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.
Workload coverage through nonsmooth optimization
- Authors: Sukhorukova, Nadezda , Ugon, Julien , Yearwood, John
- Date: 2009
- Type: Text , Journal article
- Relation: Optimization Methods and Software Vol. 24, no. 2 (2009), p. 285-298
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- Description: In this paper, workload coverage is the problem of identifying a pattern of days worked and days off, along with the number of hours worked on each work day. This pattern must satisfy certain work-related constraints and fit best to a predefined workload. In our study, we formulate the problem of workload coverage as an optimization problem. We propose a number of models which take into consideration various staffing constraints. For each of these models, our study aims to find a compromise between an accurate workload coverage and the ability to solve the corresponding optimization problems in a reasonable time. Numerical experiments on each model are carried out and the results are presented. Interestingly, the nonlinear programming approaches are found to be competitive with linear programming ones. © 2009 Taylor & Francis.