Robust semi supervised clustering with polyhedral and circular uncertainty

Date

2016-07-03

Author

Dinler, 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

Clustering, Heuristics, Second order cone programing, Semi-supervised learning, Uncertainty

URI

https://hdl.handle.net/11511/87341
https://www.euro-online.org/media_site/reports/EURO28_AB.pdf

Conference Name

EURO 2016 :28th European Conference on Operational Research, July 3-6 2016

Collections

Department of Industrial Engineering, Conference / Seminar

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Citation Formats

D. Dinler and M. K. Tural, “Robust semi supervised clustering with polyhedral and circular uncertainty,” presented at the EURO 2016 :28th European Conference on Operational Research, July 3-6 2016, Poznań, Poland, 2016, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/87341.