A unified continuous optimization framework for center-based clustering methods
Center-based partitioning clustering algorithms rely on minimizing an appropriately formulated objective function, and different formulations suggest different possible algorithms. In this paper, we start with the standard nonconvex and nonsmooth formulation of the partitioning clustering problem. We demonstrate that within this elementary formulation, convex analysis tools and optimization theory provide a unifying language and framework to design, analyze and extend hard and soft center-based clustering algorithms, through a generic algorithm which retains the computational simplicity of the popular k-means scheme. We show that several well known and more recent center-based clustering algorithms, which have been derived either heuristically, or/and have emerged from intuitive analogies in physics, statistical techniques and information theoretic perspectives can be recovered as special cases of the proposed analysis and we streamline their relationships.
clustering convex analysis k-means algorithm support and asymptotic functions distance-like functions bregman and csiszar divergences nonlinear means nonsmooth optimization smoothing algorithms fixed point methods deterministic annealing expectation maximization information theory and entropy methods