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Characterization theorem for best linear spline approximation with free knots

- Sukhorukova, Nadezda, Ugon, Julien

  • Authors: Sukhorukova, Nadezda , Ugon, Julien
  • Date: 2010
  • Type: Text , Journal article
  • Relation: Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms Vol. 17, no. 5 (2010), p. 687-708
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  • Description: A necessary condition for a best Chebyshev approximation by piecewise linear functions is derived using quasidifferential calculus. We first discover some properties of the knots joining the linear functions. Then we use these properties to obtain the optimality condition. This condition is stronger than existing results. We present an example of linear spline approximation where the existing optimality conditions are satisfied, but not the proposed one, which shows that it is not optimal. Copyright © 2010 Watam Press.

Queueing programming models in telecommunication network maintenance

- Ugon, Julien, Jia, Long, Ouveysi, Iradj

A feature selection approach for unsupervised classification based on clustering

- Rubinov, Alex, Soukhoroukova, Nadejda, Ugon, Julien

  • Authors: Rubinov, Alex , Soukhoroukova, Nadejda , Ugon, Julien
  • Date: 2004
  • Type: Text , Conference paper
  • Relation: Paper presented at Sixth International Conference on Optimization: Techniques and Applications (ICOTA) , University of Ballarat, Ballarat, Victoria : 9th-11th December 2004
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  • Description: Data have been collected for many years in different scientific (industrial, medical) research groups. Very often these groups kept all the the they could collect. It is possible that the data contains a lot of noisy features which do not bring any information, but make the problem more complicated. The additional study of eliminating non-informative and selecting informative features is very important in the area of Data Mining. There are several feature selection methods which were developed for supervised classification. The area of feature selection for unsupervised classification is not so developed. In this paper we present a new feature selection approach for unsupervised classification, based on clustering and nonsmooth optimisation techniques.
  • Description: 2003004085

Solving Euclidian travelling salesman problem using discrete-gradient based clustering and kohonen neural network

- Ghosh, Moumita, Ugon, Julien, Ghosh, Ranadhir, Bagirov, Adil

A generalized subgradient method with piecewise linear subproblem

- Bagirov, Adil, Ganjehlou, Asef Nazari, Tor, Hakan, Ugon, Julien

  • Authors: Bagirov, Adil , Ganjehlou, Asef Nazari , Tor, Hakan , Ugon, Julien
  • Date: 2010
  • Type: Text , Journal article
  • Relation: Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms Vol. 17, no. 5 (2010), p. 621-638
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  • Description: In this paper, a new version of the quasisecant method for nonsmooth nonconvex optimization is developed. Quasisecants are overestimates to the objective function in some neighborhood of a given point. Subgradients are used to obtain quasisecants. We describe classes of nonsmooth functions where quasisecants can be computed explicitly. We show that a descent direction with suffcient decrease must satisfy a set of linear inequalities. In the proposed algorithm this set of linear inequalities is solved by applying the subgradient algorithm to minimize a piecewise linear function. We compare results of numerical experiments between the proposed algorithm and subgradient method. Copyright © 2010 Watam Press.

A new modified global k-means algorithm for clustering large data sets

- Bagirov, Adil, Ugon, Julien, Webb, Dean

  • 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
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  • 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

Optimization in wireless local area network

- Kouhbor, Shahnaz, Ugon, Julien, Kruger, Alexander, Rubinov, Alex, Branch, Philip

Optimization solvers and problem formulations for solving data clustering problems

- Ugon, Julien

  • Authors: Ugon, Julien
  • Date: 2007
  • Type: Text , Journal article
  • Relation: Pacific Journal of Optimization Vol. 3, no. 2 (2007), p. 387-397
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  • Description: A popular apprach for solving complex optimization problems is through relaxation: some constraints are removed in order to have a convex problem approximating the original problem. On the other hand, direct approaches for solving such problems are becoming increasingly powerful. This paper examines two cases drawn from data analysis, in order to compare the two techniques.
  • Description: C1
  • Description: 2003004937

Patient admission prediction using a pruned fuzzy min-max neural network with rule extraction

- Wang, Jin, Lim, Cheepeng, Creighton, Douglas, Khorsavi, Abbas, Nahavandi, Saeid, Ugon, Julien, Vamplew, Peter, Stranieri, Andrew, Martin, Laura, Freischmidt, Anton

  • Authors: Wang, Jin , Lim, Cheepeng , Creighton, Douglas , Khorsavi, Abbas , Nahavandi, Saeid , Ugon, Julien , Vamplew, Peter , Stranieri, Andrew , Martin, Laura , Freischmidt, Anton
  • Date: 2015
  • Type: Text , Journal article
  • Relation: Neural Computing and Applications Vol. 26, no. 2 (2015), p. 277-289
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  • Description: A useful patient admission prediction model that helps the emergency department of a hospital admit patients efficiently is of great importance. It not only improves the care quality provided by the emergency department but also reduces waiting time of patients. This paper proposes an automatic prediction method for patient admission based on a fuzzy min–max neural network (FMM) with rules extraction. The FMM neural network forms a set of hyperboxes by learning through data samples, and the learned knowledge is used for prediction. In addition to providing predictions, decision rules are extracted from the FMM hyperboxes to provide an explanation for each prediction. In order to simplify the structure of FMM and the decision rules, an optimization method that simultaneously maximizes prediction accuracy and minimizes the number of FMM hyperboxes is proposed. Specifically, a genetic algorithm is formulated to find the optimal configuration of the decision rules. The experimental results using a large data set consisting of 450740 real patient records reveal that the proposed method achieves comparable or even better prediction accuracy than state-of-the-art classifiers with the additional ability to extract a set of explanatory rules to justify its predictions.

Analysis and comparison of co-occurrence matrix and pixel n-gram features for mammographic images

- Kulkarni, Pradnya, Stranieri, Andrew, Kulkarni, Sid, Ugon, Julien, Mittal, Manish

  • Authors: Kulkarni, Pradnya , Stranieri, Andrew , Kulkarni, Sid , Ugon, Julien , Mittal, Manish
  • Date: 2015
  • Type: Text , Conference paper
  • Relation: International Conference on Communication and Computing p. 7-14
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  • Description: Mammography is a proven way of detecting breast cancer at an early stage. Various feature extraction techniques such as histograms, co-occurrence matrix, local binary patterns, Gabor filters, wavelet transforms are used for analysing mammograms. The novel pixel N-gram feature extraction technique has been inspired from the character N-gram concept of text retrieval. In this paper, we have compared the novel N-gram feature extraction technique with the co-occurrence matrix feature extraction technique. The experiments were conducted on the benchmark miniMIAS mammography database. Classification of mammograms into normal and abnormal category using N-gram features showed promising results with greater classification accuracy, sensitivity and specificity compared to classification using co-occurrence matrix features. Moreover, N-gram features computation are found to be considerably faster than co-occurrence matrix feature computation

Optimisation of operations of a water distribution system for reduced power usage

- Bagirov, Adil, Ugon, Julien, Barton, Andrew, Briggs, Steven

  • 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
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  • 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

Fast modified global k-means algorithm for incremental cluster construction

- Bagirov, Adil, Ugon, Julien, Webb, Dean

  • Authors: Bagirov, Adil , Ugon, Julien , Webb, Dean
  • Date: 2011
  • Type: Text , Journal article
  • Relation: Pattern Recognition Vol. 44, no. 4 (2011), p. 866-876
  • Relation: http://purl.org/au-research/grants/arc/DP0666061
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  • 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 are inefficient for solving clustering problems in large datasets. Recently, incremental approaches have been developed to resolve difficulties with the choice of starting points. The global k-means and the modified global k-means algorithms are based on such an approach. They iteratively add one cluster center at a time. Numerical experiments show that these algorithms considerably improve the k-means algorithm. However, they require storing the whole affinity matrix or computing this matrix at each iteration. This makes both algorithms time consuming and memory demanding for clustering even moderately large datasets. 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 lying in different parts of the dataset. We exploit information gathered in previous iterations of the incremental algorithm to eliminate the need of computing or storing the whole affinity matrix and thereby to reduce computational effort and memory usage. Results of numerical experiments on six standard datasets demonstrate that the new algorithm is more efficient than the global and the modified global k-means algorithms. © 2010 Elsevier Ltd. All rights reserved.

An incremental approach for the construction of a piecewise linear classifier

- Bagirov, Adil, Ugon, Julien, Webb, Dean

Workload coverage through nonsmooth optimization

- Sukhorukova, Nadezda, Ugon, Julien, Yearwood, John

  • Authors: Sukhorukova, Nadezda , Ugon, Julien , Yearwood, John
  • Date: 2009
  • Type: Text , Journal article
  • Relation: Optimization Methods and Software Vol. 24, no. 2 (2009), p. 285-298
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  • Description: In this paper, workload coverage is the problem of identifying a pattern of days worked and days off, along with the number of hours worked on each work day. This pattern must satisfy certain work-related constraints and fit best to a predefined workload. In our study, we formulate the problem of workload coverage as an optimization problem. We propose a number of models which take into consideration various staffing constraints. For each of these models, our study aims to find a compromise between an accurate workload coverage and the ability to solve the corresponding optimization problems in a reasonable time. Numerical experiments on each model are carried out and the results are presented. Interestingly, the nonlinear programming approaches are found to be competitive with linear programming ones. © 2009 Taylor & Francis.

Nonsmooth DC programming approach to clusterwise linear regression : Optimality conditions and algorithms

- Bagirov, Adil, Ugon, Julien

  • Authors: Bagirov, Adil , Ugon, Julien
  • Date: 2018
  • Type: Text , Journal article
  • Relation: Optimization Methods and Software Vol. 33, no. 1 (2018), p. 194-219
  • Relation: http://purl.org/au-research/grants/arc/DP140103213
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  • Description: The clusterwise linear regression problem is formulated as a nonsmooth nonconvex optimization problem using the squared regression error function. The objective function in this problem is represented as a difference of convex functions. Optimality conditions are derived, and an algorithm is designed based on such a representation. An incremental approach is proposed to generate starting solutions. The algorithm is tested on small to large data sets. © 2017 Informa UK Limited, trading as Taylor & Francis Group.

Classification through incremental max-min separability

- Bagirov, Adil, Ugon, Julien, Webb, Dean, Karasozen, Bulent

  • Authors: Bagirov, Adil , Ugon, Julien , Webb, Dean , Karasozen, Bulent
  • Date: 2011
  • Type: Text , Journal article
  • Relation: Pattern Analysis and Applications Vol. 14, no. 2 (2011), p. 165-174
  • Relation: http://purl.org/au-research/grants/arc/DP0666061
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  • Description: Piecewise linear functions can be used to approximate non-linear decision boundaries between pattern classes. Piecewise linear boundaries are known to provide efficient real-time classifiers. However, they require a long training time. Finding piecewise linear boundaries between sets is a difficult optimization problem. Most approaches use heuristics to avoid solving this problem, which may lead to suboptimal piecewise linear boundaries. In this paper, we propose an algorithm for globally training hyperplanes using an incremental approach. Such an approach allows one to find a near global minimizer of the classification error function and to compute as few hyperplanes as needed for separating sets. We apply this algorithm for solving supervised data classification problems and report the results of numerical experiments on real-world data sets. These results demonstrate that the new algorithm requires a reasonable training time and its test set accuracy is consistently good on most data sets compared with mainstream classifiers. © 2010 Springer-Verlag London Limited.

A modified parallel optimization system for updating large-size time-evolving flow matrix

- Yu, Ting, Ugon, Julien, Yu, Wei

  • Authors: Yu, Ting , Ugon, Julien , Yu, Wei
  • Date: 2011
  • Type: Text , Journal article
  • Relation: Information Sciences Vol.194, no. (2011), p.57-67
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  • Description: Flow matrices are widely used in many disciplines, but few methods can estimate them. This paper presents a knowledge-based system as capable of estimating and updating large-size time-evolving flow matrix. The system in this paper consists of two major components with the purposes of matrix estimation and parallel optimization. The matrix estimation algorithm interprets and follows users' query scripts, retrieves data from various sources and integrates them for the matrix estimation. The parallel optimization component is built upon a supercomputing facility to utilize its computational power to efficiently process a large amount of data and estimate a large-size complex matrix. The experimental results demonstrate its outstanding performance and the acceptable accuracy by directly and indirectly comparing the estimation matrix with the actual matrix constructed by surveys. © 2011 Elsevier Inc. All rights reserved.

Codifferential method for minimizing nonsmooth DC functions

- Bagirov, Adil, Ugon, Julien

  • Authors: Bagirov, Adil , Ugon, Julien
  • Date: 2011
  • Type: Text , Journal article
  • Relation: Journal of Global Optimization Vol. 50, no. 1 (2011), p. 3-22
  • Relation: http://purl.org/au-research/grants/arc/DP0666061
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  • Description: In this paper, a new algorithm to locally minimize nonsmooth functions represented as a difference of two convex functions (DC functions) is proposed. The algorithm is based on the concept of codifferential. It is assumed that DC decomposition of the objective function is known a priori. We develop an algorithm to compute descent directions using a few elements from codifferential. The convergence of the minimization algorithm is studied and its comparison with different versions of the bundle methods using results of numerical experiments is given. © 2010 Springer Science+Business Media, LLC.

A novel piecewise linear classifier based on polyhedral conic and max-min separabilities

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

  • Authors: Bagirov, Adil , Ugon, Julien , Webb, Dean , Ozturk, Gurkan , Kasimbeyli, Refail
  • Date: 2011
  • Type: Text , Journal article
  • Relation: TOP Vol.21, no.1 (2011), p. 1-22
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  • Description: In this paper, an algorithm for finding piecewise linear boundaries between pattern classes is developed. This algorithm consists of two main stages. In the first stage, a polyhedral conic set is used to identify data points which lie inside their classes, and in the second stage we exclude those points to compute a piecewise linear boundary using the remaining data points. Piecewise linear boundaries are computed incrementally starting with one hyperplane. Such an approach allows one to significantly reduce the computational effort in many large data sets. Results of numerical experiments are reported. These results demonstrate that the new algorithm consistently produces a good test set accuracy on most data sets comparing with a number of other mainstream classifiers. © 2011 Sociedad de EstadÃstica e Investigación Operativa.

Nonsmooth DC programming approach to clusterwise linear regression : Optimality conditions and algorithms

- Bagirov, Adil, Ugon, Julien

  • Authors: Bagirov, Adil , Ugon, Julien
  • Date: 2018
  • Type: Text , Journal article
  • Relation: Optimization Methods and Software Vol. 33, no. 1 (2018), p. 194-219
  • Full Text: false
  • Reviewed:
  • Description: The clusterwise linear regression problem is formulated as a nonsmooth nonconvex optimization problem using the squared regression error function. The objective function in this problem is represented as a difference of convex functions. Optimality conditions are derived, and an algorithm is designed based on such a representation. An incremental approach is proposed to generate starting solutions. The algorithm is tested on small to large data sets.