School of Automation, Xi’an Institute of Posts and Telecommunications, Xi’an, Shaanxi, 710121 P. R.China

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Abstract—The mathematical modeling of the clustering centers problem leads to a min-sum-min formulation which, has the significant characteristic of being strongly nondifferentiable. To overcome this difficulty, a new filled function method is proposed to find centers of clusters based on entropy technique. A completely differentiable non-convex optimization model for the clustering center problem is constructed. A parameter free filled function method is adopted to search for a global optimal solution of the optimization model. For the purpose of illustrating both the reliability and the efficiency of the method, a set of computational experiments was performed. Numerical results illustrate that the proposed algorithm can effectively hunt centers of clusters and especially improve the accuracy of the clustering even with a relatively small entropy factor.

Index Terms—Nondifferentiable, entropy function, cluster centers, global minimizer, filled function method.

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Cite: Qing Wu, Lixing Yuan, "A New Filled Function method for Smooth Clustering," Journal of Computers vol. 7, no. 2, pp. 491-498, 2012.