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Robust semi-supervised clustering with polyhedral and circular uncertainty
Date
2017-11-22
Author
DİNLER, DERYA
Tural, Mustafa Kemal
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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.
Subject Keywords
Cognitive Neuroscience
,
Artificial Intelligence
,
Computer Science Applications
URI
https://hdl.handle.net/11511/41584
Journal
NEUROCOMPUTING
DOI
https://doi.org/10.1016/j.neucom.2017.04.073
Collections
Department of Industrial Engineering, Article