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Piecewise partially separable functions and a derivative-free algorithm for large scale nonsmooth optimization

  • Authors: Bagirov, Adil , Ugon, Julien
  • Date: 2006
  • Type: Text , Journal article
  • Relation: Journal of Global Optimization Vol. 35, no. 2 (Jun 2006), p. 163-195
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  • Description: This paper introduces the notion of piecewise partially separable functions and studies their properties. We also consider some of many applications of these functions. Finally, we consider the problem of minimizing of piecewise partially separable functions and develop an algorithm for its solution. This algorithm exploits the structure of such functions. We present the results of preliminary numerical experiments.
  • Description: 2003001532

Characterization theorem for best linear spline approximation with free knots

  • 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.

Visual character N-grams for classification and retrieval of radiological images

  • Authors: Kulkarni, Pradnya , Stranieri, Andrew , Kulkarni, Siddhivinayak , Ugon, Julien , Mittal, Manish
  • Date: 2014
  • Type: Text , Journal article
  • Relation: International Journal of Multimedia & Its Applications Vol. 6, no. 2 (April 2014 2014), p. 35-49
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  • Description: Diagnostic radiology struggles to maintain high interpretation accuracy. Retrieval of past similar cases would help the inexperienced radiologist in the interpretation process. Character n-gram model has been effective in text retrieval context in languages such as Chinese where there are no clear word boundaries. We propose the use of visual character n-gram model for representation of image for classification and retrieval purposes. Regions of interests in mammographic images are represented with the character n-gram features. These features are then used as input to back-propagation neural network for classification of regions into normal and abnormal categories. Experiments on miniMIAS database show that character n-gram features are useful in classifying the regions into normal and abnormal categories. Promising classification accuracies are observed (83.33%) for fatty background tissue warranting further investigation. We argue that Classifying regions of interests would reduce the number of comparisons necessary for finding similar images from the database and hence would reduce the time required for retrieval of past similar cases.

Queueing programming models in telecommunication network maintenance

A feature selection approach for unsupervised classification based on clustering

  • 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

A generalized subgradient method with piecewise linear subproblem

  • 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

  • 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

Facility location via continuous optimization with discontinuous objective functions

  • Authors: Ugon, Julien , Kouhbor, Shahnaz , Mammadov, Musa , Rubinov, Alex , Kruger, Alexander
  • Date: 2007
  • Type: Text , Journal article
  • Relation: ANZIAM Journal Vol. 48, no. 3 (2007), p. 315-325
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  • Description: Facility location problems are one of the most common applications of optimization methods. Continuous formulations are usually more accurate, but often result in complex problems that cannot be solved using traditional optimization methods. This paper examines the use of a global optimization method - AGOP - for solving location problems where the objective function is discontinuous. This approach is motivated by a real-world application in wireless networks design. © Australian Mathematical Society 2007.
  • Description: 2003004859

Coverage in WLAN : Optimization model and algorithm

Optimization solvers and problem formulations for solving data clustering problems

  • 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

The choice of a similarity measure with respect to its sensitivity to outliers

  • Authors: Rubinov, Alex , 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. 709-721
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  • Description: This paper examines differences in the choice of similarity measures with respect to their sensitivity to outliers in clustering problems, formulated as mathematical programming problems. Namely, we are focusing on the study of norms (norm-based similarity measures) and convex functions of norms (function-norm-based similarity measures). The study consists of two parts: the study of theoretical models and numerical experiments. The main result of this study is a criterion for the outliers sensitivity with respect to the corresponding similarity measure. In particular, the obtained results show that the norm-based similarity measures are not sensitive to outliers whilst a very widely used square of the Euclidean norm similarity measure (least squares) is sensitive to outliers. Copyright © 2010 Watam Press.

A new algorithm for the placement of WLAN access point based on nonsmooth optimization technique

  • Authors: Kouhbor, Shahnaz , Ugon, Julien , Kruger, Alexander , Rubinov, Alex , Branch, Philip
  • Date: 2005
  • Type: Text , Conference paper
  • Relation: Paper presented at the 7th International Conference on Advanced Communication Technology, Phoenix Park, Korea : 21st February, 2005
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  • Description: In wireless local area network (WLAN), signal coverage is obtained by proper placement of access points (APs). The impact of incorrect placement of APs is significant. If they are placed too far apart, they generate a coverage gap but if they are too close to each other, this leads to excessive co-channel interferences. In this paper, we describe a mathematical model we have developed to find the optimal number and location of APs. To solve the problem, we use an optimization algorithm developed at the University of Ballarat called discrete gradient algorithm. Results indicate that our model is able to solve optimal coverage problems for different numbers of users.
  • Description: E1
  • Description: 2003001376

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

  • 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

  • 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

New algorithm to find a shape of a finite set of points

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
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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

Optimisation solvers and problem formulations for solving a data clustering problem

Automatic sleep stage identification: difficulties and possible solutions