In this paper, a convergence proof for the recently proposed cost function optimization sparse possibilistic c-means (SPCM) algorithm is provided. Specifically, it is shown that the algorithm will converge to one of the local minima of its associated cost function. It is also shown that similar convergence results can be derived for the well-known possibilistic c-means (PCM) algorithm proposed by Krishnapuram and Keller, 1996, if we view it as a special case of SPCM. Note that the convergence results for PCM are stronger than those established in previous works.

中文翻译：

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稀疏可能性C均值算法的收敛性


本文为最近提出的成本函数优化稀疏可能 c 均值 (SPCM) 算法提供了收敛证明。具体来说，表明该算法将收敛到其相关成本函数的局部最小值之一。它还表明，如果我们将 Krishnapuram 和 Keller，1996 年提出的著名的可能 c 均值 (PCM) 算法视为 SPCM 的特例，也可以得出类似的收敛结果。请注意，PCM 的收敛结果比以前的工作中建立的结果更强。