An exact algorithm for semi-supervised minimum sum-of-squares clustering

The minimum sum-of-squares clustering (MSSC), or k-means type clustering, is traditionally considered an unsupervised learning task. In recent years, the use of background knowledge to improve cluster quality and promote interpretability process has become a hot research topic at intersection mathematical optimization machine research. problem taking advantage information in data called semi-supervised constrained clustering. this paper, we present branch-and-cut algorithm for MSSC, where incorporated as pairwise must-link cannot-link constraints. For lower bound procedure, solve semidefinite programming relaxation MSSC discrete model, cutting-plane procedure strengthening bound. upper bound, instead, by using integer tools, adaptation case. first time, proposed global efficiently manages real-world instances up 800 points with different combinations constraints generic number features. This size about four times larger than one solved state-of-the-art exact algorithms.