Fuzzy clustering with Learnable Cluster dependent Kernels

We propose a new relational clustering approach, called Fuzzy clustering with Learnable Cluster dependent Kernels (FLeCK), that learns multiple kernels while seeking compact clusters. A Gaussian kernel is learned with respect to each cluster. It reflects the relative density, size, and position of the cluster with respect to the other clusters. These kernels are learned by optimizing both the intra-cluster and the inter cluster similarities. Moreover, FLeCK is formulated to work on relational data. This makes it applicable to data where objects cannot be represented by vectors or when clusters of similar objects cannot be represented efficiently by a single prototype. The experiments show that FLeCK outperforms several other algorithms. In particular, we show that when data include clusters with various inter and intra cluster distances, learning cluster dependent kernel is crucial in obtaining a good partition.