Generalized possibilistic c-means clustering with double weighting exponents

Abstract

Considering that the improved possibilistic c-means (PCM) algorithms are sensitive to noise while addressing the issue of consistency clustering in PCM, this paper proposes the generalized possibilistic c-means clustering with double weighting exponents. Firstly, double weighting exponents are introduced into the PCM algorithm, and the generalized possibilistic c-means clustering model is established. Secondly, the difference between the double weighting exponents in the generalized possibilistic clustering model is set to 1 or −1; two improved single-exponent possibilistic clustering algorithms called IPCM1 and IPCM2 are proposed, and their local convergence is strictly proven by the Zangwill theorem. Finally, the reasonable range of the weighting exponent in IPCM1 and IPCM2 algorithms is determined by mathematical optimization. Experimental results indicate that IPCM1 and IPCM2 outperform existing PCM-related algorithms; they achieve excellent clustering performance, significantly improve the robustness to noise, and decrease the sensitivity to the weighting exponent. The work of this paper has far-reaching significance for promoting the development of the possibilistic c-means clustering theory.