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A novel optimization approach towards improving separability of clusters

- Bagirov, Adil, Hoseini-Monjezi, Najmeh, Taheri, Sona

  • Authors: Bagirov, Adil , Hoseini-Monjezi, Najmeh , Taheri, Sona
  • Date: 2023
  • Type: Text , Journal article
  • Relation: Computers and Operations Research Vol. 152, no. (2023), p.
  • Relation: http://purl.org/au-research/grants/arc/DP190100580
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  • Description: The objective functions in optimization models of the sum-of-squares clustering problem reflect intra-cluster similarity and inter-cluster dissimilarities and in general, optimal values of these functions can be considered as appropriate measures for compactness of clusters. However, the use of the objective function alone may not lead to the finding of separable clusters. To address this shortcoming in existing models for clustering, we develop a new optimization model where the objective function is represented as a sum of two terms reflecting the compactness and separability of clusters. Based on this model we develop a two-phase incremental clustering algorithm. In the first phase, the clustering function is minimized to find compact clusters and in the second phase, a new model is applied to improve the separability of clusters. The Davies–Bouldin cluster validity index is applied as an additional measure to compare the compactness of clusters and silhouette coefficients are used to estimate the separability of clusters. The performance of the proposed algorithm is demonstrated and compared with that of four other algorithms using synthetic and real-world data sets. Numerical results clearly show that in comparison with other algorithms the new algorithm is able to find clusters with better separability and similar compactness. © 2022

Bundle enrichment method for nonsmooth difference of convex programming problems

- Gaudioso, Manilo, Taheri, Sona, Bagirov, Adil, Karmitsa, Napsu

  • Authors: Gaudioso, Manilo , Taheri, Sona , Bagirov, Adil , Karmitsa, Napsu
  • Date: 2023
  • Type: Text , Journal article
  • Relation: Algorithms Vol. 16, no. 8 (2023), p.
  • Relation: http://purl.org/au-research/grants/arc/DP190100580
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  • Description: The Bundle Enrichment Method (BEM-DC) is introduced for solving nonsmooth difference of convex (DC) programming problems. The novelty of the method consists of the dynamic management of the bundle. More specifically, a DC model, being the difference of two convex piecewise affine functions, is formulated. The (global) minimization of the model is tackled by solving a set of convex problems whose cardinality depends on the number of linearizations adopted to approximate the second DC component function. The new bundle management policy distributes the information coming from previous iterations to separately model the DC components of the objective function. Such a distribution is driven by the sign of linearization errors. If the displacement suggested by the model minimization provides no sufficient decrease of the objective function, then the temporary enrichment of the cutting plane approximation of just the first DC component function takes place until either the termination of the algorithm is certified or a sufficient decrease is achieved. The convergence of the BEM-DC method is studied, and computational results on a set of academic test problems with nonsmooth DC objective functions are provided. © 2023 by the authors.

Finding compact and well-separated clusters : clustering using silhouette coefficients

- Bagirov, Adil, Aliguliyev, Ramiz, Sultanova, Nargiz

  • Authors: Bagirov, Adil , Aliguliyev, Ramiz , Sultanova, Nargiz
  • Date: 2023
  • Type: Text , Journal article
  • Relation: Pattern Recognition Vol. 135, no. (2023), p.
  • Relation: http://purl.org/au-research/grants/arc/DP190100580
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  • Description: Finding compact and well-separated clusters in data sets is a challenging task. Most clustering algorithms try to minimize certain clustering objective functions. These functions usually reflect the intra-cluster similarity and inter-cluster dissimilarity. However, the use of such functions alone may not lead to the finding of well-separated and, in some cases, compact clusters. Therefore additional measures, called cluster validity indices, are used to estimate the true number of well-separated and compact clusters. Some of these indices are well-suited to be included into the optimization model of the clustering problem. Silhouette coefficients are among such indices. In this paper, a new optimization model of the clustering problem is developed where the clustering function is used as an objective and silhouette coefficients are used to formulate constraints. Then an algorithm, called CLUSCO (CLustering Using Silhouette COefficients), is designed to construct clusters incrementally. Three schemes are discussed to reduce the computational complexity of the algorithm. Its performance is evaluated using fourteen real-world data sets and compared with that of three state-of-the-art clustering algorithms. Results show that the CLUSCO is able to compute compact clusters which are significantly better separable in comparison with those obtained by other algorithms. © 2022 Elsevier Ltd

Methods and applications of clusterwise linear regression : a survey and comparison

- Long, Qiang, Bagirov, Adil, Taheri, Sona, Sultanova, Nargiz, Wu, Xue

Nonsmooth optimization-based hyperparameter-free neural networks for large-scale regression

- Karmitsa, Napsu, Taheri, Sona, Joki, Kaisa, Paasivirta, Pauliina, Defterdarovic, J., Bagirov, Adil, Mäkelä, Marko

  • Authors: Karmitsa, Napsu , Taheri, Sona , Joki, Kaisa , Paasivirta, Pauliina , Defterdarovic, J. , Bagirov, Adil , Mäkelä, Marko
  • Date: 2023
  • Type: Text , Journal article
  • Relation: Algorithms Vol. 16, no. 9 (2023), p.
  • Relation: http://purl.org/au-research/grants/arc/DP190100580
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  • Description: In this paper, a new nonsmooth optimization-based algorithm for solving large-scale regression problems is introduced. The regression problem is modeled as fully-connected feedforward neural networks with one hidden layer, piecewise linear activation, and the (Formula presented.) -loss functions. A modified version of the limited memory bundle method is applied to minimize this nonsmooth objective. In addition, a novel constructive approach for automated determination of the proper number of hidden nodes is developed. Finally, large real-world data sets are used to evaluate the proposed algorithm and to compare it with some state-of-the-art neural network algorithms for regression. The results demonstrate the superiority of the proposed algorithm as a predictive tool in most data sets used in numerical experiments. © 2023 by the authors.

Nonsmooth optimization-based model and algorithm for semisupervised clustering

- Bagirov, Adil, Taheri, Sona, Bai, Fusheng, Zheng, Fangying

  • Authors: Bagirov, Adil , Taheri, Sona , Bai, Fusheng , Zheng, Fangying
  • Date: 2023
  • Type: Text , Journal article
  • Relation: IEEE Transactions on Neural Networks and Learning Systems Vol. 34, no. 9 (2023), p. 5517-5530
  • Relation: http://purl.org/au-research/grants/arc/DP190100580
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  • Description: Using a nonconvex nonsmooth optimization approach, we introduce a model for semisupervised clustering (SSC) with pairwise constraints. In this model, the objective function is represented as a sum of three terms: the first term reflects the clustering error for unlabeled data points, the second term expresses the error for data points with must-link (ML) constraints, and the third term represents the error for data points with cannot-link (CL) constraints. This function is nonconvex and nonsmooth. To find its optimal solutions, we introduce an adaptive SSC (A-SSC) algorithm. This algorithm is based on the combination of the nonsmooth optimization method and an incremental approach, which involves the auxiliary SSC problem. The algorithm constructs clusters incrementally starting from one cluster and gradually adding one cluster center at each iteration. The solutions to the auxiliary SSC problem are utilized as starting points for solving the nonconvex SSC problem. The discrete gradient method (DGM) of nonsmooth optimization is applied to solve the underlying nonsmooth optimization problems. This method does not require subgradient evaluations and uses only function values. The performance of the A-SSC algorithm is evaluated and compared with four benchmarking SSC algorithms on one synthetic and 12 real-world datasets. Results demonstrate that the proposed algorithm outperforms the other four algorithms in identifying compact and well-separated clusters while satisfying most constraints. © 2021 IEEE.

SMGKM : an efficient incremental algorithm for clustering document collections

- Bagirov, Adil, Seifollahi, Sattar, Piccardi, Massimo, Zare Borzeshi, Ehsan, Kruger, Bernie

High activity and high functional connectivity are mutually exclusive in resting state zebrafish and human brains

- Zarei, Mahdi, Xie, Dan, Jiang, Fei, Bagirov, Adil, Huang, Bo, Raj, Ashish, Nagarajan, Srikantan, Guo, Su

  • Authors: Zarei, Mahdi , Xie, Dan , Jiang, Fei , Bagirov, Adil , Huang, Bo , Raj, Ashish , Nagarajan, Srikantan , Guo, Su
  • Date: 2022
  • Type: Text , Journal article
  • Relation: BMC Biology Vol. 20, no. 1 (2022), p. 84-84
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  • Description: The structural connectivity of neurons in the brain allows active neurons to impact the physiology of target neuron types with which they are functionally connected. While the structural connectome is at the basis of functional connectome, it is the functional connectivity measured through correlations between time series of individual neurophysiological events that underlies behavioral and mental states. However, in light of the diverse neuronal cell types populating the brain and their unique connectivity properties, both neuronal activity and functional connectivity are heterogeneous across the brain, and the nature of their relationship is not clear. Here, we employ brain-wide calcium imaging at cellular resolution in larval zebrafish to understand the principles of resting state functional connectivity. We recorded the spontaneous activity of >12,000 neurons in the awake resting state forebrain. By classifying their activity (i.e., variances of ΔF/F across time) and functional connectivity into three levels (high, medium, low), we find that highly active neurons have low functional connections and highly connected neurons are of low activity. This finding holds true when neuronal activity and functional connectivity data are classified into five instead of three levels, and in whole brain spontaneous activity datasets. Moreover, such activity-connectivity relationship is not observed in randomly shuffled, noise-added, or simulated datasets, suggesting that it reflects an intrinsic brain network property. Intriguingly, deploying the same analytical tools on functional magnetic resonance imaging (fMRI) data from the resting state human brain, we uncover a similar relationship between activity (signal variance over time) and functional connectivity, that is, regions of high activity are non-overlapping with those of high connectivity. We found a mutually exclusive relationship between high activity (signal variance over time) and high functional connectivity of neurons in zebrafish and human brains. These findings reveal a previously unknown and evolutionarily conserved brain organizational principle, which has implications for understanding disease states and designing artificial neuronal networks.

Limited Memory Bundle Method for Clusterwise Linear Regression

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

  • 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
  • Relation: http://purl.org/au-research/grants/arc/DP190100580
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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.

Missing value imputation via clusterwise linear regression

- Karmitsa, Napsu, Taheri, Sona, Bagirov, Adil, Makinen, Pauliina

  • Authors: Karmitsa, Napsu , Taheri, Sona , Bagirov, Adil , Makinen, Pauliina
  • Date: 2022
  • Type: Text , Journal article
  • Relation: IEEE transactions on knowledge and data engineering Vol. 34, no. 4 (2020), p. 1889-1901
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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%

Robust piecewise linear L 1-regression via nonsmooth DC optimization

- Bagirov, Adil, Taheri, Sona, Karmitsa, Napsu, Sultanova, Nargiz, Asadi, Soodabeh

  • Authors: Bagirov, Adil , Taheri, Sona , Karmitsa, Napsu , Sultanova, Nargiz , Asadi, Soodabeh
  • Date: 2022
  • Type: Text , Journal article
  • Relation: Optimization Methods and Software Vol. 37, no. 4 (2022), p. 1289-1309
  • Relation: http://purl.org/au-research/grants/arc/DP190100580
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  • Description: Piecewise linear (Formula presented.) -regression problem is formulated as an unconstrained difference of convex (DC) optimization problem and an algorithm for solving this problem is developed. Auxiliary problems are introduced to design an adaptive approach to generate a suitable piecewise linear regression model and starting points for solving the underlying DC optimization problems. The performance of the proposed algorithm as both approximation and prediction tool is evaluated using synthetic and real-world data sets containing outliers. It is also compared with mainstream machine learning regression algorithms using various performance measures. Results demonstrate that the new algorithm is robust to outliers and in general, provides better predictions than the other alternative regression algorithms for most data sets used in the numerical experiments. © 2020 Informa UK Limited, trading as Taylor & Francis Group.

Aggregate subgradient method for nonsmooth DC optimization

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

  • 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

- Bagirov, Adil, Hoseini Monjezi, Najmeh, Taheri, Sona

  • 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 inform selective harvesting of inflows in complex water resource systems

- Dey, Sayani, Barton, Andrew, Kandra, Harpreet, Bagirov, Adil, Wilson, Kym

  • 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 to: Analysis of Water Quantity and Quality Trade‑Offs to Inform Selective Harvesting of Inflows in Complex Water Resource Systems (Water Resources Management, (2021), 35, 12, (4149-4165), 10.1007/s11269-021-02936-x)

Incremental DC optimization algorithm for large-scale clusterwise linear regression

- Bagirov, Adil, Taheri, Sona, Cimen, Emre

  • 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

- Black, Paul, Gondal, Iqbal, Bagirov, Adil, Moniruzzaman, Md

Multi-objective optimisation to manage trade-offs in water quality and quantity of complex water resource system

- Dey, Sayani, Barton, Andrew, Bagirov, Adil, Kandra, Harpreet, Wilson, Kym

  • Authors: Dey, Sayani , Barton, Andrew , Bagirov, Adil , Kandra, Harpreet , Wilson, Kym
  • Date: 2021
  • Type: Text , Conference paper
  • Relation: Hydrology and Water Resources Symposium 2021, HWRS 2021: Digital Water: Hydrology and Water Resources Symposium 2021, Virtual online, 31 August-1 September 2021, HWRS 2021: Digital Water: Hydrology and Water Resources Symposium 2021 p. 465-480
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  • Description: Water of adequate quality and quantity is the key to health and integrity of the environment and fundamental to good water supply. Achieving water quality and quantity objectives can conflict and has become more complicated with challenges like, climate change, growing populations and changed land uses. Therefore, a multi-objective optimisation strategy is required for achieving optimal water quality and quantity outcomes from a water resources system. This study uses a multi-objective optimisation approach to illustrate the trade-offs occurring when water quantity and quality in a reservoir system are optimised. Taylors Lake, part of the Grampians Reservoir System in Western Victoria, Australia was chosen as the case study for this research as it is quite complex and includes many contemporary water resources challenges seen around the world, such as high turbidity and salinity. The objective functions are set in a way to maximise the water quantity available for supply, while minimising the deviation of quality parameters from the accepted limits. The water system is modelled using eWater Source® modelling platform, while optimisation is undertaken using NSGA-II optimisation technique. Daily time step data over a ten-year period was used in this work. Various optimisation runs were performed with different population sizes and generations to seek out the best trade-off curve. The optimisation results indicate trade-offs between salinity, turbidity, and quantity. Key findings for this case study show that through optimisation, stored water never exceeded 19,000 ML even though the storage capacity was 27,000 ML indicating a significant loss of water to improve quality, or alternatively, a potential asset re-design opportunity.

Subgradient smoothing method for nonsmooth nonconvex optimization

- Bagirov, Adil, Sultanova, N., Taheri, S., Ozturk, G.

  • Authors: Bagirov, Adil , Sultanova, N. , Taheri, S. , Ozturk, G.
  • Date: 2021
  • Type: Text , Conference paper
  • Relation: 5th International Conference on Numerical Analysis and Optimization: Theory, Methods, Applications and Technology Transfer, NAOV, Muscan, 6-9 January 2020 Vol. 354, p. 57-79
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  • Description: In this chapter an unconstrained nonsmooth nonconvex optimization problem is considered and a method for solving this problem is developed. In this method the subproblem for finding search directions is reduced to the unconstrained minimization of a smooth function. This is achieved by using subgradients computed in some neighborhood of a current iteration point and by formulating the search direction finding problem to the minimization of the convex piecewise linear function over the unit ball. The hyperbolic smoothing technique is applied to approximate the minimization problem by a sequence of smooth problems. The convergence of the proposed method is studied and its performance is evaluated using a set of nonsmooth optimization academic test problems. In addition, the method is implemented in GAMS and numerical results using different solvers from GAMS are reported. The proposed method is compared with a number of nonsmooth optimization methods. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

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

- Ordin, Burak, Bagirov, Adil, Mohebi, Ehsam

Bundle methods for nonsmooth DC optimization

- Joki, Kaisa, Bagirov, Adil

  • Authors: Joki, Kaisa , Bagirov, Adil
  • Date: 2020
  • Type: Text , Book chapter
  • Relation: Numerical Nonsmooth Optimization: State of the Art Algorithms Chapter 8 p. 263-296
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  • Description: This chapter is devoted to algorithms for solving nonsmooth unconstrained difference of convex optimization problems. Different types of stationarity conditions are discussed and the relationship between sets of different stationary points (critical, Clarke stationary and inf-stationary) is established. Bundle methods are developed based on a nonconvex piecewise linear model of the objective function and the convergence of these methods is studied. Numerical results are presented to demonstrate the performance of the methods. © Springer Nature Switzerland AG 2020.