Kernel-based deterministic annealing algorithm for data clustering

Data clustering in kernel-induced feature space is interesting in that, by nonlinearly mapping the observed data from a low-dimensional input space into a high (possibly infinite)-dimensional feature space by means of a given kernel function, the kernel-based clustering can reveal complicated (e.g. linearly nonseparable) data structures that may be missed by traditional clustering methods in the standard Euclidean space. A kernel-based deterministic annealing (KDA) algorithm is developed for data clustering by using a Gaussian kernel function. The Gaussian parameter (width), which determines the nonlinear mapping together with the Gaussian kernel, is adaptively selected by the scaled inverse of data covariance. The effectiveness of the Gaussian parameter (width) selection method and the superiority of the KDA algorithm for clustering a variety of data structures are supported by the experimental results on artificial and real data sets.