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Nonsmooth optimization based algorithms in cluster analysis

- Bagirov, Adil, Mohebi, Ehsan

  • Authors: Bagirov, Adil , Mohebi, Ehsan
  • Date: 2015
  • Type: Text , Book chapter
  • Relation: Partitional Clustering Algorithms p. 99-146
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  • Description: Cluster analysis is an important task in data mining. It deals with the problem of organization of a collection of objects into clusters based on a similarity measure. Various distance functions can be used to define the similarity measure. Cluster analysis problems with the similarity measure defined by the squared Euclidean distance, which is also known as the minimum sum-of-squares clustering, has been studied extensively over the last five decades. L1 and L1 norms have attracted less attention. In this chapter, we consider a nonsmooth nonconvex optimization formulation of the cluster analysis problems. This formulation allows one to easily apply similarity measures defined using different distance functions. Moreover, an efficient incremental algorithm can be designed based on this formulation to solve the clustering problems. We develop incremental algorithms for solving clustering problems where the similarity measure is defined using the L1; L2 and L1 norms. We also consider different algorithms for solving nonsmooth nonconvex optimization problems in cluster analysis. The proposed algorithms are tested using several real world data sets and compared with other similar algorithms.
  • Description: Cluster analysis is an important task in data mining. It deals with the problem of organization of a collection of objects into clusters based on a similarity measure. Various distance functions can be used to define the similarity measure. Cluster analysis problems with the similarity measure defined by the squared Euclidean distance, which is also known as the minimum sum-of-squares clustering, has been studied extensively over the last five decades. However, problems with the L

Sensitivity of algorithm parameters and objective function scaling in multi-objective optimisation of water distribution systems

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

  • Authors: Mala-Jetmarova, Helena , Barton, Andrew , Bagirov, Adil
  • Date: 2015
  • Type: Text , Journal article
  • Relation: Journal of Hydroinformatics Vol. 17, no. 6 (2015), p. 891-916
  • Relation: http://purl.org/au-research/grants/arc/LP0990908
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  • Description: This paper presents an extensive analysis of the sensitivity of multi-objective algorithm parameters and objective function scaling tested on a large number of parameter setting combinations for a water distribution system optimisation problem. The optimisation model comprises two operational objectives minimised concurrently, the pump energy costs and deviations of constituent concentrations as a water quality measure. This optimisation model is applied to a regional nondrinking water distribution system, and solved using the optimisation software GANetXL incorporating the NSGA-II linked with the network analysis software EPANet. The sensitivity analysis employs a set of performance metrics, which were designed to capture the overall quality of the computed Pareto fronts. The performance and sensitivity of NSGA-II parameters using those metrics is evaluated. The results demonstrate that NSGA-II is sensitive to different parameter settings, and unlike in the single-objective problems, a range of parameter setting combinations appears to be required to reach a Pareto front of optimal solutions. Additionally, inadequately scaled objective functions cause the NSGA-II bias towards the second objective. Lastly, the methodology for performance and sensitivity analysis may be used for calibration of algorithm parameters.

Solving DC programs using the cutting angle method

- Ferrer, Albert, Bagirov, Adil, Beliakov, Gleb

A convolutional recursive modified Self Organizing Map for handwritten digits recognition

- Mohebi, Ehsan, Bagirov, Adil

  • Authors: Mohebi, Ehsan , Bagirov, Adil
  • Date: 2014
  • Type: Text , Journal article
  • Relation: Neural Networks Vol. 60, no. (2014), p. 104-118
  • Relation: http://purl.org/au-research/grants/arc/DP140103213
  • Full Text: false
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  • Description: It is well known that the handwritten digits recognition is a challenging problem. Different classification algorithms have been applied to solve it. Among them, the Self Organizing Maps (SOM) produced promising results. In this paper, first we introduce a Modified SOM for the vector quantization problem with improved initialization process and topology preservation. Then we develop a Convolutional Recursive Modified SOM and apply it to the problem of handwritten digits recognition. The computational results obtained using the well known MNIST dataset demonstrate the superiority of the proposed algorithm over the existing SOM-based algorithms.

Aggregate codifferential method for nonsmooth DC optimization

- Tor, Ali, Bagirov, Adil, Karasozen, Bulent

  • Authors: Tor, Ali , Bagirov, Adil , Karasozen, Bulent
  • Date: 2014
  • Type: Text , Journal article
  • Relation: Journal of Computational and Applied Mathematics Vol. 259, no. Part B (2014), p. 851-867
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  • Description: A new algorithm is developed based on the concept of codifferential for minimizing the difference of convex nonsmooth functions. Since the computation of the whole codifferential is not always possible, we use a fixed number of elements from the codifferential to compute the search directions. The convergence of the proposed algorithm is proved. The efficiency of the algorithm is demonstrated by comparing it with the subgradient, the truncated codifferential and the proximal bundle methods using nonsmooth optimization test problems.

An algorithm for clusterwise linear regression based on smoothing techniques

- Bagirov, Adil, Ugon, Julien, Mirzayeva, Hijran

  • Authors: Bagirov, Adil , Ugon, Julien , Mirzayeva, Hijran
  • Date: 2014
  • Type: Text , Journal article
  • Relation: Optimization Letters Vol. 9, no. 2 (2014), p. 375-390
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  • Description: We propose an algorithm based on an incremental approach and smoothing techniques to solve clusterwise linear regression (CLR) problems. This algorithm incrementally divides the whole data set into groups which can be easily approximated by one linear regression function. A special procedure is introduced to generate an initial solution for solving global optimization problems at each iteration of the incremental algorithm. Such an approach allows one to find global or approximate global solutions to the CLR problems. The algorithm is tested using several data sets for regression analysis and compared with the multistart and incremental Spath algorithms.

CR-Modified SOM to the problem of handwritten digits recognition

- Mohebi, Ehsan, Bagirov, Adil

Introduction to Nonsmooth Optimization : Theory, practice and software

- Bagirov, Adil, Karmitsa, Napsu, Makela, Marko

  • Authors: Bagirov, Adil , Karmitsa, Napsu , Makela, Marko
  • Date: 2014
  • Type: Text , Book
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  • Description: This book is the first easy-to-read text on nonsmooth optimization (NSO, not necessarily differentiable optimization). Soving these kinds of problems plays a critical role in many industrial applications and real-world modeling systems, for example in the context of image denoising, optimal control, neural network training, data mining, ecomonics, and computational chemistry and physics. The book covers both the theory and the numerical methods used in NSO, and provides an overview of different problems arising in the field. It is organized into three parts: 1. convex and nonconvex analysis and the theory of NSO; 2. test problems and practical applications; 3. a guide to NSO software. The book is ideal for anyone teaching or attending NSO courses. As an accessible introduction to the field, it is also well suited as an independent learning guide for practitioners already familiar with the basics of optimization.

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

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

Piecewise linear classifiers based on nonsmooth optimization approaches

- Bagirov, Adil, Kasimbeyli, Refail, Ozturk, Gurkan, Ugon, Julien

  • Authors: Bagirov, Adil , Kasimbeyli, Refail , Ozturk, Gurkan , Ugon, Julien
  • Date: 2014
  • Type: Text , Book chapter
  • Relation: Optimization in Science and Engineering p. 1-32
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  • Description: Nonsmooth optimization provides efficient algorithms for solving many machine learning problems. In particular, nonsmooth optimization approaches to supervised data classification problems lead to the design of very efficient algorithms for their solution. In this chapter, we demonstrate how nonsmooth optimization algorithms can be applied to design efficient piecewise linear classifiers for supervised data classification problems. Such classifiers are developed using a max–min and a polyhedral conic separabilities as well as an incremental approach. We report results of numerical experiments and compare the piecewise linear classifiers with a number of other mainstream classifiers.

Preface of the special issue OR: Connecting sciences supported by global optimization related to the 25th European conference on operational research (EURO XXV 2012)

- Bagirov, Adil, Miettinen, Kaisa, Weber, Gerhard-Wilhelm

A new modification of Kohonen neural network for VQ and clustering problems

- Mohebi, Ehsan, Bagirov, Adil

  • Authors: Mohebi, Ehsan , Bagirov, Adil
  • Date: 2013
  • Type: Text , Conference paper
  • Relation: Proceedings of the 11-th Australasian Data Mining Conference (AusDM'13) Vol. 146, p. 81-88
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  • Description: Vector Quantization (VQ) and Clustering are significantly important in the field of data mining and pattern recognition. The Self Organizing Maps has been widely used for clustering and topology visualization. The topology of the SOM and its initial neurons play an important role in the convergence of the Kohonen neural network. In this paper, in order to improve the convergence of the SOM we introduce an algorithm based on the split and merging of clusters to initialize neurons. We also introduce a topology based on this initialization to optimize the vector quantization error. Such an approach allows one to find global or near global solution to the vector quantization and consequently clustering problem. The numerical results on 4 small to large real-world data sets are reported to demonstrate the performance of the proposed algorithm.

An algorithm for minimization of pumping costs in water distribution systems using a novel approach to pump scheduling

- Bagirov, Adil, Barton, Andrew, Mala-Jetmarova, Helena, Al Nuaimat, Alia, Ahmed, S. T., Sultanova, Nargiz, Yearwood, John

  • Authors: Bagirov, Adil , Barton, Andrew , Mala-Jetmarova, Helena , Al Nuaimat, Alia , Ahmed, S. T. , Sultanova, Nargiz , Yearwood, John
  • Date: 2013
  • Type: Text , Journal article
  • Relation: Mathematical and Computer Modelling Vol. 57, no. 3-4 (2013), p. 873-886
  • Relation: http://purl.org/au-research/grants/arc/LP0990908
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  • Description: The operation of a water distribution system is a complex task which involves scheduling of pumps, regulating water levels of storages, and providing satisfactory water quality to customers at required flow and pressure. Pump scheduling is one of the most important tasks of the operation of a water distribution system as it represents the major part of its operating costs. In this paper, a novel approach for modeling of explicit pump scheduling to minimize energy consumption by pumps is introduced which uses the pump start/end run times as continuous variables, and binary integer variables to describe the pump status at the beginning of the scheduling period. This is different from other approaches where binary integer variables for each hour are typically used, which is considered very impractical from an operational perspective. The problem is formulated as a mixed integer nonlinear programming problem, and a new algorithm is developed for its solution. This algorithm is based on the combination of the grid search with the Hooke-Jeeves pattern search method. The performance of the algorithm is evaluated using literature test problems applying the hydraulic simulation model EPANet. © 2012 Elsevier Ltd.
  • Description: 2003010583

Capped K-NN Editing in definition lacking environments

- Stranieri, Andrew, Yatsko, Andrew, Golden, Isaac, Mammadov, Musa, Bagirov, Adil

  • Authors: Stranieri, Andrew , Yatsko, Andrew , Golden, Isaac , Mammadov, Musa , Bagirov, Adil
  • Date: 2013
  • Type: Text , Journal article
  • Relation: Journal of Pattern Recognition Research Vol. 8, no. 1 (2013), p. 39-58
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  • Description: While any input may be contributing, imprecise specification of class of data subdivided into classes identifies as rather common a source of noise. The misrepresentation may be characteristic of the data or be caused by forcing of a regression problem into the classification type. Consideration is given to examples of this nature, and an alternative is proposed. In the main part, the approach is based on a well-known technique of data treatment for noise using k-NN. The paper advances an editing technique designed around idea of variable number of authenticating instances. Test runs performed on publicly available and proprietary data demonstrate high retention ability of the new procedure without loss of classification accuracy. Noise reduction methods in a broader classification context are extensively surveyed.

Hyperbolic smoothing function method for minimax problems

- Bagirov, Adil, Al Nuaimat, Alia, Sultanova, Nargiz

  • Authors: Bagirov, Adil , Al Nuaimat, Alia , Sultanova, Nargiz
  • Date: 2013
  • Type: Text , Journal article
  • Relation: Optimization Vol. 62, no. 6 (2013), p. 759-782
  • Full Text: false
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  • Description: In this article, an approach for solving finite minimax problems is proposed. This approach is based on the use of hyperbolic smoothing functions. In order to apply the hyperbolic smoothing we reformulate the objective function in the minimax problem and study the relationship between the original minimax and reformulated problems. We also study main properties of the hyperbolic smoothing function. Based on these results an algorithm for solving the finite minimax problem is proposed and this algorithm is implemented in general algebraic modelling system. We present preliminary results of numerical experiments with well-known nonsmooth optimization test problems. We also compare the proposed algorithm with the algorithm that uses the exponential smoothing function as well as with the algorithm based on nonlinear programming reformulation of the finite minimax problem. © 2013 Copyright Taylor and Francis Group, LLC.
  • Description: 2003011099

Nonsmooth nonconvex optimization approach to clusterwise linear regression problems

- Bagirov, Adil, Ugon, Julien, Mirzayeva, Hijran

  • Authors: Bagirov, Adil , Ugon, Julien , Mirzayeva, Hijran
  • Date: 2013
  • Type: Text , Journal article
  • Relation: European Journal of Operational Research Vol. 229, no. 1 (2013), p. 132-142
  • Full Text: false
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  • Description: Clusterwise regression consists of finding a number of regression functions each approximating a subset of the data. In this paper, a new approach for solving the clusterwise linear regression problems is proposed based on a nonsmooth nonconvex formulation. We present an algorithm for minimizing this nonsmooth nonconvex function. This algorithm incrementally divides the whole data set into groups which can be easily approximated by one linear regression function. A special procedure is introduced to generate a good starting point for solving global optimization problems at each iteration of the incremental algorithm. Such an approach allows one to find global or near global solution to the problem when the data sets are sufficiently dense. The algorithm is compared with the multistart Späth algorithm on several publicly available data sets for regression analysis. © 2013 Elsevier B.V. All rights reserved.
  • Description: 2003011018

Pumping costs and water quality in the battlefield of optimal operation of water distribution networks

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

Subgradient and bundle methods for nonsmooth optimization

- Makela, Marko, Karmitsa, Napsu, Bagirov, Adil

  • Authors: Makela, Marko , Karmitsa, Napsu , Bagirov, Adil
  • Date: 2013
  • Type: Text , Book chapter
  • Relation: Numerical methods for differential equations, optimization, and technological problems p.
  • Full Text: false
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  • Description: The nonsmooth optimization methods can mainly be divided into two groups: subgradient and bundle methods. Usually, when developing new algorithms and testing them, the comparison is made between similar kinds of methods. The goal of this work is to test and compare different bundle and subgradient methods as well as some hybrids of these two and/or some others. The test set included a large amount of different unconstrained nonsmooth minimization problems, e.g., convex and nonconvex problems, piecewise linear and quadratic problems, and problems with different sizes. Rather than foreground some method over the others, our aim is to get some insight on which method is suitable for certain types of problems.

A novel approach to optimal pump scheduling in water distribution systems

- Bagirov, Adil, Barton, Andrew, Mala-Jetmarova, Helena, Al Nuaimat, Alia, Ahmed, S. T., Sultanova, Nargiz, Yearwood, John

  • Authors: Bagirov, Adil , Barton, Andrew , Mala-Jetmarova, Helena , Al Nuaimat, Alia , Ahmed, S. T. , Sultanova, Nargiz , Yearwood, John
  • Date: 2012
  • Type: Text , Conference paper
  • Relation: 14th Water Distribution Systems Analysis Conference 2012, WDSA 2012 Vol. 1; Adelaide, Australia; 24th-27th September; p. 618-631
  • Relation: http://purl.org/au-research/grants/arc/LP0990908
  • Full Text: false
  • Reviewed:
  • Description: The operation of a water distribution system is a complex task which involves scheduling of pumps, regulating water levels of storages, and providing satisfactory water quality to customers at required flow and pressure. Pump scheduling is one of the most important tasks of the operation of a water distribution system as it represents the major part of its operating costs. In this paper, a novel approach for modeling of pump scheduling to minimize energy consumption by pumps is introduced which uses pump's start/end run times as continuous variables. This is different from other approaches where binary integer variables for each hour are typically used which is considered very impractical from an operational perspective. The problem is formulated as a nonlinear programming problem and a new algorithm is developed for its solution. This algorithm is based on the combination of the grid search with the Hooke-Jeeves pattern search method. The performance of the algorithm is evaluated using literature test problems applying the hydraulic simulation model EPANet.
  • Description: E1

Application of optimisation-based data mining techniques to medical data sets: A comparative analysis

- Dzalilov, Zari, Bagirov, Adil, Mammadov, Musa

  • Authors: Dzalilov, Zari , Bagirov, Adil , Mammadov, Musa
  • Date: 2012
  • Type: Text , Conference paper
  • Relation: IMMM 2102: The Second International Conference on Advances in Information Mining and Management p. 41-46
  • Full Text: false
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  • Description: Abstract - Computational methods have become an important tool in the analysis of medical data sets. In this paper, we apply three optimisation-based data mining methods to the following data sets: (i) a cystic fibrosis data set and (ii) a tobacco control data set. Three algorithms used in the analysis of these data sets include: the modified linear least square fit, an optimization based heuristic algorithm for feature selection and an optimization based clustering algorithm. All these methods explore the relationship between features and classes, with the aim of determining contribution of specific features to the class outcome. However, the three algorithms are based on completely different approaches. We apply these methods to solve feature selection and classification problems. We also present comparative analysis of the algorithms using computational results. Results obtained confirm that these algorithms may be effectively applied to the analysis of other (bio)medical data sets