Robust semi supervised clustering with polyhedral and circular uncertainty

2016-07-03
Dinler, Derya
Tural, Mustafa Kemal
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.
EURO 2016 :28th European Conference on Operational Research, July 3-6 2016

Suggestions

Robust semi-supervised clustering with polyhedral and circular uncertainty
DİNLER, DERYA; Tural, Mustafa Kemal (Elsevier BV, 2017-11-22)
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 b...
Dimension reduction using global and local pattern information-based maximum margin criterion
Sakarya, Ufuk (2016-07-01)
Dimension reduction is an important research area in pattern recognition when dealing with high-dimensional data. In this paper, a novel supervised dimension reduction approach is introduced for classification. Advantages of using not only global pattern information but also local pattern information are examined in the maximum margin criterion framework. Experimental comparative results in object recognition, handwritten digit recognition, and hyperspectral image classification are presented. According to ...
Geometric measures of entanglement
UYANIK, KIVANÇ; Turgut, Sadi (American Physical Society (APS), 2010-03-01)
The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three-qubit case is discussed and it is argued that the distance to the W states is a new monotone.
Numerical Improvement of Terahertz Time-Domain Spectroscopic Measurements
Koseoglu, D.; Berberoglu, H.; Altan, Hakan (2009-11-06)
We have developed an algorithm to efficiently eliminate unwanted reflections typically observed in the data obtained by Terahertz time-domain spectroscopic (THz-TDS) methods. The algorithm works by eliminating the reflections from the boundaries. The numerical improvement of the data allows better analysis of the critical parameters obtained by THz-TDS systems.
Quantum systems and representation theorem
Dosi, Anar (2013-09-01)
In this paper we investigate quantum systems which are locally convex versions of abstract operator systems. Our approach is based on the duality theory for unital quantum cones. We prove the unital bipolar theorem and provide a representation theorem for a quantum system being represented as a quantum -system.
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.