Kernelized fuzzy c-means clustering for uncertain data using quadratic penalty-vector regularization with explicit mappings

Recently, fuzzy c-means clustering with kernel functions is remarkable in the reason that these algorithms can handle datasets which consist of some clusters with nonlinear boundaries. However the algorithms have the following problems: (1) the cluster centers can not be calculated explicitly, (2) it takes long time to calculate clustering results. By the way, we have proposed the clustering algorithms using penalty-vector regularization to handle uncertain data. In this paper, we propose new clustering algorithms using quadratic penalty-vector regularization by introducing explicit mappings of kernel functions to solve the following problems. Moreover, we construct fuzzy classification functions for our proposed clustering methods.