Hard Clustering by Fuzzy c-Means

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  • ファジィc-Meansによるハードクラスタリング
  • ファジィ c-Means ニヨル ハードクラスタリング

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This paper proposes an efficient usage of the fuzzy c-Means clustering algorithm to obtain optimum solutions of the k-Means hard clustering problem with reasonable certainty. The k-Means clustering problem is formLllated as a mixed integer programming problem. Based on the studies about the stability of solution in a multi-linear form of the energy function of the Hopfield neural network, it is shown that by estimating a local minimum solution in the hypercube of solution space, the coefficients of energy function and a threshold value for deciding 0-1 integer valued solution can be properly estimated. The fuzzy c-Means problem is solved by the affine scaling interior point method for linear programming problems and the Lagrangian multiplier method for maximizing entropy fuzzy clustering. It is shown by numerical simulations that both of the methods outperform the conventional A-Means algorithm in the quality of solutions found.

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