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
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
Coverage in WLAN : Optimization model and algorithm
- Authors: Kouhbor, Shahnaz , Ugon, Julien , Mammadov, Musa , Rubinov, Alex , Kruger, Alexander
- Date: 2006
- Type: Text , Conference paper
- Relation: Paper presented at the First International Conference on Wireless Broadband and Ultra Wideband Communications, AusWireless 2006, Sydney : 13th March, 2006
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- Description: When designing wireless communication systems, it is very important to know the optimum numbers of access points (APs) in order to provide a reliable design. In this paper we describe a mathematical model developed for finding the optimal number and location of APs. A new Global Optimization Algorithm (AGOP) is used to solve the problem. Results obtained demonstrate that the model and software are able to solve optimal coverage problems for design areas with different types of obstacles and number of users.
- Description: 2003001757
Coverage in WLAN with minimum number of access points
- Authors: Kouhbor, Shahnaz , Ugon, Julien , Rubinov, Alex , Kruger, Alexander , Mammadov, Musa
- Date: 2006
- Type: Text , Conference paper
- Relation: Paper presented at VTC 2006 - Spring, 2006 IEEE 63rd Vehicular Technology Conference, Melbourne : 7th May, 2006
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- Description: E1
- Description: 2003001610
A new algorithm for the placement of WLAN access point based on nonsmooth optimization technique
- Authors: Kouhbor, Shahnaz , Ugon, Julien , Kruger, Alexander , Rubinov, Alex , Branch, Philip
- Date: 2005
- Type: Text , Conference paper
- Relation: Paper presented at the 7th International Conference on Advanced Communication Technology, Phoenix Park, Korea : 21st February, 2005
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- Description: In wireless local area network (WLAN), signal coverage is obtained by proper placement of access points (APs). The impact of incorrect placement of APs is significant. If they are placed too far apart, they generate a coverage gap but if they are too close to each other, this leads to excessive co-channel interferences. In this paper, we describe a mathematical model we have developed to find the optimal number and location of APs. To solve the problem, we use an optimization algorithm developed at the University of Ballarat called discrete gradient algorithm. Results indicate that our model is able to solve optimal coverage problems for different numbers of users.
- Description: E1
- Description: 2003001376
Minimization of the sum of minima of convex functions and its application to clustering
- Authors: Rubinov, Alex , Soukhoroukova, Nadejda , Ugon, Julien
- Date: 2005
- Type: Text , Book chapter
- Relation: Continuous Optimization Chapter p. 409-434
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- Description: We study functions that can be represented as the sum of minima of convex functions. Minimization of such functions can be used for approximation of finite sets and their clustering. We suggest to use the local discrete gradient (DG) method [Bag99] and the hybrid method between the cutting angle method and the discrete gradient method (DG+CAM) [BRZ05b] for the minimization of these functions. We report and analyze the results of numerical experiments.
- Description: 2003004082
Optimal placement of access point in WLAN based on a new algorithm
- Authors: Kouhbor, Shahnaz , Ugon, Julien , Kruger, Alexander , Rubinov, Alex
- Date: 2005
- Type: Text , Conference paper
- Relation: Paper presented at ICMB 2005, International Conference on Mobile Business, Sydney, Australia, 11-13 July 2005, Sydney : 11th - 13th July, 2005
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- Description: When designing wireless communication systems, it is very important to know the optimum numbers and locations for the access points (APs). The impact of incorrect placement of APs is significant. If they are placed too far apart, they will generate a coverage gap, but if they are too close to each other, this will lead to excessive co-channel interferences. In this paper we describe a mathematical model developed to find the optimal number and location of APs. To solve the problem, we use the Discrete Gradient optimization algorithm developed at the University of Ballarat. Results indicate that our model is able to solve optimal coverage problems for different numbers of users.
- Description: 2003001377
Optimisation solvers and problem formulations for solving a data clustering problem
- Authors: Ugon, Julien , Rubinov, Alex
- Date: 2005
- Type: Text , Conference paper
- Relation: Paper presented at the Sixteenth Australasian Workshop on Combinatorial Algorithms, Ballarat, Victoria : 18th - 21st September, 2005
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- Description: A popular apprach for solving complex optimization problems is through relaxation: some constraints are removed in order to have a convex problem approximating the original problem. On the other hand, direct approaches for solving such problems are becoming increasingly powerful. This paper examines two cases drawn from data analysis, in order to compare the two techniques.
- Description: E1
- Description: 2003001437
A feature selection approach for unsupervised classification based on clustering
- Authors: Rubinov, Alex , Soukhoroukova, Nadejda , Ugon, Julien
- Date: 2004
- Type: Text , Conference paper
- Relation: Paper presented at Sixth International Conference on Optimization: Techniques and Applications (ICOTA) , University of Ballarat, Ballarat, Victoria : 9th-11th December 2004
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- Description: Data have been collected for many years in different scientific (industrial, medical) research groups. Very often these groups kept all the the they could collect. It is possible that the data contains a lot of noisy features which do not bring any information, but make the problem more complicated. The additional study of eliminating non-informative and selecting informative features is very important in the area of Data Mining. There are several feature selection methods which were developed for supervised classification. The area of feature selection for unsupervised classification is not so developed. In this paper we present a new feature selection approach for unsupervised classification, based on clustering and nonsmooth optimisation techniques.
- Description: 2003004085
Optimization in wireless local area network
- Authors: Kouhbor, Shahnaz , Ugon, Julien , Kruger, Alexander , Rubinov, Alex , Branch, Philip
- Date: 2004
- Type: Text , Conference paper
- Relation: Paper presented at ICOTA6: 6th International Conference on Optimization - Techniques and Applications, Ballarat, Victoria : 9th December, 2004
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- Description: 2003000886