Relational Fuzzy Clustering with Multiple Kernels

In this paper, the relational 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 Relational Fuzzy C-Means with Multiple Kernels (RFCM-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 multi-resolution 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 while addressing the problem of variable width kernels. The effectiveness of the proposed algorithm is demonstrated for synthetic and real data sets.