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A global optimisation approach to classification in medical diagnosis and prognosis

- Bagirov, Adil, Rubinov, Alex, Yearwood, John, Stranieri, Andrew

  • Authors: Bagirov, Adil , Rubinov, Alex , Yearwood, John , Stranieri, Andrew
  • Date: 2001
  • Type: Text , Conference paper
  • Relation: Paper presented at 34th Hawaii International Conference on System Sciences, HICSS-34, Maui, Hawaii, USA : 3rd-6th January 2001
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  • Description: In this paper global optimisation-based techniques are studied in order to increase the accuracy of medical diagnosis and prognosis with FNA image data from the Wisconsin Diagnostic and Prognostic Breast Cancer databases. First we discuss the problem of determining the most informative features for the classification of cancerous cases in the databases under consideration. Then we apply a technique based on convex and global optimisation to breast cancer diagnosis. It allows the classification of benign cases and malignant ones and the subsequent diagnosis of patients with very high accuracy. The third application of this technique is a method that calculates centres of clusters to predict when breast cancer is likely to recur in patients for which cancer has been removed. The technique achieves higher accuracy with these databases than reported elsewhere in the literature.
  • Description: 2003003950

A nonsmooth optimization approach to sensor network localization

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

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
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  • 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.

Adaption to water shortage through the implementation of a unique pipeline system in Victoria, Australia

- Mala-Jetmarova, Helena, Barton, Andrew, Bagirov, Adil, McRae-Williams, Pamela, Caris, Rob, Jackson, Peter

  • Authors: Mala-Jetmarova, Helena , Barton, Andrew , Bagirov, Adil , McRae-Williams, Pamela , Caris, Rob , Jackson, Peter
  • Date: 2010
  • Type: Conference paper
  • Relation: Paper presented at Hydropredict' 2010, 2nd International Interdisciplinary Conference on predications for Hydrology, Ecology, and Water Resources Management
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  • Description: Abstract Water resource development has played a crucial role in the Grampians, Wimmera and Mallee regions of Australia, with the main source of surface water located in several reservoirs in the Grampians mountain ranges. Historically, water was delivered by gravity through a vast 19 500 km earthen channel system from the reservoirs to the townships and farms. As a result of the severe and protracted drought experienced in the region over the past 13 years and the projected drying climate, there have been fundamental changes made to the management of water in order to better cope with water scarcity. The primary strategic effort to sustainably manage water resources was by removing the unsustainable transport of water via the open channels which resulted in very high losses through seepage and evaporation. This inefficient system has been replaced by a pressurised pipeline, the largest geographical water infrastructure project of its type in Australia, spreading across an area of approximately 20 000 km2. To manage the change in water balance as a result of the pipeline and drying climate, the regions water corporations and environmental agencies have designed a scheme for water allocations intended to sustain local communities, allow for regional development and improve environmental conditions. This paper describes the unique pipeline system recently completed, provides a brief summary of water sharing arrangements and introduces the research program currently underway to optimise the performance of the pipeline system.

An algorithm for minimizing clustering functions

- Bagirov, Adil, Ugon, Julien

  • Authors: Bagirov, Adil , Ugon, Julien
  • Date: 2005
  • Type: Text , Journal article
  • Relation: Optimization Vol. 54, no. 4-5 (Aug-Oct 2005), p. 351-368
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  • 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

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
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  • 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
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  • 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

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
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  • 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.

Comparative analysis of the cutting angle and simulated annealing methods in global optimization

- Bagirov, Adil, Zhang, Jiapu

  • Authors: Bagirov, Adil , Zhang, Jiapu
  • Date: 2003
  • Type: Text , Journal article
  • Relation: Optimization Vol. 52, no. 4-5 (2003), p. 363-378
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  • Description: This article presents a comparative analysis of two methods of global optimization: the simulated annealing method and a method based on a combination of the cutting angle method and a local search. This analysis is carried out using results of numerical experiments. These results demonstrate that the combined method is more effective than the simulated annealing method.
  • Description: C1
  • Description: 2003000436

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
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  • 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

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
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  • 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.

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
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  • 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

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
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  • 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.

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
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  • 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.

Feature selection using misclassification counts

- Bagirov, Adil, Yatsko, Andrew, Stranieri, Andrew

  • Authors: Bagirov, Adil , Yatsko, Andrew , Stranieri, Andrew
  • Date: 2011
  • Type: Conference proceedings , Unpublished work
  • Relation: Proceedings of the 9th Australasian Data Mining Conference (AusDM 2011), 51-62. Conferences in Research and Practice in Information Technology (CRPIT), Vol. 121.
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  • Description: Dimensionality reduction of the problem space through detection and removal of variables, contributing little or not at all to classification, is able to relieve the computational load and instance acquisition effort, considering all the data attributes accessed each time around. The approach to feature selection in this paper is based on the concept of coherent accumulation of data about class centers with respect to coordinates of informative features. Ranking is done on the degree to which different variables exhibit random characteristics. The results are being verified using the Nearest Neighbor classifier. This also helps to address the feature irrelevance and redundancy, what ranking does not immediately decide. Additionally, feature ranking methods from different independent sources are called in for the direct comparison.
  • Description: Dimensionality reduction of the problem space through detection and removal of variables, contributing little or not at all to classification, is able to relieve the computational load and the data acquisition effort, considering all data components being accessed each time around. The approach to feature selection in this paper is based on the concept of coherent accumulation of data about class centers with respect to coordinates of informative features. Ranking is done on the degree, to which different variables exhibit random characteristics. The results are being verified using the Nearest Neighbor classifier. This also helps to address the feature irrelevance, what ranking does not immediately decide. Additionally, feature ranking methods available from different independent sources are called in for direct comparison.

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
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  • 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

Improving risk grouping rules for prostate cancer patients with optimization

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

  • Authors: Churilov, Leonid , Bagirov, Adil , Schwartz, Daniel , Smith, Kate , Dally, Michael
  • Date: 2004
  • Type: Text , Conference paper
  • Relation: Paper presented at the 37th Annual Hawaii International Conference on System Sciences, Big Island, Hawaii : 5th January, 2004
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  • Description: Data mining techniques provide a popular and powerful toolset to address both clinical and management issues in the area of health care. This paper describes the study of assigning prostate cancer patients into homogenous groups with the aim to support future clinical treatment decisions. The cluster analysis based model is suggested and an application of non-smooth non-convex optimization techniques to solve this model is discussed. It is demonstrated that using the optimization based approach to data mining of a prostate cancer patients database can lead to generation of a significant amount of new knowledge that can be effectively utilized to enhance clinical decision making.
  • Description: E1
  • Description: 2003000846

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
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  • 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

Local optimization method with global multidimensional search

- Bagirov, Adil, Rubinov, Alex, Zhang, Jiapu

  • Authors: Bagirov, Adil , Rubinov, Alex , Zhang, Jiapu
  • Date: 2005
  • Type: Text , Journal article
  • Relation: Journal of Global Optimization Vol. 32, no. 2 (2005), p. 161-179
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  • Description: This paper presents a new method for solving global optimization problems. We use a local technique based on the notion of discrete gradients for finding a cone of descent directions and then we use a global cutting angle algorithm for finding global minimum within the intersection of the cone and the feasible region. We present results of numerical experiments with well-known test problems and with the so-called cluster function. These results confirm that the proposed algorithms allows one to find a global minimizer or at least a deep local minimizer of a function with a huge amount of shallow local minima. © Springer 2005.
  • Description: C1
  • Description: 2003001351

Max-min separability

- Bagirov, Adil

  • Authors: Bagirov, Adil
  • Date: 2005
  • Type: Text , Journal article
  • Relation: Optimization Methods and Software Vol. 20, no. 2-3 (2005), p. 271-290
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  • Description: We consider the problem of discriminating two finite point sets in the n-dimensional space by a finite number of hyperplanes generating a piecewise linear function. If the intersection of these sets is empty, then they can be strictly separated by a max-min of linear functions. An error function is introduced. This function is nonconvex piecewise linear. We discuss an algorithm for its minimization. The results of numerical experiments using some real-world datasets are presented, which show the effectiveness of the proposed approach.
  • Description: C1
  • Description: 2003001350