Classes and clusters in data analysis
- Authors: Rubinov, Alex , Sukhorukova, Nadezda , Ugon, Julien
- Date: 2006
- Type: Text , Journal article
- Relation: European Journal of Operational Research Vol. 173, no. 3 (Sep 2006), p. 849-865
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- Description: We discuss the relation between classes and clusters in datasets with given classes. We examine the distribution of classes within obtained clusters, using different clustering methods which are based on different techniques. We also study the structure of the obtained clusters. One of the main conclusions, obtained in this research is that the notion purity cannot be always used for evaluation of accuracy of clustering techniques. (c) 2005 Elsevier B.V. All rights reserved.
- Description: C1
- Description: 2003001593
The choice of a similarity measure with respect to its sensitivity to outliers
- Authors: Rubinov, Alex , Sukhorukova, Nadezda , Ugon, Julien
- Date: 2010
- Type: Text , Journal article
- Relation: Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms Vol. 17, no. 5 (2010), p. 709-721
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- Description: This paper examines differences in the choice of similarity measures with respect to their sensitivity to outliers in clustering problems, formulated as mathematical programming problems. Namely, we are focusing on the study of norms (norm-based similarity measures) and convex functions of norms (function-norm-based similarity measures). The study consists of two parts: the study of theoretical models and numerical experiments. The main result of this study is a criterion for the outliers sensitivity with respect to the corresponding similarity measure. In particular, the obtained results show that the norm-based similarity measures are not sensitive to outliers whilst a very widely used square of the Euclidean norm similarity measure (least squares) is sensitive to outliers. Copyright © 2010 Watam Press.
Facility location via continuous optimization with discontinuous objective functions
- Authors: Ugon, Julien , Kouhbor, Shahnaz , Mammadov, Musa , Rubinov, Alex , Kruger, Alexander
- Date: 2007
- Type: Text , Journal article
- Relation: ANZIAM Journal Vol. 48, no. 3 (2007), p. 315-325
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- Description: Facility location problems are one of the most common applications of optimization methods. Continuous formulations are usually more accurate, but often result in complex problems that cannot be solved using traditional optimization methods. This paper examines the use of a global optimization method - AGOP - for solving location problems where the objective function is discontinuous. This approach is motivated by a real-world application in wireless networks design. © Australian Mathematical Society 2007.
- Description: 2003004859