Double-suppressed possibilistic fuzzy Gustafson–Kessel clustering algorithm

Possibilistic fuzzy c-means clustering (PFCM) is an unsupervised hybrid clustering algorithm, which can partly inherit the stability of fuzzy c-means clustering (FCM) algorithm and the noise robustness of possibilistic c-means clustering (PCM) algorithm. However, there are still several limitations in the PFCM when clustering complex data with multiple characteristics: sensitivity to strong noise, coincident clustering problem in multi-class clustering, and disability to deal with strong correlations of feature components. Therefore, a double-suppressed possibilistic fuzzy Gustafson–Kessel​ clustering algorithm (DS-PFGK) is presented. Firstly, we design a new objective function with a modified Mahalanobis distance and an improved weight parameter setting method based on the stability of fuzzy memberships and the anti-noise ability of possibilistic memberships. Moreover, combined with the absolute attribute of possibilistic memberships and the covariance matrix in the modified Mahalanobis distance, an ellipsoidal cluster core which can depict the distribution of sample data is generated to divide each cluster into different regions for selecting appropriate learning objects and identifying noisy data adaptively. Then, a “double-suppressed competitive learning” strategy is designed for the selected learning objects to solve the coincident clustering problem in multi-class clustering by suppressing the nonwinner possibilistic memberships, and to reduce the iteration number by suppressing nonwinner fuzzy memberships and rewarding winner fuzzy memberships. Finally, a segmentation algorithm on noisy color images based on the DS-PFGK is proposed based on the generated cluster cores. Experiments on synthetic datasets, real datasets, and color images show the good performance of the proposed methods compared with several classical and state-of-the-art clustering algorithms.