Continuous optimization approaches for clustering via minimum sum of squares

In this paper, we survey the usage of semidefinite programming (SDP), and nonsmooth optimization approaches for solving the minimum sum of squares problem which is of fundamental importance in clustering. We point out that the main clustering idea of support vector clustering (SVC) method could be interpreted as a minimum sum of squares problem and explain the derivation of semidefinite programming and a nonsmooth optimization formulation for the minimum sum of squares problem. We compare the numerical results produced by the semidefinite formulation of minimum sum of squares with the results obtained from approaching it via nonsmooth optimization on two datasets.