General kernel clustering only concern relationship within clusters while ignoring the issue between clusters. Misclassification easily occurs when clustering data sets with fuzzy and noisy boundaries. To solve this problem, a new clustering algorithm was proposed based on Kernel Fuzzy C-Means (KFCM) clustering algorithm, which was called Kernel Fuzzy C-Means with Maximum distance between clusters (MKFCM). Considering the relationship between within-cluster elements and between-cluster elements, a penalty term representing the distance between centers in feature space and a control parameter were introduced. In this way, the distance between clustering centers was broadened and the samples near boundaries were better classified. Compared with traditional clustering algorithms, the experiments results on simulated data sets show that the proposed algorithm reduces the offset distance of clustering centers obviously. On man-made Gaussian data sets, the ACCuracy (ACC), Normalized Mutual Information (NMI) and Rand Index (RI) of the proposed algorithm were improved to 0.9132, 0.7575 and 0.9138. The proposed algorithm shows its theoretical research significance on data sets with fuzzy and noisy boundaries.

In image segmentation based on clustering analysis, spatial constraints were imposed so as to reduce noise but preserve details. Based on Fuzzy C-Means (FCM) method, a multi-dimensional fuzzy clustering image segmentation algorithm based on kernel metric and local information was proposed to compromise noise and details in the image. In the algorithm, two extra images based on local information derived from the original one through a smoothing and a sharpening filter respectively were introduced to construct a multi-dimensional gray level vector to replace the original one-dimensional gray level. And then kernel method was employed to strengthen its robustness. In addition, a penalty term, which represents the diversity between local pixel and its neighbors, was used to modify the objective function so as to improve its anti-noise ability further. Compared with NNcut (Nystrom Normalized cut) and FLICM (Fuzzy Local Information C-Means), its segmentation accuracy achieved almost 99%. The experimental results on natural and medical images and parameter adjusting demonstrate its favorable advantages of flexibility and robustness when dealing with noise and details.