Generalized multiplicative fuzzy possibilistic product partition C-means clustering - Wu, Chengmao; Li, Meng (Information sciences, 2024)
Regarding the defects of Ruspini partition-based clustering in revealing the intrinsic correlation between classes, this paper proposes a series of generalized multiplicative fuzzy possibilistic product partition clustering algorithms. First, based on the existing concept of generalized multiplicative intuitionistic fuzzy sets, this paper introduces a new concept of generalized multiplicative fuzzy sets and further defines the corresponding multiplicative fuzzy partition. Then, based on the concept of multiplicative fuzzy partition, a novel generalized multiplicative fuzzy possibilistic product partition C-means (GMFPCM) clustering algorithm is presented, and its local convergence is strictly proved using Zangwill’s theorem. Meanwhile, a robust Gaussian-base radial kernel based on the M-estimator is introduced into the GMFPCM algorithm to improve its robustness against noise and outliers in numerical data. Additionally, a multiplicative fuzzy possibilistic local information factor is constructed and embedded into the GMFPCM algorithm to strengthen its ability to suppress noise in images. Finally, the comparison with existing fuzzy possibilistic clustering algorithms in the literature confirms the competitiveness of the proposed algorithms.