Spectral clustering with the probabilistic cluster kernel

This letter introduces a probabilistic cluster kernel for data clustering. The proposed kernel is computed with the composition of dot products between the posterior probabilities obtained via GMM clustering. The kernel is directly learned from the data, is parameter-free, and captures the data manifold structure at different scales. The projections in the kernel space induced by this kernel are useful for general feature extraction purposes and are here exploited in spectral clustering with the canonical k-means. The kernel structure, informative content and optimality are studied. Analysis and performance are illustrated in several real datasets.