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
- 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. 693-694
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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.
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
- Authors: Bagirov, Adil , Taheri, Sona , Asadi, Soodabeh
- Date: 2019
- Type: Text , Journal article
- Relation: Journal of Industrial and Management Optimization Vol. 15, no. 2 (2019), p. 909-932
- Relation: http://purl.org/au-research/grants/arc/DP140103213
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- Description: The problem of finding a continuous piecewise linear function approximating a regression function is considered. This problem is formulated as a nonconvex nonsmooth optimization problem where the objective function is represented as a difference of convex (DC) functions. Subdifferentials of DC components are computed and an algorithm is designed based on these subdifferentials to find piecewise linear functions. The algorithm is tested using some synthetic and real world data sets and compared with other regression algorithms.
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.
A simulated annealing-based maximum-margin clustering algorithm
- 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.
An approximate ADMM for solving linearly constrained nonsmooth optimization problems with two blocks of variables
- Authors: Bagirov, Adil , Taheri, Sona , Bai, Fusheng , Wu, Zhiyou
- Date: 2019
- Type: Text , Book chapter
- Relation: Nonsmooth Optimization and Its Applications (part of the International Series of Numerical Mathematics book series) Chapter 2 p. 17-44
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- Description: Nonsmooth convex optimization problems with two blocks of variables subject to linear constraints are considered. A new version of the alternating direction method of multipliers is developed for solving these problems. In this method the subproblems are solved approximately. The convergence of the method is studied. New test problems are designed and used to verify the efficiency of the proposed method and to compare it with two versions of the proximal bundle method.
Multi-source cyber-attacks detection using machine learning
- 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
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- 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
A comparative assessment of models to predict monthly rainfall in Australia
- Authors: Bagirov, Adil , Mahmood, Arshad
- Date: 2018
- Type: Text , Journal article
- Relation: Water Resources Management Vol. 32, no. 5 (2018), p. 1777-1794
- Relation: http://purl.org/au-research/grants/arc/DP140103213
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- Description: Accurate rainfall prediction is a challenging task. It is especially challenging in Australia where the climate is highly variable. Australia’s climatic zones range from high rainfall tropical regions in the north to the driest desert region in the interior. The performance of prediction models may vary depending on climatic conditions. It is, therefore, important to assess and compare the performance of these models in different climatic zones. This paper examines the performance of data driven models such as the support vector machines for regression, the multiple linear regression, the k-nearest neighbors and the artificial neural networks for monthly rainfall prediction in Australia depending on climatic conditions. Rainfall data with five meteorological variables over the period of 1970–2014 from 24 geographically diverse weather stations are used for this purpose. The prediction performance of each model was evaluated by comparing observed and predicted rainfall using various measures for prediction accuracy. © 2018, Springer Science+Business Media B.V., part of Springer Nature.
A server side solution for detecting webInject : A machine learning approach
- Authors: Moniruzzaman, Md , Bagirov, Adil , Gondal, Iqbal , Brown, Simon
- Date: 2018
- Type: Text , Conference proceedings , Conference paper
- Relation: 22nd Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2018; Melbourne, Australia; 3rd June 2018; published in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) Vol. 11154 LNAI, p. 162-167
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- Description: With the advancement of client-side on the fly web content generation techniques, it becomes easier for attackers to modify the content of a website dynamically and gain access to valuable information. A majority portion of online attacks is now done by WebInject. The end users are not always skilled enough to differentiate between injected content and actual contents of a webpage. Some of the existing solutions are designed for client side and all the users have to install it in their system, which is a challenging task. In addition, various platforms and tools are used by individuals, so different solutions needed to be designed. Existing server side solution often focuses on sanitizing and filtering the inputs. It will fail to detect obfuscated and hidden scripts. In this paper, we propose a server side solution using a machine learning approach to detect WebInject in banking websites. Unlike other techniques, our method collects features of a Document Object Model (DOM) and classifies it with the help of a pre-trained model.
Clustering in large data sets with the limited memory bundle method
- Authors: Karmitsa, Napsu , Bagirov, Adil , Taheri, Sona
- Date: 2018
- Type: Text , Journal article
- Relation: Pattern Recognition Vol. 83, no. (2018), p. 245-259
- Relation: http://purl.org/au-research/grants/arc/DP140103213
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- Description: The aim of this paper is to design an algorithm based on nonsmooth optimization techniques to solve the minimum sum-of-squares clustering problems in very large data sets. First, the clustering problem is formulated as a nonsmooth optimization problem. Then the limited memory bundle method [Haarala et al., 2007] is modified and combined with an incremental approach to design a new clustering algorithm. The algorithm is evaluated using real world data sets with both the large number of attributes and the large number of data points. It is also compared with some other optimization based clustering algorithms. The numerical results demonstrate the efficiency of the proposed algorithm for clustering in very large data sets.
Double bundle method for finding clarke stationary points in nonsmooth dc programming
- 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.
Minimizing nonsmooth DC functions via successive DC piecewise-affine approximations
- Authors: Gaudioso, Manlio , Giallombardo, Giovanni , Miglionico, Giovanna , Bagirov, Adil
- Date: 2018
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 71, no. 1 (2018), p. 37-55
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- Description: We introduce a proximal bundle method for the numerical minimization of a nonsmooth difference-of-convex (DC) function. Exploiting some classic ideas coming from cutting-plane approaches for the convex case, we iteratively build two separate piecewise-affine approximations of the component functions, grouping the corresponding information in two separate bundles. In the bundle of the first component, only information related to points close to the current iterate are maintained, while the second bundle only refers to a global model of the corresponding component function. We combine the two convex piecewise-affine approximations, and generate a DC piecewise-affine model, which can also be seen as the pointwise maximum of several concave piecewise-affine functions. Such a nonconvex model is locally approximated by means of an auxiliary quadratic program, whose solution is used to certify approximate criticality or to generate a descent search-direction, along with a predicted reduction, that is next explored in a line-search setting. To improve the approximation properties at points that are far from the current iterate a supplementary quadratic program is also introduced to generate an alternative more promising search-direction. We discuss the main convergence issues of the line-search based proximal bundle method, and provide computational results on a set of academic benchmark test problems. © 2017, Springer Science+Business Media, LLC.