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4Rubinov, Alex
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A simulated annealing-based maximum-margin clustering algorithm

- Seifollahi, Sattar, Bagirov, Adil, Borzeshi, Ehsan, Piccardi, Massimo

**Authors:**Seifollahi, Sattar , Bagirov, Adil , Borzeshi, Ehsan , Piccardi, Massimo**Date:**2019**Type:**Text , Journal article**Relation:**Computational Intelligence Vol. 35, no. 1 (2019), p. 23-41**Full Text:****Reviewed:****Description:**Maximum-margin clustering is an extension of the support vector machine (SVM) to clustering. It partitions a set of unlabeled data into multiple groups by finding hyperplanes with the largest margins. Although existing algorithms have shown promising results, there is no guarantee of convergence of these algorithms to global solutions due to the nonconvexity of the optimization problem. In this paper, we propose a simulated annealing-based algorithm that is able to mitigate the issue of local minima in the maximum-margin clustering problem. The novelty of our algorithm is twofold, ie, (i) it comprises a comprehensive cluster modification scheme based on simulated annealing, and (ii) it introduces a new approach based on the combination of k-means++ and SVM at each step of the annealing process. More precisely, k-means++ is initially applied to extract subsets of the data points. Then, an unsupervised SVM is applied to improve the clustering results. Experimental results on various benchmark data sets (of up to over a million points) give evidence that the proposed algorithm is more effective at solving the clustering problem than a number of popular clustering algorithms.

**Authors:**Seifollahi, Sattar , Bagirov, Adil , Borzeshi, Ehsan , Piccardi, Massimo**Date:**2019**Type:**Text , Journal article**Relation:**Computational Intelligence Vol. 35, no. 1 (2019), p. 23-41**Full Text:****Reviewed:****Description:**Maximum-margin clustering is an extension of the support vector machine (SVM) to clustering. It partitions a set of unlabeled data into multiple groups by finding hyperplanes with the largest margins. Although existing algorithms have shown promising results, there is no guarantee of convergence of these algorithms to global solutions due to the nonconvexity of the optimization problem. In this paper, we propose a simulated annealing-based algorithm that is able to mitigate the issue of local minima in the maximum-margin clustering problem. The novelty of our algorithm is twofold, ie, (i) it comprises a comprehensive cluster modification scheme based on simulated annealing, and (ii) it introduces a new approach based on the combination of k-means++ and SVM at each step of the annealing process. More precisely, k-means++ is initially applied to extract subsets of the data points. Then, an unsupervised SVM is applied to improve the clustering results. Experimental results on various benchmark data sets (of up to over a million points) give evidence that the proposed algorithm is more effective at solving the clustering problem than a number of popular clustering algorithms.

Multi-source cyber-attacks detection using machine learning

- Taheri, Sona, Gondal, Iqbal, Bagirov, Adil, Harkness, Greg, Brown, Simon, Chi, Chihung

**Authors:**Taheri, Sona , Gondal, Iqbal , Bagirov, Adil , Harkness, Greg , Brown, Simon , Chi, Chihung**Date:**2019**Type:**Text , Conference proceedings , Conference Paper**Relation:**2019 IEEE International Conference on Industrial Technology, ICIT 2019; Melbourne, Australia; 13th-15th February 2019 Vol. 2019-February, p. 1167-1172**Full Text:****Reviewed:****Description:**The Internet of Things (IoT) has significantly increased the number of devices connected to the Internet ranging from sensors to multi-source data information. As the IoT continues to evolve with new technologies number of threats and attacks against IoT devices are on the increase. Analyzing and detecting these attacks originating from different sources needs machine learning models. These models provide proactive solutions for detecting attacks and their sources. In this paper, we propose to apply a supervised machine learning classification technique to identify cyber-attacks from each source. More precisely, we apply the incremental piecewise linear classifier that constructs boundary between sources/classes incrementally starting with one hyperplane and adding more hyperplanes at each iteration. The algorithm terminates when no further significant improvement of the separation of sources/classes is possible. The construction and usage of piecewise linear boundaries allows us to avoid any possible overfitting. We apply the incremental piecewise linear classifier on the multi-source real world cyber security data set to identify cyber-attacks and their sources.**Description:**Proceedings of the IEEE International Conference on Industrial Technology

**Authors:**Taheri, Sona , Gondal, Iqbal , Bagirov, Adil , Harkness, Greg , Brown, Simon , Chi, Chihung**Date:**2019**Type:**Text , Conference proceedings , Conference Paper**Relation:**2019 IEEE International Conference on Industrial Technology, ICIT 2019; Melbourne, Australia; 13th-15th February 2019 Vol. 2019-February, p. 1167-1172**Full Text:****Reviewed:****Description:**The Internet of Things (IoT) has significantly increased the number of devices connected to the Internet ranging from sensors to multi-source data information. As the IoT continues to evolve with new technologies number of threats and attacks against IoT devices are on the increase. Analyzing and detecting these attacks originating from different sources needs machine learning models. These models provide proactive solutions for detecting attacks and their sources. In this paper, we propose to apply a supervised machine learning classification technique to identify cyber-attacks from each source. More precisely, we apply the incremental piecewise linear classifier that constructs boundary between sources/classes incrementally starting with one hyperplane and adding more hyperplanes at each iteration. The algorithm terminates when no further significant improvement of the separation of sources/classes is possible. The construction and usage of piecewise linear boundaries allows us to avoid any possible overfitting. We apply the incremental piecewise linear classifier on the multi-source real world cyber security data set to identify cyber-attacks and their sources.**Description:**Proceedings of the IEEE International Conference on Industrial Technology

Double bundle method for finding clarke stationary points in nonsmooth dc programming

- Joki, Kaisa, Bagirov, Adil, Karmitsa, Napsu, Makela, Marko, Taheri, Sona

**Authors:**Joki, Kaisa , Bagirov, Adil , Karmitsa, Napsu , Makela, Marko , Taheri, Sona**Date:**2018**Type:**Text , Journal article**Relation:**SIAM Journal on Optimization Vol. 28, no. 2 (2018), p. 1892-1919**Relation:**http://purl.org/au-research/grants/arc/DP140103213**Full Text:****Reviewed:****Description:**The aim of this paper is to introduce a new proximal double bundle method for unconstrained nonsmooth optimization, where the objective function is presented as a difference of two convex (DC) functions. The novelty in our method is a new escape procedure which enables us to guarantee approximate Clarke stationarity for solutions by utilizing the DC components of the objective function. This optimality condition is stronger than the criticality condition typically used in DC programming. Moreover, if a candidate solution is not approximate Clarke stationary, then the escape procedure returns a descent direction. With this escape procedure, we can avoid some shortcomings encountered when criticality is used. The finite termination of the double bundle method to an approximate Clarke stationary point is proved by assuming that the subdifferentials of DC components are polytopes. Finally, some encouraging numerical results are presented.

**Authors:**Joki, Kaisa , Bagirov, Adil , Karmitsa, Napsu , Makela, Marko , Taheri, Sona**Date:**2018**Type:**Text , Journal article**Relation:**SIAM Journal on Optimization Vol. 28, no. 2 (2018), p. 1892-1919**Relation:**http://purl.org/au-research/grants/arc/DP140103213**Full Text:****Reviewed:****Description:**The aim of this paper is to introduce a new proximal double bundle method for unconstrained nonsmooth optimization, where the objective function is presented as a difference of two convex (DC) functions. The novelty in our method is a new escape procedure which enables us to guarantee approximate Clarke stationarity for solutions by utilizing the DC components of the objective function. This optimality condition is stronger than the criticality condition typically used in DC programming. Moreover, if a candidate solution is not approximate Clarke stationary, then the escape procedure returns a descent direction. With this escape procedure, we can avoid some shortcomings encountered when criticality is used. The finite termination of the double bundle method to an approximate Clarke stationary point is proved by assuming that the subdifferentials of DC components are polytopes. Finally, some encouraging numerical results are presented.

Diagnostic with incomplete nominal/discrete data

- Jelinek, Herbert, Yatsko, Andrew, Stranieri, Andrew, Venkatraman, Sitalakshmi, Bagirov, Adil

**Authors:**Jelinek, Herbert , Yatsko, Andrew , Stranieri, Andrew , Venkatraman, Sitalakshmi , Bagirov, Adil**Date:**2015**Type:**Text , Journal article**Relation:**Artificial Intelligence Research Vol. 4, no. 1 (2015), p. 22-35**Full Text:****Reviewed:****Description:**Missing values may be present in data without undermining its use for diagnostic / classification purposes but compromise application of readily available software. Surrogate entries can remedy the situation, although the outcome is generally unknown. Discretization of continuous attributes renders all data nominal and is helpful in dealing with missing values; particularly, no special handling is required for different attribute types. A number of classifiers exist or can be reformulated for this representation. Some classifiers can be reinvented as data completion methods. In this work the Decision Tree, Nearest Neighbour, and Naive Bayesian methods are demonstrated to have the required aptness. An approach is implemented whereby the entered missing values are not necessarily a close match of the true data; however, they intend to cause the least hindrance for classification. The proposed techniques find their application particularly in medical diagnostics. Where clinical data represents a number of related conditions, taking Cartesian product of class values of the underlying sub-problems allows narrowing down of the selection of missing value substitutes. Real-world data examples, some publically available, are enlisted for testing. The proposed and benchmark methods are compared by classifying the data before and after missing value imputation, indicating a significant improvement.

**Authors:**Jelinek, Herbert , Yatsko, Andrew , Stranieri, Andrew , Venkatraman, Sitalakshmi , Bagirov, Adil**Date:**2015**Type:**Text , Journal article**Relation:**Artificial Intelligence Research Vol. 4, no. 1 (2015), p. 22-35**Full Text:****Reviewed:****Description:**Missing values may be present in data without undermining its use for diagnostic / classification purposes but compromise application of readily available software. Surrogate entries can remedy the situation, although the outcome is generally unknown. Discretization of continuous attributes renders all data nominal and is helpful in dealing with missing values; particularly, no special handling is required for different attribute types. A number of classifiers exist or can be reformulated for this representation. Some classifiers can be reinvented as data completion methods. In this work the Decision Tree, Nearest Neighbour, and Naive Bayesian methods are demonstrated to have the required aptness. An approach is implemented whereby the entered missing values are not necessarily a close match of the true data; however, they intend to cause the least hindrance for classification. The proposed techniques find their application particularly in medical diagnostics. Where clinical data represents a number of related conditions, taking Cartesian product of class values of the underlying sub-problems allows narrowing down of the selection of missing value substitutes. Real-world data examples, some publically available, are enlisted for testing. The proposed and benchmark methods are compared by classifying the data before and after missing value imputation, indicating a significant improvement.

Optimal operation of a multi-quality water distribution system with changing turbidity and salinity levels in source reservoirs

- Mala-Jetmarova, Helena, Barton, Andrew, Bagirov, Adil

**Authors:**Mala-Jetmarova, Helena , Barton, Andrew , Bagirov, Adil**Date:**2014**Type:**Text , Conference proceedings**Relation:**http://purl.org/au-research/grants/arc/LP0990908**Relation:**16th International Conference on Water Distribution System Analysis, WDSA 2014; Bari, Italy; 14th-17th July 2014**Full Text:****Description:**Impact of water quality conditions in sources on the optimal operation of a regional multiquality water distribution system is analysed. Three operational objectives are concurrently minimised, being pump energy costs, turbidity and salinity deviations at customer nodes. The optimisation problem is solved using GANetXL (NSGA-II) linked with EPANet. The example network incorporates scenarios with different water quality in sources. It was discovered that two types of tradeoffs, competing and non-competing, exist between the objectives and that the type of tradeoff is not unique between a particular pair of objectives across scenarios. The findings may be used for system operational planning.

**Authors:**Mala-Jetmarova, Helena , Barton, Andrew , Bagirov, Adil**Date:**2014**Type:**Text , Conference proceedings**Relation:**http://purl.org/au-research/grants/arc/LP0990908**Relation:**16th International Conference on Water Distribution System Analysis, WDSA 2014; Bari, Italy; 14th-17th July 2014**Full Text:****Description:**Impact of water quality conditions in sources on the optimal operation of a regional multiquality water distribution system is analysed. Three operational objectives are concurrently minimised, being pump energy costs, turbidity and salinity deviations at customer nodes. The optimisation problem is solved using GANetXL (NSGA-II) linked with EPANet. The example network incorporates scenarios with different water quality in sources. It was discovered that two types of tradeoffs, competing and non-competing, exist between the objectives and that the type of tradeoff is not unique between a particular pair of objectives across scenarios. The findings may be used for system operational planning.

An L-2-Boosting Algorithm for Estimation of a Regression Function

- Bagirov, Adil, Clausen, Conny, Kohler, Michael

**Authors:**Bagirov, Adil , Clausen, Conny , Kohler, Michael**Date:**2010**Type:**Text , Journal article**Relation:**IEEE Transactions on Information Theory Vol. 56, no. 3 (2010), p. 1417-1429**Full Text:****Reviewed:****Description:**An L-2-boosting algorithm for estimation of a regression function from random design is presented, which consists of fitting repeatedly a function from a fixed nonlinear function space to the residuals of the data by least squares and by defining the estimate as a linear combination of the resulting least squares estimates. Splitting of the sample is used to decide after how many iterations of smoothing of the residuals the algorithm terminates. The rate of convergence of the algorithm is analyzed in case of an unbounded response variable. The method is used to fit a sum of maxima of minima of linear functions to a given data set, and is compared with other nonparametric regression estimates using simulated data.

**Authors:**Bagirov, Adil , Clausen, Conny , Kohler, Michael**Date:**2010**Type:**Text , Journal article**Relation:**IEEE Transactions on Information Theory Vol. 56, no. 3 (2010), p. 1417-1429**Full Text:****Reviewed:****Description:**An L-2-boosting algorithm for estimation of a regression function from random design is presented, which consists of fitting repeatedly a function from a fixed nonlinear function space to the residuals of the data by least squares and by defining the estimate as a linear combination of the resulting least squares estimates. Splitting of the sample is used to decide after how many iterations of smoothing of the residuals the algorithm terminates. The rate of convergence of the algorithm is analyzed in case of an unbounded response variable. The method is used to fit a sum of maxima of minima of linear functions to a given data set, and is compared with other nonparametric regression estimates using simulated data.

Improving Naive Bayes classifier using conditional probabilities

- Taheri, Sona, Mammadov, Musa, Bagirov, Adil

**Authors:**Taheri, Sona , Mammadov, Musa , Bagirov, Adil**Date:**2010**Type:**Text , Conference proceedings**Full Text:****Description:**Naive Bayes classifier is the simplest among Bayesian Network classifiers. It has shown to be very efficient on a variety of data classification problems. However, the strong assumption that all features are conditionally independent given the class is often violated on many real world applications. Therefore, improvement of the Naive Bayes classifier by alleviating the feature independence assumption has attracted much attention. In this paper, we develop a new version of the Naive Bayes classifier without assuming independence of features. The proposed algorithm approximates the interactions between features by using conditional probabilities. We present results of numerical experiments on several real world data sets, where continuous features are discretized by applying two different methods. These results demonstrate that the proposed algorithm significantly improve the performance of the Naive Bayes classifier, yet at the same time maintains its robustness. © 2011, Australian Computer Society, Inc.**Description:**2003009505

**Authors:**Taheri, Sona , Mammadov, Musa , Bagirov, Adil**Date:**2010**Type:**Text , Conference proceedings**Full Text:****Description:**Naive Bayes classifier is the simplest among Bayesian Network classifiers. It has shown to be very efficient on a variety of data classification problems. However, the strong assumption that all features are conditionally independent given the class is often violated on many real world applications. Therefore, improvement of the Naive Bayes classifier by alleviating the feature independence assumption has attracted much attention. In this paper, we develop a new version of the Naive Bayes classifier without assuming independence of features. The proposed algorithm approximates the interactions between features by using conditional probabilities. We present results of numerical experiments on several real world data sets, where continuous features are discretized by applying two different methods. These results demonstrate that the proposed algorithm significantly improve the performance of the Naive Bayes classifier, yet at the same time maintains its robustness. © 2011, Australian Computer Society, Inc.**Description:**2003009505

Estimation of a regression function by maxima of minima of linear functions

- Bagirov, Adil, Clausen, Conny, Kohler, Michael

**Authors:**Bagirov, Adil , Clausen, Conny , Kohler, Michael**Date:**2009**Type:**Text , Journal article**Relation:**IEEE Transactions on Information Theory Vol. 55, no. 2 (2009), p. 833-845**Full Text:****Reviewed:****Description:**In this paper, estimation of a regression function from independent and identically distributed random variables is considered. Estimates are defined by minimization of the empirical L2 risk over a class of functions, which are defined as maxima of minima of linear functions. Results concerning the rate of convergence of the estimates are derived. In particular, it is shown that for smooth regression functions satisfying the assumption of single index models, the estimate is able to achieve (up to some logarithmic factor) the corresponding optimal one-dimensional rate of convergence. Hence, under these assumptions, the estimate is able to circumvent the so-called curse of dimensionality. The small sample behavior of the estimates is illustrated by applying them to simulated data. © 2009 IEEE.

**Authors:**Bagirov, Adil , Clausen, Conny , Kohler, Michael**Date:**2009**Type:**Text , Journal article**Relation:**IEEE Transactions on Information Theory Vol. 55, no. 2 (2009), p. 833-845**Full Text:****Reviewed:****Description:**In this paper, estimation of a regression function from independent and identically distributed random variables is considered. Estimates are defined by minimization of the empirical L2 risk over a class of functions, which are defined as maxima of minima of linear functions. Results concerning the rate of convergence of the estimates are derived. In particular, it is shown that for smooth regression functions satisfying the assumption of single index models, the estimate is able to achieve (up to some logarithmic factor) the corresponding optimal one-dimensional rate of convergence. Hence, under these assumptions, the estimate is able to circumvent the so-called curse of dimensionality. The small sample behavior of the estimates is illustrated by applying them to simulated data. © 2009 IEEE.

An algorithm for the estimation of a regression function by continuous piecewise linear functions

- Bagirov, Adil, Clausen, Conny, Kohler, Michael

**Authors:**Bagirov, Adil , Clausen, Conny , Kohler, Michael**Date:**2008**Type:**Text , Journal article**Relation:**Computational Optimization and Applications Vol. 45, no. (2008), p. 159-179**Relation:**http://purl.org/au-research/grants/arc/DP0666061**Full Text:****Reviewed:****Description:**The problem of the estimation of a regression function by continuous piecewise linear functions is formulated as a nonconvex, nonsmooth optimization problem. Estimates are defined by minimization of the empirical L 2 risk over a class of functions, which are defined as maxima of minima of linear functions. An algorithm for finding continuous piecewise linear functions is presented. We observe that the objective function in the optimization problem is semismooth, quasidifferentiable and piecewise partially separable. The use of these properties allow us to design an efficient algorithm for approximation of subgradients of the objective function and to apply the discrete gradient method for its minimization. We present computational results with some simulated data and compare the new estimator with a number of existing ones.**Description:**The problem of the estimation of a regression function by continuous piecewise linear functions is formulated as a nonconvex, nonsmooth optimization problem. Estimates are defined by minimization of the empirical L 2 risk over a class of functions, which are defined as maxima of minima of linear functions. An algorithm for finding continuous piecewise linear functions is presented. We observe that the objective function in the optimization problem is semismooth, quasidifferentiable and piecewise partially separable. The use of these properties allow us to design an efficient algorithm for approximation of subgradients of the objective function and to apply the discrete gradient method for its minimization. We present computational results with some simulated data and compare the new estimator with a number of existing ones. © 2008 Springer Science+Business Media, LLC.

An approximate subgradient algorithm for unconstrained nonsmooth, nonconvex optimization

- Bagirov, Adil, Ganjehlou, Asef Nazari

**Authors:**Bagirov, Adil , Ganjehlou, Asef Nazari**Date:**2008**Type:**Text , Journal article**Relation:**Mathematical Methods of Operations Research Vol. 67, no. 2 (2008), p. 187-206**Relation:**http://purl.org/au-research/grants/arc/DP0666061**Full Text:****Reviewed:****Description:**In this paper a new algorithm for minimizing locally Lipschitz functions is developed. Descent directions in this algorithm are computed by solving a system of linear inequalities. The convergence of the algorithm is proved for quasidifferentiable semismooth functions. We present the results of numerical experiments with both regular and nonregular objective functions. We also compare the proposed algorithm with two different versions of the subgradient method using the results of numerical experiments. These results demonstrate the superiority of the proposed algorithm over the subgradient method. © 2007 Springer-Verlag.**Description:**C1

**Authors:**Bagirov, Adil , Ganjehlou, Asef Nazari**Date:**2008**Type:**Text , Journal article**Relation:**Mathematical Methods of Operations Research Vol. 67, no. 2 (2008), p. 187-206**Relation:**http://purl.org/au-research/grants/arc/DP0666061**Full Text:****Reviewed:****Description:**In this paper a new algorithm for minimizing locally Lipschitz functions is developed. Descent directions in this algorithm are computed by solving a system of linear inequalities. The convergence of the algorithm is proved for quasidifferentiable semismooth functions. We present the results of numerical experiments with both regular and nonregular objective functions. We also compare the proposed algorithm with two different versions of the subgradient method using the results of numerical experiments. These results demonstrate the superiority of the proposed algorithm over the subgradient method. © 2007 Springer-Verlag.**Description:**C1

Discrete gradient method : Derivative-free method for nonsmooth optimization

- Bagirov, Adil, Karasozen, Bulent, Sezer, Monsalve

**Authors:**Bagirov, Adil , Karasozen, Bulent , Sezer, Monsalve**Date:**2008**Type:**Text , Journal article**Relation:**Journal of Optimization Theory and Applications Vol. 137, no. 2 (2008), p. 317-334**Relation:**http://purl.org/au-research/grants/arc/DP0666061**Full Text:****Reviewed:****Description:**A new derivative-free method is developed for solving unconstrained nonsmooth optimization problems. This method is based on the notion of a discrete gradient. It is demonstrated that the discrete gradients can be used to approximate subgradients of a broad class of nonsmooth functions. It is also shown that the discrete gradients can be applied to find descent directions of nonsmooth functions. The preliminary results of numerical experiments with unconstrained nonsmooth optimization problems as well as the comparison of the proposed method with the nonsmooth optimization solver DNLP from CONOPT-GAMS and the derivative-free optimization solver CONDOR are presented. © 2007 Springer Science+Business Media, LLC.**Description:**C1

Modified global k-means algorithm for minimum sum-of-squares clustering problems

**Authors:**Bagirov, Adil**Date:**2008**Type:**Text , Journal article**Relation:**Pattern Recognition Vol. 41, no. 10 (2008), p. 3192-3199**Relation:**http://purl.org/au-research/grants/arc/DP0666061**Full Text:****Reviewed:****Description:**k-Means algorithm and its variations are known to be fast clustering algorithms. However, they are sensitive to the choice of starting points and inefficient for solving clustering problems in large data sets. Recently, a new version of the k-means algorithm, the global k-means algorithm has been developed. It is an incremental algorithm that dynamically adds one cluster center at a time and uses each data point as a candidate for the k-th cluster center. Results of numerical experiments show that the global k-means algorithm considerably outperforms the k-means algorithms. In this paper, a new version of the global k-means algorithm is proposed. A starting point for the k-th cluster center in this algorithm is computed by minimizing an auxiliary cluster function. Results of numerical experiments on 14 data sets demonstrate the superiority of the new algorithm, however, it requires more computational time than the global k-means algorithm.**Description:**k-Means algorithm and its variations are known to be fast clustering algorithms. However, they are sensitive to the choice of starting points and inefficient for solving clustering problems in large data sets. Recently, a new version of the k-means algorithm, the global k-means algorithm has been developed. It is an incremental algorithm that dynamically adds one cluster center at a time and uses each data point as a candidate for the k-th cluster center. Results of numerical experiments show that the global k-means algorithm considerably outperforms the k-means algorithms. In this paper, a new version of the global k-means algorithm is proposed. A starting point for the k-th cluster center in this algorithm is computed by minimizing an auxiliary cluster function. Results of numerical experiments on 14 data sets demonstrate the superiority of the new algorithm, however, it requires more computational time than the global k-means algorithm. © 2008 Elsevier Ltd. All rights reserved.**Description:**2003001713

**Authors:**Bagirov, Adil**Date:**2008**Type:**Text , Journal article**Relation:**Pattern Recognition Vol. 41, no. 10 (2008), p. 3192-3199**Relation:**http://purl.org/au-research/grants/arc/DP0666061**Full Text:****Reviewed:****Description:**k-Means algorithm and its variations are known to be fast clustering algorithms. However, they are sensitive to the choice of starting points and inefficient for solving clustering problems in large data sets. Recently, a new version of the k-means algorithm, the global k-means algorithm has been developed. It is an incremental algorithm that dynamically adds one cluster center at a time and uses each data point as a candidate for the k-th cluster center. Results of numerical experiments show that the global k-means algorithm considerably outperforms the k-means algorithms. In this paper, a new version of the global k-means algorithm is proposed. A starting point for the k-th cluster center in this algorithm is computed by minimizing an auxiliary cluster function. Results of numerical experiments on 14 data sets demonstrate the superiority of the new algorithm, however, it requires more computational time than the global k-means algorithm.**Description:**k-Means algorithm and its variations are known to be fast clustering algorithms. However, they are sensitive to the choice of starting points and inefficient for solving clustering problems in large data sets. Recently, a new version of the k-means algorithm, the global k-means algorithm has been developed. It is an incremental algorithm that dynamically adds one cluster center at a time and uses each data point as a candidate for the k-th cluster center. Results of numerical experiments show that the global k-means algorithm considerably outperforms the k-means algorithms. In this paper, a new version of the global k-means algorithm is proposed. A starting point for the k-th cluster center in this algorithm is computed by minimizing an auxiliary cluster function. Results of numerical experiments on 14 data sets demonstrate the superiority of the new algorithm, however, it requires more computational time than the global k-means algorithm. © 2008 Elsevier Ltd. All rights reserved.**Description:**2003001713

A nonsmooth optimization approach to sensor network localization

- Bagirov, Adil, Lai, Daniel, Palaniswami, M.

**Authors:**Bagirov, Adil , Lai, Daniel , Palaniswami, M.**Date:**2007**Type:**Text , Conference paper**Relation:**Paper presented at 3rd International Conference on Intelligent Sensors, Sensor Networks and Information, ISSNIP 2007, Melbourne, Victoria : 3rd-6th December 2007 p. 727-732**Relation:**http://purl.org/au-research/grants/arc/DP0666061**Full Text:****Description:**In this paper the problem of localization of wireless sensor network is formulated as an unconstrained nonsmooth optimization problem. We minimize a distance objective function which incorporates unknown sensor nodes and nodes with known positions (anchors) in contrast to popular semidefinite programming (SDP) methods which use artificial objective functions. We study the main properties of the objective function in this problem and design an algorithm for its minimization. Our algorithm is a derivative-free discrete gradient method that allows one to find a near global solution. The algorithm can handle a large number of sensors in the network. This paper contains the theory of our proposed formulation and algorithm while experimental results are included in later work.**Description:**2003004949

**Authors:**Bagirov, Adil , Lai, Daniel , Palaniswami, M.**Date:**2007**Type:**Text , Conference paper**Relation:**Paper presented at 3rd International Conference on Intelligent Sensors, Sensor Networks and Information, ISSNIP 2007, Melbourne, Victoria : 3rd-6th December 2007 p. 727-732**Relation:**http://purl.org/au-research/grants/arc/DP0666061**Full Text:****Description:**In this paper the problem of localization of wireless sensor network is formulated as an unconstrained nonsmooth optimization problem. We minimize a distance objective function which incorporates unknown sensor nodes and nodes with known positions (anchors) in contrast to popular semidefinite programming (SDP) methods which use artificial objective functions. We study the main properties of the objective function in this problem and design an algorithm for its minimization. Our algorithm is a derivative-free discrete gradient method that allows one to find a near global solution. The algorithm can handle a large number of sensors in the network. This paper contains the theory of our proposed formulation and algorithm while experimental results are included in later work.**Description:**2003004949

Integrated production system optimization using global optimization techniques

- Mason, T. L., Emelle, C., Van Berkel, J., Bagirov, Adil, Kampas, F., Pinter, J. D.

**Authors:**Mason, T. L. , Emelle, C. , Van Berkel, J. , Bagirov, Adil , Kampas, F. , Pinter, J. D.**Date:**2007**Type:**Text , Journal article**Relation:**Journal of Industrial and Management Optimization Vol. 3, no. 2 (May 2007), p. 257-277**Full Text:****Reviewed:****Description:**Many optimization problems related to integrated oil and gas production systems are nonconvex and multimodal. Additionally, apart from the innate nonsmoothness of many optimization problems, nonsmooth functions such as minimum and maximum functions may be used to model flow/pressure controllers and cascade mass in the gas gathering and blending networks. In this paper we study the application of different versions of the derivative free Discrete Gradient Method (DGM) as well as the Lipschitz Global Optimizer (LGO) suite to production optimization in integrated oil and gas production systems and their comparison with various local and global solvers used with the General Algebraic Modeling System (GAMS). Four nonconvex and nonsmooth test cases were constructed from a small but realistic integrated gas production system optimization problem. The derivation of the system of equations for the various test cases is also presented. Results demonstrate that DGM is especially effective for solving nonsmooth optimization problems and its two versions are capable global optimization algorithms. We also demonstrate that LGO solves successfully the presented test (as well as other related real-world) problems.**Description:**C1**Description:**2003004725

**Authors:**Mason, T. L. , Emelle, C. , Van Berkel, J. , Bagirov, Adil , Kampas, F. , Pinter, J. D.**Date:**2007**Type:**Text , Journal article**Relation:**Journal of Industrial and Management Optimization Vol. 3, no. 2 (May 2007), p. 257-277**Full Text:****Reviewed:****Description:**Many optimization problems related to integrated oil and gas production systems are nonconvex and multimodal. Additionally, apart from the innate nonsmoothness of many optimization problems, nonsmooth functions such as minimum and maximum functions may be used to model flow/pressure controllers and cascade mass in the gas gathering and blending networks. In this paper we study the application of different versions of the derivative free Discrete Gradient Method (DGM) as well as the Lipschitz Global Optimizer (LGO) suite to production optimization in integrated oil and gas production systems and their comparison with various local and global solvers used with the General Algebraic Modeling System (GAMS). Four nonconvex and nonsmooth test cases were constructed from a small but realistic integrated gas production system optimization problem. The derivation of the system of equations for the various test cases is also presented. Results demonstrate that DGM is especially effective for solving nonsmooth optimization problems and its two versions are capable global optimization algorithms. We also demonstrate that LGO solves successfully the presented test (as well as other related real-world) problems.**Description:**C1**Description:**2003004725

Visual tools for analysing evolution, emergence, and error in data streams

- Hart, Sol, Yearwood, John, Bagirov, Adil

**Authors:**Hart, Sol , Yearwood, John , Bagirov, Adil**Date:**2007**Type:**Text , Conference paper**Relation:**Paper presented at 6th IEEE/ACIS International Conference on Computer and Information Science, ICIS 2007, Melbourne, Victoria : 11th-13th July 2007 p. 987-992**Full Text:****Description:**The relatively new field of stream mining has necessitated the development of robust drift-aware algorithms that provide accurate, real time, data handling capabilities. Tools are needed to assess and diagnose important trends and investigate drift evolution parameters. In this paper, we present two new and novel visualisation techniques, Pixie and Luna graphs, which incorporate salient group statistics coupled with intuitive visual representations of multidimensional groupings over time. Through the novel representations presented here, spatial interactions between temporal divisions can be diagnosed and overall distribution patterns identified. It provides a means of evaluating in non-constrained capacity, commonly constrained evolutionary problems.**Description:**2003005432

**Authors:**Hart, Sol , Yearwood, John , Bagirov, Adil**Date:**2007**Type:**Text , Conference paper**Relation:**Paper presented at 6th IEEE/ACIS International Conference on Computer and Information Science, ICIS 2007, Melbourne, Victoria : 11th-13th July 2007 p. 987-992**Full Text:****Description:**The relatively new field of stream mining has necessitated the development of robust drift-aware algorithms that provide accurate, real time, data handling capabilities. Tools are needed to assess and diagnose important trends and investigate drift evolution parameters. In this paper, we present two new and novel visualisation techniques, Pixie and Luna graphs, which incorporate salient group statistics coupled with intuitive visual representations of multidimensional groupings over time. Through the novel representations presented here, spatial interactions between temporal divisions can be diagnosed and overall distribution patterns identified. It provides a means of evaluating in non-constrained capacity, commonly constrained evolutionary problems.**Description:**2003005432

Modified global k-means algorithm for clustering in gene expression data sets

- Bagirov, Adil, Mardaneh, Karim

**Authors:**Bagirov, Adil , Mardaneh, Karim**Date:**2006**Type:**Text , Conference paper**Relation:**Paper presented at Intelligent Systems for Bioinformatics 2006, proceedings of the AI 2006 Workshop on Intelligent Systems of Bioinformatics, Hobart, Tasmania : 4th December, 2006**Full Text:****Reviewed:****Description:**Clustering in gene expression data sets is a challenging problem. Different algorithms for clustering of genes have been proposed. However due to the large number of genes only a few algorithms can be applied for the clustering of samples. k-means algorithm and its different variations are among those algorithms. But these algorithms in general can converge only to local minima and these local minima are significantly different from global solutions as the number of clusters increases. Over the last several years different approaches have been proposed to improve global search properties of k-means algorithm and its performance on large data sets. One of them is the global k-means algorithm. In this paper we develop a new version of the global k-means algorithm: the modified global k-means algorithm which is effective for solving clustering problems in gene expression data sets. We present preliminary computational results using gene expression data sets which demonstrate that the modified k-means algorithm improves and sometimes significantly results by k-means and global k-means algorithms.**Description:**E1**Description:**2003001713

**Authors:**Bagirov, Adil , Mardaneh, Karim**Date:**2006**Type:**Text , Conference paper**Relation:**Paper presented at Intelligent Systems for Bioinformatics 2006, proceedings of the AI 2006 Workshop on Intelligent Systems of Bioinformatics, Hobart, Tasmania : 4th December, 2006**Full Text:****Reviewed:****Description:**Clustering in gene expression data sets is a challenging problem. Different algorithms for clustering of genes have been proposed. However due to the large number of genes only a few algorithms can be applied for the clustering of samples. k-means algorithm and its different variations are among those algorithms. But these algorithms in general can converge only to local minima and these local minima are significantly different from global solutions as the number of clusters increases. Over the last several years different approaches have been proposed to improve global search properties of k-means algorithm and its performance on large data sets. One of them is the global k-means algorithm. In this paper we develop a new version of the global k-means algorithm: the modified global k-means algorithm which is effective for solving clustering problems in gene expression data sets. We present preliminary computational results using gene expression data sets which demonstrate that the modified k-means algorithm improves and sometimes significantly results by k-means and global k-means algorithms.**Description:**E1**Description:**2003001713

Non-smooth optimization methods for computation of the conditional value-at-risk and portfolio optimization

- Beliakov, Gleb, Bagirov, Adil

**Authors:**Beliakov, Gleb , Bagirov, Adil**Date:**2006**Type:**Text , Journal article**Relation:**Optimization Vol. 55, no. 5-6 (2006), p. 459-479**Full Text:****Reviewed:****Description:**We examine numerical performance of various methods of calculation of the Conditional Value-at-risk (CVaR), and portfolio optimization with respect to this risk measure. We concentrate on the method proposed by Rockafellar and Uryasev in (Rockafellar, R.T. and Uryasev, S., 2000, Optimization of conditional value-at-risk. Journal of Risk, 2, 21-41), which converts this problem to that of convex optimization. We compare the use of linear programming techniques against a non-smooth optimization method of the discrete gradient, and establish the supremacy of the latter. We show that non-smooth optimization can be used efficiently for large portfolio optimization, and also examine parallel execution of this method on computer clusters. © 2006 Taylor & Francis.**Description:**C1**Description:**2003002156

**Authors:**Beliakov, Gleb , Bagirov, Adil**Date:**2006**Type:**Text , Journal article**Relation:**Optimization Vol. 55, no. 5-6 (2006), p. 459-479**Full Text:****Reviewed:****Description:**We examine numerical performance of various methods of calculation of the Conditional Value-at-risk (CVaR), and portfolio optimization with respect to this risk measure. We concentrate on the method proposed by Rockafellar and Uryasev in (Rockafellar, R.T. and Uryasev, S., 2000, Optimization of conditional value-at-risk. Journal of Risk, 2, 21-41), which converts this problem to that of convex optimization. We compare the use of linear programming techniques against a non-smooth optimization method of the discrete gradient, and establish the supremacy of the latter. We show that non-smooth optimization can be used efficiently for large portfolio optimization, and also examine parallel execution of this method on computer clusters. © 2006 Taylor & Francis.**Description:**C1**Description:**2003002156

Piecewise partially separable functions and a derivative-free algorithm for large scale nonsmooth optimization

**Authors:**Bagirov, Adil , Ugon, Julien**Date:**2006**Type:**Text , Journal article**Relation:**Journal of Global Optimization Vol. 35, no. 2 (Jun 2006), p. 163-195**Full Text:****Reviewed:****Description:**This paper introduces the notion of piecewise partially separable functions and studies their properties. We also consider some of many applications of these functions. Finally, we consider the problem of minimizing of piecewise partially separable functions and develop an algorithm for its solution. This algorithm exploits the structure of such functions. We present the results of preliminary numerical experiments.**Description:**2003001532

**Authors:**Bagirov, Adil , Ugon, Julien**Date:**2006**Type:**Text , Journal article**Relation:**Journal of Global Optimization Vol. 35, no. 2 (Jun 2006), p. 163-195**Full Text:****Reviewed:****Description:**This paper introduces the notion of piecewise partially separable functions and studies their properties. We also consider some of many applications of these functions. Finally, we consider the problem of minimizing of piecewise partially separable functions and develop an algorithm for its solution. This algorithm exploits the structure of such functions. We present the results of preliminary numerical experiments.**Description:**2003001532

An algorithm for minimizing clustering functions

**Authors:**Bagirov, Adil , Ugon, Julien**Date:**2005**Type:**Text , Journal article**Relation:**Optimization Vol. 54, no. 4-5 (Aug-Oct 2005), p. 351-368**Full Text:****Reviewed:****Description:**The problem of cluster analysis is formulated as a problem of nonsmooth, nonconvex optimization. An algorithm for solving the latter optimization problem is developed which allows one to significantly reduce the computational efforts. This algorithm is based on the so-called discrete gradient method. Results of numerical experiments are presented which demonstrate the effectiveness of the proposed algorithm.**Description:**C1**Description:**2003001266

**Authors:**Bagirov, Adil , Ugon, Julien**Date:**2005**Type:**Text , Journal article**Relation:**Optimization Vol. 54, no. 4-5 (Aug-Oct 2005), p. 351-368**Full Text:****Reviewed:****Description:**The problem of cluster analysis is formulated as a problem of nonsmooth, nonconvex optimization. An algorithm for solving the latter optimization problem is developed which allows one to significantly reduce the computational efforts. This algorithm is based on the so-called discrete gradient method. Results of numerical experiments are presented which demonstrate the effectiveness of the proposed algorithm.**Description:**C1**Description:**2003001266

Data mining with combined use of optimization techniques and self-organizing maps for improving risk grouping rules : Application to prostate cancer patients

- Churilov, Leonid, Bagirov, Adil, Schwartz, Daniel, Smith, Kate, Dally, Michael

**Authors:**Churilov, Leonid , Bagirov, Adil , Schwartz, Daniel , Smith, Kate , Dally, Michael**Date:**2005**Type:**Text , Journal article**Relation:**Journal of Management Information Systems Vol. 21, no. 4 (2005), p. 85-100**Full Text:****Reviewed:****Description:**Data mining techniques provide a popular and powerful tool set to generate various data-driven classification systems. In this paper, we investigate the combined use of self-organizing maps (SOM) and nonsmooth nonconvex optimization techniques in order to produce a working case of a data-driven risk classification system. The optimization approach strengthens the validity of SOM results, and the improved classification system increases both the quality of prediction and the homogeneity within the risk groups. Accurate classification of prostate cancer patients into risk groups is important to assist in the identification of appropriate treatment paths. We start with the existing rules and aim to improve classification accuracy by identifying inconsistencies utilizing self-organizing maps as a data visualization tool. Then, we progress to the study of assigning prostate cancer patients into homogenous groups with the aim to support future clinical treatment decisions. Using the case of prostate cancer patients grouping, we demonstrate strong potential of data-driven risk classification schemes for addressing the risk grouping issues in more general organizational settings. © 2005 M.E. Sharpe, Inc.**Description:**C1**Description:**2003001265

**Authors:**Churilov, Leonid , Bagirov, Adil , Schwartz, Daniel , Smith, Kate , Dally, Michael**Date:**2005**Type:**Text , Journal article**Relation:**Journal of Management Information Systems Vol. 21, no. 4 (2005), p. 85-100**Full Text:****Reviewed:****Description:**Data mining techniques provide a popular and powerful tool set to generate various data-driven classification systems. In this paper, we investigate the combined use of self-organizing maps (SOM) and nonsmooth nonconvex optimization techniques in order to produce a working case of a data-driven risk classification system. The optimization approach strengthens the validity of SOM results, and the improved classification system increases both the quality of prediction and the homogeneity within the risk groups. Accurate classification of prostate cancer patients into risk groups is important to assist in the identification of appropriate treatment paths. We start with the existing rules and aim to improve classification accuracy by identifying inconsistencies utilizing self-organizing maps as a data visualization tool. Then, we progress to the study of assigning prostate cancer patients into homogenous groups with the aim to support future clinical treatment decisions. Using the case of prostate cancer patients grouping, we demonstrate strong potential of data-driven risk classification schemes for addressing the risk grouping issues in more general organizational settings. © 2005 M.E. Sharpe, Inc.**Description:**C1**Description:**2003001265

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