that global solutions of large problems cannot be found with reasonable amount of computation effort. In order to overcome local optima problem lots of studies done in clustering. Over the last decade, modeling the behavior of social insects, such as ants and bees, for the purpose of search and problem solving has been the context of the emerging area of swarm intelligence. Honeybees are among the most closely studied social insects. Honeybee mating may also be considered as a typical swarm-based approach to optimization, in which the search algorithm is inspired by the process of marriage in real honeybee. Neural networks algorithms are useful for clustering analysis in data mining. This study proposes a two-stage method, which first uses self-organizing feature maps (SOM) neural network to determine the number of clusters and then uses honeybee mating optimization algorithm based on K-means algorithm to find the final solution. We compared proposed algorithm with other heuristic algorithms in clustering, such as GA, SA, TS, and ACO, by implementing them on several well-known datasets. Our finding shows that the proposed algorithm works better than others. In order to further demonstration of the proposed approach’s capability, a real-world problem of an Internet bookstore market segmentation based on customer loyalty is employed.
Similar content being viewed by others
References
Chang S (1998) Internet segmentation: state-of-the-art marketing applications. J Segm Marketing 2(1):19–34
O’Connor GC, O’Keefe B (1997) Viewing the web as a marketplace: the case of small companies. Decis Support Syst 21(3):171–183
Dillon WR, Kumar A, Borrero MS (1993) Capturing individual differences in paired comparisons: an extended BTL model incorporating descriptor variables. J Mark Res 30:42–51
Wedel M, Kamakura WA (1998) Market segmentation: conceptual and methodological foundations. Kluwer Academic, Boston
Anil C, Carroll D, Green PE, Rotondo JA (1997) A feature-based approach to market segmentation via overlapping K-centroids clustering. J Mark Res 34(3):370–377 (August)
Vellido A, Lisboa PJG, Vaughan J (1999) Neural networks in business: a survey of applications (1992–1998). Expert Syst Appl 17(1):51–70
Balakrishnan PV, Cooper MC, Jacob VS, Lewis PA (1996) Comparative performance of the FSCL neural net and K-means algorithm for market segmentation. Eur J Oper Res 93:346–357
Kuo RJ, Ho LM, Hu CM (2002) Integration of self-organizing feature map and K-means algorithm for market segmentation. International Journal of Computers and Operations Research 29:1475–1493
Kuo RJ, Xue KC (1998) A decision support system for sales forecasting through fuzzy neural network with asymmetric fuzzy weights. Journal of Decision Support Systems 24(2):105–126
Cadden DT (1991) Neural networks and the mathematics of chaos-an investigation of these methodologies as accurate predictors of corporate bankruptcy First international conference on artificial intelligence applications on wall street (pp.582–589). IEEE Computer Society Press
Lee RCT, Slagle JR, Blum H (1977) A triangulation method for the sequential mapping of points from N-space to two-space. IEEE Trans Comput 26:288–292
Pykett CE (1978) Improving the efficiency of Sammon’s nonlinear mapping by using clustering archetypes. Electron Lett 14:799–800
Forgy EW (1965) Cluster analysis of multivariate data: efficiency versus interpretability of classifications. Biometrics 21:768–769
Selim SZ, Ismail MA (1984) K-means type algorithms: a generalized convergence theorem and characterization of local optimality. IEEE Trans Pattern Anal Mach Intell 6:81–87
Spath H (1989) Clustering analysis algorithms. Ellis Horwood, Chichester, UK.
Ujjwal M, Sanghamitra B (2000) Genetic algorithm-based clustering technique. Pattern Recogn 33:1455–1465
Krishna K, Murty M (1999) Genetic K-means Algorithm. IEEE Transaction on Systems, man, and Cybernetics-Part B: Cybernetics 29:433–439
Shokri Z, Selim, Al-Sultan K (1991) A simulated annealing algorithm for the clustering problem. Pattern Recogn 24:1003–1008
Sung CS, Jin HW (2000) A tabu-search-based heuristic for clustering. Pattern Recogn 33:849–858
Kuo RI, Wang HS, Tung-Lai Hu, Chou SH (2005) Application of ant K-means on clustering analysis. Comput Math Appl 50:1709–1724
Shelokar PS, Jayaraman VK, Kulkarni BD (2004) An ant colony approach for clustering. Anal Chim Acta 509:187–195
Perez U, Hirsbrunner B (2000) Learning and foraging in robot-bees. SAB Proceedings Supplement Book, International Society for Adaptive Behavior, Honolulu, Hawaii 185–194
Afshar A (2001) A monogenous MBO approach to satisfiability. Proceeding of the International Conference on Computational Intelligence for Modelling, Control and Automation, CIMCA, Las Vegas, NV, USA
Afshar A (2001) Marriage in honey-bee optimization (MBO): a haplometrosis polygynous swarming approach. in: The Congress on Evolutionary Computation, Seoul, Korea, 207–214
Bozorg Haddad O, Afshar A (2004) MBO (Marriage Bees Optimization), A new heuristic approach in hydro systems design and operation. Proceedings of 1st International Conference on Managing Rivers in the 21st Century: Issues and Challenges, Penang, Malaysia, pp. 499–504
Bozorg Haddad O, Afshar A, Marin MA (2005) Honeybees mating optimization algorithm (HBMO); a new heuristic approach for engineering optimization. Proceeding of the First International Conference on Modeling, Simulation and Applied Optimization (ICMSA0/05), Sharjah, UAE
Afshar A, Bozog Haddad O, Marino MA, Adams BJ (2006) Honey-bee mating optimization (HBMO) algorithm for optimal reservoir operation. Journal of the Franklin Institute, Article in Press
Garey MR, Johnson DS, Witsenhausen HS (1982) The complexity of the generalized Lloyd-Max problem. IEEE Trans Inform Theory 28:255–256
Gungor Z, Unler A (2006) K-harmonic means data clustering with simulated annealing heuristic. Applied Mathematics and Computation, Article in Press
Kohonen T (1982) A simple paradigm for the self-organized formation of structured feature maps. In: Amari S, Berlin M (eds) Competition and cooperation in neural nets, Lecture notes in biomathematics. Springer, Berlin
Page RE (1980) The evolution of multiple mating behaviors by honey-bee queens (Apis mellifera L.). J Genet 96:263–273
Blake CL, Merz CJ, UCI repository of machine learning databases. Available from: <http://www.ics.uci.edu/~mlearn/MLRepository.html>
Coomans D, Jonckheer M, Massart DL, Broechaert I, Blockx P (1978) Anal Chim Acta 103:409–415
Raphael M (2002) Where did you come from? Direct Mark 62:36–38
Cullinan GJ (1977) Picking them by their batting averages: recency-frequency-monetary method of controlling circulation. Direct Mail/Marketing Association, New York, NY
Armando LF, Eber AS, Priscila L, Fernando SPM (2006) Optimized RFV analysis. Mark Intell Plann 24:106–118
Kohonen T (1991). Self-organizing maps: optimization approaches. In: Kohonen T, Makisara K, Simula O, Kangas J (eds.), Artificial neural networks. Elsevier, Amsterdam, The Netherlands, pp 981–990
Chang P-C, Liu CH, Wang YW (2006) A hybrid model by clustering and evolving fuzzy rules for sale forecasting in printed circuit board industry. Decis Support Syst 42(3):1254–1269
Chang, P-C, Hsieh JC, Warren Liao T (2005) Evolving Fuzzy Rules for due-date assignment problem in Semiconductor manufacturing factory. J Intell Manuf 16(5):549–557
Author information
Authors and Affiliations
Corresponding author
Additional information
An erratum to this article can be found at http://dx.doi.org/10.1007/s00170-008-1778-9
Rights and permissions
About this article
Cite this article
Fathian, M., Amiri, B. A honeybee-mating approach for cluster analysis. Int J Adv Manuf Technol 38, 809–821 (2008). https://doi.org/10.1007/s00170-007-1132-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-007-1132-7