# SOS-SDP: An Exact Solver for Minimum Sum-of-Squares Clustering

@article{Piccialli2021SOSSDPAE, title={SOS-SDP: An Exact Solver for Minimum Sum-of-Squares Clustering}, author={Veronica Piccialli and Antonio M. Sudoso and Angelika Wiegele}, journal={INFORMS Journal on Computing}, year={2021} }

The minimum sum-of-squares clustering problem (MSSC) consists of partitioning n observations into k clusters in order to minimize the sum of squared distances from the points to the centroid of their cluster. In this paper, we propose an exact algorithm for the MSSC problem based on the branch-and-bound technique. The lower bound is computed by using a cutting-plane procedure in which valid inequalities are iteratively added to the Peng–Wei semidefinite programming (SDP) relaxation. The upper…

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