Fuzzy clustering with Multiple Kernels

In this paper, the kernel fuzzy c-means clustering algorithm is extended to an adaptive cluster model which maps data points to a high dimensional feature space through an optimal convex combination of homogenous kernels with respect to each cluster. This generalized model, called Fuzzy C Means with Multiple Kernels (FCM-MK), strives to find a good partitioning of the data into meaningful clusters and the optimal kernel-induced feature map in a completely unsupervised way. It constructs the kernel from a number of Gaussian kernels and learns a resolution specific weight for each kernel function in each cluster. This allows better characterization and adaptability to each individual cluster. The effectiveness of the proposed algorithm is demonstrated for several toy and real data sets.