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Limited Memory Bundle Method for Clusterwise Linear Regression

  • Authors: Karmitsa, Napsu , Bagirov, Adil , Taheri, Sona , Joki, Kaisa
  • Date: 2022
  • Type: Text , Book chapter
  • Relation: Intelligent Systems, Control and Automation: Science and Engineering p. 109-122
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  • Description: A clusterwise linear regression problem consists of finding a number of linear functions each approximating a subset of the given data. In this paper, the limited memory bundle method is modified and combined with the incremental approach to solve this problem using its nonsmooth optimization formulation. The main contribution of the proposed method is to obtain a fast solution time for large-scale clusterwise linear regression problems. The proposed algorithm is tested on small and large real-world data sets and compared with other algorithms for clusterwise linear regression. Numerical results demonstrate that the proposed algorithm is especially efficient in data sets with large numbers of data points and input variables. © 2022, Springer Nature Switzerland AG.

Aggregate subgradient method for nonsmooth DC optimization

  • Authors: Bagirov, Adil , Taheri, Sona , Joki, Kaisa , Karmitsa, Napsu , Mäkelä, Marko
  • Date: 2021
  • Type: Text , Journal article
  • Relation: Optimization Letters Vol. 15, no. 1 (2021), p. 83-96
  • Relation: http://purl.org/au-research/grants/arc/DP190100580
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  • Description: The aggregate subgradient method is developed for solving unconstrained nonsmooth difference of convex (DC) optimization problems. The proposed method shares some similarities with both the subgradient and the bundle methods. Aggregate subgradients are defined as a convex combination of subgradients computed at null steps between two serious steps. At each iteration search directions are found using only two subgradients: the aggregate subgradient and a subgradient computed at the current null step. It is proved that the proposed method converges to a critical point of the DC optimization problem and also that the number of null steps between two serious steps is finite. The new method is tested using some academic test problems and compared with several other nonsmooth DC optimization solvers. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.

An augmented subgradient method for minimizing nonsmooth DC functions

  • Authors: Bagirov, Adil , Hoseini Monjezi, Najmeh , Taheri, Sona
  • Date: 2021
  • Type: Text , Journal article
  • Relation: Computational Optimization and Applications Vol. 80, no. 2 (2021), p. 411-438
  • Relation: http://purl.org/au-research/grants/arc/DP190100580
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  • Description: A method, called an augmented subgradient method, is developed to solve unconstrained nonsmooth difference of convex (DC) optimization problems. At each iteration of this method search directions are found by using several subgradients of the first DC component and one subgradient of the second DC component of the objective function. The developed method applies an Armijo-type line search procedure to find the next iteration point. It is proved that the sequence of points generated by the method converges to a critical point of the unconstrained DC optimization problem. The performance of the method is demonstrated using academic test problems with nonsmooth DC objective functions and its performance is compared with that of two general nonsmooth optimization solvers and five solvers specifically designed for unconstrained DC optimization. Computational results show that the developed method is efficient and robust for solving nonsmooth DC optimization problems. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Analysis of water quantity and quality trade-offs to iInform selective harvesting of inflows in complex water resource systems

  • Authors: Dey, Sayani , Barton, Andrew , Kandra, Harpreet , Bagirov, Adil , Wilson, Kym
  • Date: 2021
  • Type: Text , Journal article
  • Relation: Water Resources Management Vol. 35, no. 12 (2021), p. 4149-4165
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  • Description: Challenges faced by water resource systems are multi-faceted. The problem can be even more pronounced in a dry continent like Australia where the water resources can often be afflicted by high salinity and turbidity. Therefore, modern water resource systems require to appropriately manage both water quality and quantity. This study aims to illustrate the trade-offs between water quantity and quality in a reservoir, based on decisions to harvest different inflow sources. Taylors Lake of the Grampians reservoir system in Western Victoria, Australia was chosen as the case study for this research as it is sufficiently complex and includes many of the contemporary water resources challenges seen around the world. Different operational scenarios were analysed which included increasingly stringent water quality criteria before the water was harvested or otherwise allowed to by-pass the storage. The study suggests that selective harvesting of water can be an option to improve the overall and long-term water quality within a reservoir, but stringent water quality measures can lead to an associated loss of overall water quantity. This research study provides useful insight to water planners and stakeholders in similar catchment settings around the world, to identify water harvesting regimes with competing water quality constraints. © 2021, The Author(s), under exclusive licence to Springer Nature B.V. **Correction: The wrong Supplementary file was originally published with this article. The original article has been corrected https://doi.org/10.1007/s11269-021-03019-7**
  • Description: Challenges faced by water resource systems are multi-faceted. The problem can be even more pronounced in a dry continent like Australia where the water resources can often be afflicted by high salinity and turbidity. Therefore, modern water resource systems require to appropriately manage both water quality and quantity. This study aims to illustrate the trade-offs between water quantity and quality in a reservoir, based on decisions to harvest different inflow sources. Taylors Lake of the Grampians reservoir system in Western Victoria, Australia was chosen as the case study for this research as it is sufficiently complex and includes many of the contemporary water resources challenges seen around the world. Different operational scenarios were analysed which included increasingly stringent water quality criteria before the water was harvested or otherwise allowed to by-pass the storage. The study suggests that selective harvesting of water can be an option to improve the overall and long-term water quality within a reservoir, but stringent water quality measures can lead to an associated loss of overall water quantity. This research study provides useful insight to water planners and stakeholders in similar catchment settings around the world, to identify water harvesting regimes with competing water quality constraints. © 2021, The Author(s), under exclusive licence to Springer Nature B.V. **Correction: The wrong Supplementary file was originally published with this article. The original article has been corrected. 10.1007/s11269-021-03019-7**

Incremental DC optimization algorithm for large-scale clusterwise linear regression

  • Authors: Bagirov, Adil , Taheri, Sona , Cimen, Emre
  • Date: 2021
  • Type: Text , Journal article
  • Relation: Journal of Computational and Applied Mathematics Vol. 389, no. (2021), p. 1-17
  • Relation: https://purl.org/au-research/grants/arc/DP190100580
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  • Description: The objective function in the nonsmooth optimization model of the clusterwise linear regression (CLR) problem with the squared regression error is represented as a difference of two convex functions. Then using the difference of convex algorithm (DCA) approach the CLR problem is replaced by the sequence of smooth unconstrained optimization subproblems. A new algorithm based on the DCA and the incremental approach is designed to solve the CLR problem. We apply the Quasi-Newton method to solve the subproblems. The proposed algorithm is evaluated using several synthetic and real-world data sets for regression and compared with other algorithms for CLR. Results demonstrate that the DCA based algorithm is efficient for solving CLR problems with the large number of data points and in particular, outperforms other algorithms when the number of input variables is small. © 2020 Elsevier B.V.

Malware variant identification using incremental clustering

An incremental nonsmooth optimization algorithm for clustering using L1 and L∞ norms

Clusterwise support vector linear regression

  • Authors: Joki, Kaisa , Bagirov, Adil , Karmitsa, Napsu , Mäkelä, Marko , Taheri, Sona
  • Date: 2020
  • Type: Text , Journal article
  • Relation: European Journal of Operational Research Vol. 287, no. 1 (2020), p. 19-35
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  • Description: In clusterwise linear regression (CLR), the aim is to simultaneously partition data into a given number of clusters and to find regression coefficients for each cluster. In this paper, we propose a novel approach to model and solve the CLR problem. The main idea is to utilize the support vector machine (SVM) approach to model the CLR problem by using the SVM for regression to approximate each cluster. This new formulation of the CLR problem is represented as an unconstrained nonsmooth optimization problem, where we minimize a difference of two convex (DC) functions. To solve this problem, a method based on the combination of the incremental algorithm and the double bundle method for DC optimization is designed. Numerical experiments are performed to validate the reliability of the new formulation for CLR and the efficiency of the proposed method. The results show that the SVM approach is suitable for solving CLR problems, especially, when there are outliers in data. © 2020 Elsevier B.V.
  • Description: Funding details: Academy of Finland, 289500, 294002, 319274 Funding details: Turun Yliopisto Funding details: Australian Research Council, ARC, (Project no. DP190100580 ).

Cyberattack triage using incremental clustering for intrusion detection systems

  • Authors: Taheri, Sona , Bagirov, Adil , Gondal, Iqbal , Brown, Simon
  • Date: 2020
  • Type: Text , Journal article
  • Relation: International Journal of Information Security Vol. 19, no. 5 (2020), p. 597-607
  • Relation: http://purl.org/au-research/grants/arc/DP190100580
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  • Description: Intrusion detection systems (IDSs) are devices or software applications that monitor networks or systems for malicious activities and signals alerts/alarms when such activity is discovered. However, an IDS may generate many false alerts which affect its accuracy. In this paper, we develop a cyberattack triage algorithm to detect these alerts (so-called outliers). The proposed algorithm is designed using the clustering, optimization and distance-based approaches. An optimization-based incremental clustering algorithm is proposed to find clusters of different types of cyberattacks. Using a special procedure, a set of clusters is divided into two subsets: normal and stable clusters. Then, outliers are found among stable clusters using an average distance between centroids of normal clusters. The proposed algorithm is evaluated using the well-known IDS data sets—Knowledge Discovery and Data mining Cup 1999 and UNSW-NB15—and compared with some other existing algorithms. Results show that the proposed algorithm has a high detection accuracy and its false negative rate is very low. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
  • Description: This research was conducted in Internet Commerce Security Laboratory (ICSL) funded by Westpac Banking Corporation Australia. In addition, the research by Dr. Sona Taheri and A/Prof. Adil Bagirov was supported by the Australian Government through the Australian Research Council’s Discovery Projects funding scheme (DP190100580).

Discrete gradient methods

  • Authors: Bagirov, Adil , Taheri, Sona , Karmitsa, Napsu
  • Date: 2020
  • Type: Text , Book chapter
  • Relation: Numerical Nonsmooth Optimization: State of the Art Algorithms p. 621-654
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  • Description: In this chapter, the notion of a discrete gradient is introduced and it is shown that the discrete gradients can be used to approximate subdifferentials of a broad class of nonsmooth functions. Two methods based on such approximations, more specifically, the discrete gradient method (DGM) and its limited memory version (LDGB), are described. These methods are semi derivative-free methods for solving nonsmooth and, in general, nonconvex optimization problems. The performance of the methods is demonstrated using some academic test problems. © Springer Nature Switzerland AG 2020.

Final words

Introduction

  • Authors: Bagirov, Adil , Gaudioso, Manlio , Karmitsa, Napsu , Mäkelä, Marko , Taheri, Sona
  • Date: 2020
  • Type: Text , Book chapter
  • Relation: Numerical Nonsmooth Optimization: State of the Art Algorithms p. 1-16
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  • Description: Nonsmooth optimization (NSO) is among the most challenging tasks in the field of mathematical programming. It addresses optimization problems where objective and/or constraint functions have discontinuous gradients. NSO problems arise in many real life applications. Moreover, some smooth optimization techniques like different decomposition methods, dual formulations and exact penalty methods may lead us to solve NSO problems being either smaller in dimension or simpler in structure. In addition, some optimization problems may be analytically smooth but numerically nonsmooth. This is the case, for instance, with noisy input data and so-called stiff problems, which are numerically unstable and behave like nonsmooth problems. © Springer Nature Switzerland AG 2020.

Missing value imputation via clusterwise linear regression

  • Authors: Karmitsa, Napsu , Taheri, Sona , Bagirov, Adil , Makinen, Pauliina
  • Date: 2020
  • Type: Text , Journal article
  • Relation: IEEE transactions on knowledge and data engineering Vol. , no. (2020), p. 1-1
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  • Description:

    In this paper a new method of preprocessing incomplete data is introduced. The method is based on clusterwise linear regression and it combines two well-known approaches for missing value imputation: linear regression and clustering. The idea is to approximate missing values using only those data points that are somewhat similar to the incomplete data point. A similar idea is used also in clustering based imputation methods. Nevertheless, here the linear regression approach is used within each cluster to accurately predict the missing values, and this is done simultaneously to clustering. The proposed method is tested using some synthetic and real-world data sets and compared with other algorithms for missing value imputations. Numerical results demonstrate that the proposed method produces the most accurate imputations in MCAR and MAR data sets with a clear structure and the percentages of missing data no more than 25%

New gene selection algorithm using hypeboxes to improve performance of classifiers

  • Authors: Bagirov, Adil , Mardaneh, Karim
  • Date: 2020
  • Type: Text , Journal article
  • Relation: International Journal of Bioinformatics Research and Applications Vol. 16, no. 3 (2020), p. 269-289
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  • Description: The use of DNA microarray technology allows to measure the expression levels of thousands of genes in one single experiment which makes possible to apply classification techniques to classify tumours. However, the large number of genes and relatively small number of tumours in gene expression datasets may (and in some cases significantly) diminish the accuracy of many classifiers. Therefore, efficient gene selection algorithms are required to identify most informative genes or groups of genes to improve the performance of classifiers. In this paper, a new gene selection algorithm is developed using marginal hyberboxes of genes or groups of genes for each tumour type. Informative genes are defined using overlaps between hyberboxes. The results on six gene expression datasets demonstrate that the proposed algorithm is able to considerably reduce the number of genes and significantly improve the performance of classifiers. © 2020 Inderscience Enterprises Ltd.

Partial undersampling of imbalanced data for cyber threats detection

  • Authors: Moniruzzaman, Md , Bagirov, Adil , Gondal, Iqbal
  • Date: 2020
  • Type: Text , Conference proceedings , Conference paper
  • Relation: 2020 Australasian Computer Science Week Multiconference, ACSW 2020
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  • Description: Real-time detection of cyber threats is a challenging task in cyber security. With the advancement of technology and ease of access to the internet, more and more individuals and organizations are becoming the target for various cyber attacks such as malware, ransomware, spyware. The target of these attacks is to steal money or valuable information from the victims. Signature-based detection methods fail to keep up with the constantly evolving new threats. Machine learning based detection has drawn more attention of researchers due to its capability of detecting new and modified attacks based on previous attack's behaviour. The number of malicious activities in a certain domain is significantly low compared to the number of normal activities. Therefore, cyber threats detection data sets are imbalanced. In this paper, we proposed a partial undersampling method to deal with imbalanced data for detecting cyber threats. © 2020 ACM.
  • Description: E1

Prediction of gold-bearing localised occurrences from limited exploration data

  • Authors: Grigoryev, Igor , Bagirov, Adil , Tuck, Michael
  • Date: 2020
  • Type: Text , Journal article
  • Relation: International Journal of Computational Science and Engineering Vol. 21, no. 4 (2020), p. 503-512
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  • Description: Inaccurate drill-core assay interpretation in the exploration stage presents challenges to long-term profit of gold mining operations. Predicting the gold distribution within a deposit as precisely as possible is one of the most important aspects of the methodologies employed to avoid problems associated with financial expectations. The prediction of the variability of gold using a very limited number of drill-core samples is a very challenging problem. This is often intractable using traditional statistical tools where with less than complete spatial information certain assumptions are made about gold distribution and mineralisation. The decision-support predictive modelling methodology based on the unsupervised machine learning technique, presented in this paper avoids some of the restrictive limitations of traditional methods. It identifies promising exploration targets missed during exploration and recovers hidden spatial and physical characteristics of the explored deposit using information directly from drill hole database. Copyright © 2020 Inderscience Enterprises Ltd.

The non-smooth and bi-objective team orienteering problem with soft constraints

  • Authors: Estrada-Moreno, Alejandro , Ferrer, Albert , Juan, Angel , Panadero, Javier , Bagirov, Adil
  • Date: 2020
  • Type: Text , Journal article
  • Relation: Mathematics Vol. 8, no. 9 (2020), p.
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  • Description: In the classical team orienteering problem (TOP), a fixed fleet of vehicles is employed, each of them with a limited driving range. The manager has to decide about the subset of customers to visit, as well as the visiting order (routes). Each customer offers a different reward, which is gathered the first time that it is visited. The goal is then to maximize the total reward collected without exceeding the driving range constraint. This paper analyzes a more realistic version of the TOP in which the driving range limitation is considered as a soft constraint: every time that this range is exceeded, a penalty cost is triggered. This cost is modeled as a piece-wise function, which depends on factors such as the distance of the vehicle to the destination depot. As a result, the traditional reward-maximization objective becomes a non-smooth function. In addition, a second objective, regarding the design of balanced routing plans, is considered as well. A mathematical model for this non-smooth and bi-objective TOP is provided, and a biased-randomized algorithm is proposed as a solving approach. © 2020 by the authors.
  • Description: This work has been partially supported by the Spanish Ministry of Economy and Competitiveness & FEDER (SEV-2015-0563), the Spanish Ministry of Science (PID2019-111100RB-C21, RED2018-102642-T), and the Erasmus+ Program (2019-I-ES01-KA103-062602).

A comparative study of unsupervised classification algorithms in multi-sized data sets

  • Authors: Quddus, Syed , Bagirov, Adil
  • Date: 2019
  • Type: Text , Conference paper
  • Relation: 2nd Artificial Intelligence and Cloud Computing Conference, AICCC 2019, Kobe, 21-23 December 2019 p. 26-32
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  • Description: The ability to mine and extract useful information automatically, from large data sets, is a common concern for organizations, for the last few decades. Over the internet, data is vastly increasing gradually and consequently the capacity to collect and store very large data is significantly increasing. Existing clustering algorithms are not always efficient and accurate in solving clustering problems for large data sets. However, the development of accurate and fast data classification algorithms for very large scale data sets is still a challenge. In this paper, we present an overview of various algorithms and approaches which are recently being used for Clustering of large data and E-document. In this paper, a comparative study of the performance of various algorithms: the global kmeans algorithm (GKM), the multi-start modified global kmeans algorithm (MS-MGKM), the multi-start kmeans algorithm (MS-KM), the difference of convex clustering algorithm (DCA), the clustering algorithm based on the difference of convex representation of the cluster function and non-smooth optimization (DC-L2), is carried out using C++. © 2019 ACM.

A difference of convex optimization algorithm for piecewise linear regression

A sharp augmented Lagrangian-based method in constrained non-convex optimization

  • Authors: Bagirov, Adil , Ozturk, Gurkan , Kasimbeyli, Refail
  • Date: 2019
  • Type: Text , Journal article
  • Relation: Optimization Methods and Software Vol. 34, no. 3 (2019), p. 462-488
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  • Description: In this paper, a novel sharp Augmented Lagrangian-based global optimization method is developed for solving constrained non-convex optimization problems. The algorithm consists of outer and inner loops. At each inner iteration, the discrete gradient method is applied to minimize the sharp augmented Lagrangian function. Depending on the solution found the algorithm stops or updates the dual variables in the inner loop, or updates the upper or lower bounds by going to the outer loop. The convergence results for the proposed method are presented. The performance of the method is demonstrated using a wide range of nonlinear smooth and non-smooth constrained optimization test problems from the literature.