Robust semi-supervised clustering with polyhedral and circular uncertainty

• Published in: Neurocomputing (Amsterdam) Vol. 265; pp. 4 - 27
• Main Authors: Dinler, Derya, Tural, Mustafa Kemal
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 22.11.2017
• Subjects: Clustering; Heuristics; Second order cone programing; Semi-supervised learning; Uncertainty; Uncertainty; Clustering; Semi-supervised learning; Second order cone programing; Heuristics
• ISSN: 0925-2312; 1872-8286; 1872-8286
• DOI: 10.1016/j.neucom.2017.04.073

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.