We consider a semi-supervised clustering problem where the locations of the data objects are subject to uncertainty. Each uncertainty set is assumed to be either a closed convex bounded polyhedron or a closed disk. The final clustering is expected to be in accordance with a given number of instance level constraints. The objective function considered minimizes the total of the sum of the violation costs of the unsatisfied instance level constraints and a weighted sum of squared maximum Euclidean distances between the locations of the data objects and the centroids of the clusters they are assigned to. Given a cluster, we first consider the problem of computing its centroid, namely the centroid computation problem under uncertainty (CCPU). We show that the CCPU can be modeled as a second order cone programing problem and hence can be efficiently solved to optimality. As the CCPU is one of the key ingredients of the several algorithms considered in this paper, a subgradient algorithm is also adopted for its faster solution. We then propose a mixed-integer second order cone programing formulation for the considered clustering problem which is only able to solve small-size instances to optimality. For larger instances, approaches from the semi-supervised clustering literature are modified and compared in terms of computational time and quality.
CITATION STYLE
Dinler, D., & Tural, M. K. (2017). Robust semi-supervised clustering with polyhedral and circular uncertainty. Neurocomputing, 265, 4–27. https://doi.org/10.1016/j.neucom.2017.04.073
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