Cluster analysis of a tobacco control data set
- Authors: Dzalilov, Zari , Bagirov, Adil
- Date: 2010
- Type: Text , Journal article
- Relation: International Journal of Lean Thinking Vol. 1, no. 2 (2010), p.
- Full Text: false
- Reviewed:
- Description: Development of theoretical and methodological frameworks in data analysis is fundamental for modeling complex tobacco control systems. Following this idea, a new optimization based approach was introduced in the paper through two distinct methods: the modified linear least square fit and a heuristic algorithm for feature slection based on optimization-based methods have the potential to detect nonlinearity, and therefore to be more effective analysis tools of complex data set. In this study we evaluate the modified global k-means clustering algorithm by applying it to a massive set of real-time tobacco control survey data. Cluster analysis identified fixed and stable clusters in the studied data. These clusters correspond to groups of smokers with similar behaviour and the identification of these clusters may allow us to give recommendations on modification of existing tobacco control systems and on the design of future data acquistion surveys.
Improving Naive Bayes classifier using conditional probabilities
- Authors: Taheri, Sona , Mammadov, Musa , Bagirov, Adil
- Date: 2010
- Type: Text , Conference proceedings
- Full Text:
- Description: Naive Bayes classifier is the simplest among Bayesian Network classifiers. It has shown to be very efficient on a variety of data classification problems. However, the strong assumption that all features are conditionally independent given the class is often violated on many real world applications. Therefore, improvement of the Naive Bayes classifier by alleviating the feature independence assumption has attracted much attention. In this paper, we develop a new version of the Naive Bayes classifier without assuming independence of features. The proposed algorithm approximates the interactions between features by using conditional probabilities. We present results of numerical experiments on several real world data sets, where continuous features are discretized by applying two different methods. These results demonstrate that the proposed algorithm significantly improve the performance of the Naive Bayes classifier, yet at the same time maintains its robustness. © 2011, Australian Computer Society, Inc.
- Description: 2003009505
Truncated codifferential method for linearly constrained nonsmooth optimization
- Authors: Tor, Ali , Karasozen, Bulent , Bagirov, Adil
- Date: 2010
- Type: Text , Conference proceedings
- Full Text: false
- Description: In this paper a new algorithm is developed to minimize linearly constrained non-smooth optimization problem for convex objective functions. The algorithm is based on the concept of codifferential. The convergence of the proposed minimization algorithm is proved and results of numerical experiments using a set of test problems with nonsmooth convex objective function are reported.
A multidimensional descent method for global optimization
- Authors: Bagirov, Adil , Rubinov, Alex , Zhang, Jiapu
- Date: 2009
- Type: Text , Journal article
- Relation: Optimization Vol. 58, no. 5 (2009), p. 611-625
- Full Text: false
- Reviewed:
- Description: This article presents a new multidimensional descent method for solving global optimization problems with box-constraints. This is a hybrid method where local search method is used for a local descent and global search is used for further multidimensional search on the subsets of intersection of cones generated by the local search method and the feasible region. The discrete gradient method is used for local search and the cutting angle method is used for global search. Two-and three-dimensional cones are used for the global search. Such an approach allows one, as a rule, to escape local minimizers which are not global ones. The proposed method is local optimization method with strong global search properties. We present results of numerical experiments using both smooth and non-smooth global optimization test problems. These results demonstrate that the proposed algorithm allows one to find a global or a near global minimizer.
A new modified global k-means algorithm for clustering large data sets
- Authors: Bagirov, Adil , Ugon, Julien , Webb, Dean
- Date: 2009
- Type: Text , Conference paper
- Relation: Paper presented at XIIIth International Conference : Applied Stochastic Models and Data Analysis, ASMDA 2009, Vilnius, Lithuania : 30th June - 3rd July 2009 p. 1-5
- Full Text: false
- Description: The k-means algorithm and its variations are known to be fast clustering algorithms. However, they are sensitive to the choice of starting points and inefficient for solving clustering problems in large data sets. Recently, in order to resolve difficulties with the choice of starting points, incremental approaches have been developed. The modified global k-means algorithm is based on such an approach. It iteratively adds one cluster center at a time. Numerical experiments show that this algorithm considerably improve the k-means algorithm. However, this algorithm is not suitable for clustering very large data sets. In this paper, a new version of the modified global k-means algorithm is proposed. We introduce an auxiliary cluster function to generate a set of starting points spanning different parts of the data set. We exploit information gathered in previous iterations of the incremental algorithm to reduce its complexity.
- Description: 2003007558
An incremental approach for the construction of a piecewise linear classifier
- Authors: Bagirov, Adil , Ugon, Julien , Webb, Dean
- Date: 2009
- Type: Text , Conference paper
- Relation: Paper presented at XIIIth International Conference : Applied Stochastic Models and Data Analysis, ASMDA 2009, Vilnius, Lithuania : 30th June - 3rd July 2009 p. 507–511
- Relation: https://purl.org/au-research/grants/arc/DP0666061
- Full Text: false
- Description: In this paper the problem of finding piecewise linear boundaries between sets is considered and is applied for solving supervised data classification problems. An algorithm for the computation of piecewise linear boundaries, consisting of two main steps, is proposed. In the first step sets are approximated by hyperboxes to find so-called “indeterminate” regions between sets. In the second step sets are separated inside these “indeterminate” regions by piecewise linear functions. These functions are computed incrementally starting with a linear function. Results of numerical experiments are reported. These results demonstrate that the new algorithm requires a reasonable training time and it produces consistently good test set accuracy on most data sets comparing with mainstream classifiers.
- Description: 2003007559
Comments on : Optimization and data mining in medicine
- Authors: Bagirov, Adil
- Date: 2009
- Type: Text , Journal article
- Relation: Top Vol. 17, no. 2 (2009), p. 1-3
- Full Text: false
- Reviewed:
Continuous approximations to subdifferentials
- Authors: Bagirov, Adil
- Date: 2009
- Type: Text , Book chapter
- Relation: Encyclopedia of Optimization Chapter p. 475-482
- Full Text: false
Derivative-free methods for non-smooth optimization
- Authors: Bagirov, Adil
- Date: 2009
- Type: Text , Book chapter
- Relation: Encyclopedia of Optimization Chapter p. 648-655
- Full Text: false
- Description: 2003007530
Estimation of a regression function by maxima of minima of linear functions
- Authors: Bagirov, Adil , Clausen, Conny , Kohler, Michael
- Date: 2009
- Type: Text , Journal article
- Relation: IEEE Transactions on Information Theory Vol. 55, no. 2 (2009), p. 833-845
- Full Text:
- Reviewed:
- Description: In this paper, estimation of a regression function from independent and identically distributed random variables is considered. Estimates are defined by minimization of the empirical L2 risk over a class of functions, which are defined as maxima of minima of linear functions. Results concerning the rate of convergence of the estimates are derived. In particular, it is shown that for smooth regression functions satisfying the assumption of single index models, the estimate is able to achieve (up to some logarithmic factor) the corresponding optimal one-dimensional rate of convergence. Hence, under these assumptions, the estimate is able to circumvent the so-called curse of dimensionality. The small sample behavior of the estimates is illustrated by applying them to simulated data. © 2009 IEEE.
Global optimization : Cutting angle method
- Authors: Bagirov, Adil , Beliakov, Gleb
- Date: 2009
- Type: Text , Book chapter
- Relation: Encyclopedia of Optimization Chapter p. 1304-1311
- Full Text: false
Nonsmooth optimization approach to clustering
- Authors: Bagirov, Adil
- Date: 2009
- Type: Text , Book chapter
- Relation: Encyclopedia of Optimization Chapter p. 2664-2671
- Full Text: false
- Description: 2003007532
Optimization methods and the k-committees algorithm for clustering of sequence data
- Authors: Yearwood, John , Bagirov, Adil , Kelarev, Andrei
- Date: 2009
- Type: Text , Journal article
- Relation: Applied and Computational Mathematics Vol. 8, no. 1 (2009), p. 92-101
- Relation: http://purl.org/au-research/grants/arc/DP0211866
- Relation: http://purl.org/au-research/grants/arc/DP0666061
- Full Text: false
- Description: The present paper is devoted to new algorithms for unsupervised clustering based on the optimization approaches due to [2], [3] and [4]. We consider a novel situation, where the datasets consist of nucleotide or protein sequences and rather sophisticated biologically significant alignment scores have to be used as a measure of distance. Sequences of this kind cannot be regarded as points in a finite dimensional space. Besides, the alignment scores do not satisfy properties of Minkowski metrics. Nevertheless the optimization approaches have made it possible to introduce a new k-committees algorithm and compare its performance with previous algorithms for two datasets. Our experimental results show that the k-committees algorithms achieves intermediate accuracy for a dataset of ITS sequences, and it can perform better than the discrete k-means and Nearest Neighbour algorithms for certain datasets. All three algorithms achieve good agreement with clusters published in the biological literature before and can be used to obtain biologically significant clusterings.
Special issue of Optimization, dedicated to the development of the ideas of the late Prof. A. Rubinov
- Authors: Bagirov, Adil , Beliakov, Gleb
- Date: 2009
- Type: Text , Journal article
- Relation: Optimization Vol. 58, no. 5 (2009), p. 479-481
- Full Text: false
- Reviewed:
An algorithm for the estimation of a regression function by continuous piecewise linear functions
- Authors: Bagirov, Adil , Clausen, Conny , Kohler, Michael
- Date: 2008
- Type: Text , Journal article
- Relation: Computational Optimization and Applications Vol. 45, no. (2008), p. 159-179
- Relation: http://purl.org/au-research/grants/arc/DP0666061
- Full Text:
- Reviewed:
- Description: The problem of the estimation of a regression function by continuous piecewise linear functions is formulated as a nonconvex, nonsmooth optimization problem. Estimates are defined by minimization of the empirical L 2 risk over a class of functions, which are defined as maxima of minima of linear functions. An algorithm for finding continuous piecewise linear functions is presented. We observe that the objective function in the optimization problem is semismooth, quasidifferentiable and piecewise partially separable. The use of these properties allow us to design an efficient algorithm for approximation of subgradients of the objective function and to apply the discrete gradient method for its minimization. We present computational results with some simulated data and compare the new estimator with a number of existing ones.
- Description: The problem of the estimation of a regression function by continuous piecewise linear functions is formulated as a nonconvex, nonsmooth optimization problem. Estimates are defined by minimization of the empirical L 2 risk over a class of functions, which are defined as maxima of minima of linear functions. An algorithm for finding continuous piecewise linear functions is presented. We observe that the objective function in the optimization problem is semismooth, quasidifferentiable and piecewise partially separable. The use of these properties allow us to design an efficient algorithm for approximation of subgradients of the objective function and to apply the discrete gradient method for its minimization. We present computational results with some simulated data and compare the new estimator with a number of existing ones. © 2008 Springer Science+Business Media, LLC.
An approximate subgradient algorithm for unconstrained nonsmooth, nonconvex optimization
- Authors: Bagirov, Adil , Ganjehlou, Asef Nazari
- Date: 2008
- Type: Text , Journal article
- Relation: Mathematical Methods of Operations Research Vol. 67, no. 2 (2008), p. 187-206
- Relation: http://purl.org/au-research/grants/arc/DP0666061
- Full Text:
- Reviewed:
- Description: In this paper a new algorithm for minimizing locally Lipschitz functions is developed. Descent directions in this algorithm are computed by solving a system of linear inequalities. The convergence of the algorithm is proved for quasidifferentiable semismooth functions. We present the results of numerical experiments with both regular and nonregular objective functions. We also compare the proposed algorithm with two different versions of the subgradient method using the results of numerical experiments. These results demonstrate the superiority of the proposed algorithm over the subgradient method. © 2007 Springer-Verlag.
- Description: C1
Discrete gradient method : Derivative-free method for nonsmooth optimization
- Authors: Bagirov, Adil , Karasozen, Bulent , Sezer, Monsalve
- Date: 2008
- Type: Text , Journal article
- Relation: Journal of Optimization Theory and Applications Vol. 137, no. 2 (2008), p. 317-334
- Relation: http://purl.org/au-research/grants/arc/DP0666061
- Full Text:
- Reviewed:
- Description: A new derivative-free method is developed for solving unconstrained nonsmooth optimization problems. This method is based on the notion of a discrete gradient. It is demonstrated that the discrete gradients can be used to approximate subgradients of a broad class of nonsmooth functions. It is also shown that the discrete gradients can be applied to find descent directions of nonsmooth functions. The preliminary results of numerical experiments with unconstrained nonsmooth optimization problems as well as the comparison of the proposed method with the nonsmooth optimization solver DNLP from CONOPT-GAMS and the derivative-free optimization solver CONDOR are presented. © 2007 Springer Science+Business Media, LLC.
- Description: C1
Modified global k-means algorithm for minimum sum-of-squares clustering problems
- Authors: Bagirov, Adil
- Date: 2008
- Type: Text , Journal article
- Relation: Pattern Recognition Vol. 41, no. 10 (2008), p. 3192-3199
- Relation: http://purl.org/au-research/grants/arc/DP0666061
- Full Text:
- Reviewed:
- Description: k-Means algorithm and its variations are known to be fast clustering algorithms. However, they are sensitive to the choice of starting points and inefficient for solving clustering problems in large data sets. Recently, a new version of the k-means algorithm, the global k-means algorithm has been developed. It is an incremental algorithm that dynamically adds one cluster center at a time and uses each data point as a candidate for the k-th cluster center. Results of numerical experiments show that the global k-means algorithm considerably outperforms the k-means algorithms. In this paper, a new version of the global k-means algorithm is proposed. A starting point for the k-th cluster center in this algorithm is computed by minimizing an auxiliary cluster function. Results of numerical experiments on 14 data sets demonstrate the superiority of the new algorithm, however, it requires more computational time than the global k-means algorithm.
- Description: k-Means algorithm and its variations are known to be fast clustering algorithms. However, they are sensitive to the choice of starting points and inefficient for solving clustering problems in large data sets. Recently, a new version of the k-means algorithm, the global k-means algorithm has been developed. It is an incremental algorithm that dynamically adds one cluster center at a time and uses each data point as a candidate for the k-th cluster center. Results of numerical experiments show that the global k-means algorithm considerably outperforms the k-means algorithms. In this paper, a new version of the global k-means algorithm is proposed. A starting point for the k-th cluster center in this algorithm is computed by minimizing an auxiliary cluster function. Results of numerical experiments on 14 data sets demonstrate the superiority of the new algorithm, however, it requires more computational time than the global k-means algorithm. © 2008 Elsevier Ltd. All rights reserved.
- Description: 2003001713
Optimisation of operations of a water distribution system for reduced power usage
- Authors: Bagirov, Adil , Ugon, Julien , Barton, Andrew , Briggs, Steven
- Date: 2008
- Type: Text , Conference paper
- Relation: Paper presented at 9th National Conference on Hydraulics in Water Engineering: Hydraulics 2008, Darwin, Northern Territory : 22nd-26th September 2008
- Full Text: false
- Description: There are many improvements to operation that can be made to a water distribution system once it has been constructed and placed in ground. Pipes and associated storages and pumps are typically designed to meet average peak daily demands, offer some capacity for growth, and also allow for some deterioration of performance over time. However, the 'as constructed' performance of the pipeline is invariably different to what was designed on paper, and this is particularly so for anything other than design flows, such as during times of water restrictions when there are significantly reduced flows. Because of this, there remain significant benefits to owners and operators for the adaptive and global optimisation of such systems. The present paper uses the Ouyen subsystem of the Northern Mallee Pipeline, in Victoria, as a case study for the development of an optimisation model. This has been done with the intent of using this model to reduce costs and provide better service to customers on this system. The Ouyen subsystem consists of 1600 km of trunk and distribution pipeline servicing an area of 456,000 Ha. The system includes 2 fixed speed pumps diverting water from the Murray River at Liparoo into two 150 ML balancing storages at Ouyen, 4 variable speed pumps feeding water from the balancing storages into the pipeline system, 2 variable speed pressure booster pumps and 5 town balancing storages. When considering all these components of the system, power consumption becomes an important part of the overall operation. The present paper considers a global optimisation model to minimise power consumption while maintaining reasonable performance of the system. The main components of the model are described including the network structure and the costs functions associated with the system. The final model presents the cost functions associated with the pump scheduling, including the penalties descriptions associated with maintaining appropriate storages levels and pressure bounds within the water distribution network.
- Description: 2003006758
A nonsmooth optimization approach to sensor network localization
- Authors: Bagirov, Adil , Lai, Daniel , Palaniswami, M.
- Date: 2007
- Type: Text , Conference paper
- Relation: Paper presented at 3rd International Conference on Intelligent Sensors, Sensor Networks and Information, ISSNIP 2007, Melbourne, Victoria : 3rd-6th December 2007 p. 727-732
- Relation: http://purl.org/au-research/grants/arc/DP0666061
- Full Text:
- Description: In this paper the problem of localization of wireless sensor network is formulated as an unconstrained nonsmooth optimization problem. We minimize a distance objective function which incorporates unknown sensor nodes and nodes with known positions (anchors) in contrast to popular semidefinite programming (SDP) methods which use artificial objective functions. We study the main properties of the objective function in this problem and design an algorithm for its minimization. Our algorithm is a derivative-free discrete gradient method that allows one to find a near global solution. The algorithm can handle a large number of sensors in the network. This paper contains the theory of our proposed formulation and algorithm while experimental results are included in later work.
- Description: 2003004949