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A MaxMin clustering method for $k$means algorithm of data clustering
1.  School of Information Engineering, Hangzhou Dianzi University, Hangzhou 310012, China 
2.  School of Software Engineering, Hangzhou Dianzi University, Hangzhou 310012, China 
3.  School of Information Science and Engineering, East China University of Science and Technology, Shanghai 200237, China 
References:
[1] 
V. S. Ananthanarayana, M. Narasimha Murty and D. K. Subramanian, Rapid and brief communication efficient clustering of large data sets, Pattern Recognition, 34 (2001), 25612563. 
[2] 
Sanghamitra Bandyopadhyay and Ujjwal Maulik, An evolutionary technique based on Kmeans algorithm for optimal clustering in $R^N$, Information Sciences, 146 (2002), 221237. 
[3] 
Bjarni Bodvarsson, M. Morkebjerg, L. K. Hansen, G. M. Knudsen and C. Svarer, Extraction of time activity curves from positron emission tomography: Kmeans clustering or nonnegative matrix factorization, NeuroImage, 31 (2006), 185186. 
[4] 
Paul S. Bradley and Usama M. Fayyad, Refining maxmin points for Kmeans clustering, in "Proc. 15^{th} International Conf. on Machine Learning," Morgan Kaufmann, San Francisco, CA, (1998), 9199. 
[5] 
P. S. Bradley, O. L. Mangasarian and W. N. Street, Clustering via concave minimization, in "Advances in Neural Information Systems," (eds. M. C. Mozer, M. I. Jordan and T. Petsche), MIT Press, Cambridge, MA, (1996), 368374. 
[6] 
R. O. Duda, P. E. Hart and D. G. Stork, "Pattern Classification," second edition, WileyInterscience, New York, 2001. 
[7] 
David J. Hand and Wojtek J. Krzanowski, Optimising kmeans clustering results with standard software packages, Computational Statistics & Data Analysis, 49 (2005), 969973. 
[8] 
A. K. Jain and R. C. Dubes, "Algorithms for Clustering Data," Prentice Hall Advanced Reference Series, PrenticeHall, Englewood Cliffs, NJ, 1988. 
[9] 
Tapas Kanungo, David M. Mount, Nathan S. Netanyahu, Christine D. Piatko, Ruth Silverman and Angela Y. Wu, A local search approximation algorithm for kmeans clustering, Computational Geometry, 28 (2004), 89112. 
[10] 
Shehroz S. Khan and Amir Ahmad, Cluster center maxminization algorithm for Kmeans clustering, Pattern Recognition Letters, 25 (2004), 12931302. doi: 10.1016/j.patrec.2004.04.007. 
[11] 
R. J. Kuo, H. S. Wang, TungLai Hu and S. H. Chou, Application of ant Kmeans on clustering analysis, Computers & Mathematics with Applications, 50 (2005), 17091724. 
[12] 
Youssef M. Marzouk and Ahmed F. Ghoniem, Kmeans clustering for optimal partitioning and dynamic load balancing of parallel hierarchical Nbody simulations, Journal of Computational Physics, 207 (2005), 493528. 
[13] 
Boris Mirkin, Clustering algorithms: A review, in "Mathematical Classification and Clustering," Chapter 3, Kluwer Academic Publishers, (1996), 109169. 
[14] 
Boris Mirkin, Kmeans clustering, in "Clustering for Data Mining," Chapter 3, Taylor & Francis Group, (2005), 75110. 
[15] 
Boris Mirkin, Concept learning and feature selection based on squareerror clustering, Machine Learning, 35 (1999), 2539. 
[16] 
D. J. Newman, S. Hettich, C. L. Blake and C. J. Merz, "UCI Repository of Machine Learning Databases," University of California, Department of Information and Computer Science, Irvine, CA, 1998. Available from: http://www.ics.uci.edu/~mlearn/MLRepository.html. 
[17] 
Makoto Otsubo, Katsushi Sato and Atsushi Yamaji, Computerized identification of stress tensors determined from heterogeneous faultslip data by combining the multiple inverse method and kmeans clustering, Journal of Structural Geology, 28 (2006), 991997. 
[18] 
Georg Peters, Some refinements of rough kmeans clustering, Pattern Recognition, 39 (2006), 14811491. 
[19] 
S. Z. Selim and M. A. Ismail, Kmeans type algorithms: A generalized convergence theorem and characterization of local optimality, IEEE Trans. Pattern Anal. Mach. Inteli, 6 (1984), 8187. 
[20] 
Y. Yuan, J. Yan and C. Xu, Polynomial Smooth Support Vector Machine(PSSVM), Chinese Journal Of Computers, 28 (2005), 917. 
[21] 
Y. Yuan and T. Huang, A Polynomial Smooth Support Vector Machine for Classification, Lecture Note in Artificial Intelligence, 3584 (2005), 157164. 
[22] 
Y. Yuan, W. G. Fan and D. M. Pu, Spline function smooth support vector machine for classification, Journal of Industrial Management and Optimization, 3 (2007), 529542. 
show all references
References:
[1] 
V. S. Ananthanarayana, M. Narasimha Murty and D. K. Subramanian, Rapid and brief communication efficient clustering of large data sets, Pattern Recognition, 34 (2001), 25612563. 
[2] 
Sanghamitra Bandyopadhyay and Ujjwal Maulik, An evolutionary technique based on Kmeans algorithm for optimal clustering in $R^N$, Information Sciences, 146 (2002), 221237. 
[3] 
Bjarni Bodvarsson, M. Morkebjerg, L. K. Hansen, G. M. Knudsen and C. Svarer, Extraction of time activity curves from positron emission tomography: Kmeans clustering or nonnegative matrix factorization, NeuroImage, 31 (2006), 185186. 
[4] 
Paul S. Bradley and Usama M. Fayyad, Refining maxmin points for Kmeans clustering, in "Proc. 15^{th} International Conf. on Machine Learning," Morgan Kaufmann, San Francisco, CA, (1998), 9199. 
[5] 
P. S. Bradley, O. L. Mangasarian and W. N. Street, Clustering via concave minimization, in "Advances in Neural Information Systems," (eds. M. C. Mozer, M. I. Jordan and T. Petsche), MIT Press, Cambridge, MA, (1996), 368374. 
[6] 
R. O. Duda, P. E. Hart and D. G. Stork, "Pattern Classification," second edition, WileyInterscience, New York, 2001. 
[7] 
David J. Hand and Wojtek J. Krzanowski, Optimising kmeans clustering results with standard software packages, Computational Statistics & Data Analysis, 49 (2005), 969973. 
[8] 
A. K. Jain and R. C. Dubes, "Algorithms for Clustering Data," Prentice Hall Advanced Reference Series, PrenticeHall, Englewood Cliffs, NJ, 1988. 
[9] 
Tapas Kanungo, David M. Mount, Nathan S. Netanyahu, Christine D. Piatko, Ruth Silverman and Angela Y. Wu, A local search approximation algorithm for kmeans clustering, Computational Geometry, 28 (2004), 89112. 
[10] 
Shehroz S. Khan and Amir Ahmad, Cluster center maxminization algorithm for Kmeans clustering, Pattern Recognition Letters, 25 (2004), 12931302. doi: 10.1016/j.patrec.2004.04.007. 
[11] 
R. J. Kuo, H. S. Wang, TungLai Hu and S. H. Chou, Application of ant Kmeans on clustering analysis, Computers & Mathematics with Applications, 50 (2005), 17091724. 
[12] 
Youssef M. Marzouk and Ahmed F. Ghoniem, Kmeans clustering for optimal partitioning and dynamic load balancing of parallel hierarchical Nbody simulations, Journal of Computational Physics, 207 (2005), 493528. 
[13] 
Boris Mirkin, Clustering algorithms: A review, in "Mathematical Classification and Clustering," Chapter 3, Kluwer Academic Publishers, (1996), 109169. 
[14] 
Boris Mirkin, Kmeans clustering, in "Clustering for Data Mining," Chapter 3, Taylor & Francis Group, (2005), 75110. 
[15] 
Boris Mirkin, Concept learning and feature selection based on squareerror clustering, Machine Learning, 35 (1999), 2539. 
[16] 
D. J. Newman, S. Hettich, C. L. Blake and C. J. Merz, "UCI Repository of Machine Learning Databases," University of California, Department of Information and Computer Science, Irvine, CA, 1998. Available from: http://www.ics.uci.edu/~mlearn/MLRepository.html. 
[17] 
Makoto Otsubo, Katsushi Sato and Atsushi Yamaji, Computerized identification of stress tensors determined from heterogeneous faultslip data by combining the multiple inverse method and kmeans clustering, Journal of Structural Geology, 28 (2006), 991997. 
[18] 
Georg Peters, Some refinements of rough kmeans clustering, Pattern Recognition, 39 (2006), 14811491. 
[19] 
S. Z. Selim and M. A. Ismail, Kmeans type algorithms: A generalized convergence theorem and characterization of local optimality, IEEE Trans. Pattern Anal. Mach. Inteli, 6 (1984), 8187. 
[20] 
Y. Yuan, J. Yan and C. Xu, Polynomial Smooth Support Vector Machine(PSSVM), Chinese Journal Of Computers, 28 (2005), 917. 
[21] 
Y. Yuan and T. Huang, A Polynomial Smooth Support Vector Machine for Classification, Lecture Note in Artificial Intelligence, 3584 (2005), 157164. 
[22] 
Y. Yuan, W. G. Fan and D. M. Pu, Spline function smooth support vector machine for classification, Journal of Industrial Management and Optimization, 3 (2007), 529542. 
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