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1
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Learning the naive Bayes classifier with optimization models

100%
Taheri S., Mammadov M.
International Journal of Applied Mathematics and Computer Science
|
2013
|
tom 23
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nr 4
787-795
EN
Naive Bayes is among the simplest probabilistic classifiers. It often performs surprisingly well in many real world applications, despite the strong assumption that all features are conditionally independent given the class. In the learning process of this classifier with the known structure, class probabilities and conditional probabilities are calculated using training data, and then values of these probabilities are used to classify new observations. In this paper, we introduce three novel optimization models for the naive Bayes classifier where both class probabilities and conditional probabilities are considered as variables. The values of these variables are found by solving the corresponding optimization problems. Numerical experiments are conducted on several real world binary classification data sets, where continuous features are discretized by applying three different methods. The performances of these models are compared with the naive Bayes classifier, tree augmented naive Bayes, the SVM, C4.5 and the nearest neighbor classifier. The obtained results demonstrate that the proposed models can significantly improve the performance of the naive Bayes classifier, yet at the same time maintain its simple structure.
2
Content available remote

Center-based l₁-clustering method

100%
Sabo K.
International Journal of Applied Mathematics and Computer Science
|
2014
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tom 24
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nr 1
151-163
EN
In this paper, we consider the l₁-clustering problem for a finite data-point set which should be partitioned into k disjoint nonempty subsets. In that case, the objective function does not have to be either convex or differentiable, and generally it may have many local or global minima. Therefore, it becomes a complex global optimization problem. A method of searching for a locally optimal solution is proposed in the paper, the convergence of the corresponding iterative process is proved and the corresponding algorithm is given. The method is illustrated by and compared with some other clustering methods, especially with the l₂-clustering method, which is also known in the literature as a smooth k-means method, on a few typical situations, such as the presence of outliers among the data and the clustering of incomplete data. Numerical experiments show in this case that the proposed l₁-clustering algorithm is faster and gives significantly better results than the l₂-clustering algorithm.
3
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Iterative Learning Control - monotonicity and optimization

100%
Owens D., Daley S.
International Journal of Applied Mathematics and Computer Science
|
2008
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tom 18
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nr 3
279-293
EN
The area if Iterative Learning Control (ILC) has great potential for applications to systems with a naturally repetitive action where the transfer of data from repetition (trial or iteration) can lead to substantial improvements in tracking performance. There are several serious issues arising from the "2D" structure of ILC and a number of new problems requiring new ways of thinking and design. This paper introduces some of these issues from the point of view of the research group at Sheffield University and concentrates on linear systems and the potential for the use of optimization methods and switching strategies to achieve effective control.
4
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Control structure in optimization problems of bar systems

100%
Mikulski L.
International Journal of Applied Mathematics and Computer Science
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2004
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tom 14
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nr 4
515-529
EN
Optimal design problems in mechanics can be mathematically formulated as optimal control tasks. The minimum principle is employed in solving such problems. This principle allows us to write down optimal design problems as Multipoint Boundary Value Problems (MPBVPs). The dimension of MPBVPs is an essential restriction that decides on numerical difficulties. Optimal control theory does not give much information about the control structure, i.e., about the sequence of the forms of the right-hand sides of state equations appearing successively in time. The correctness of the assumed control structure can be checked after obtaining the solution of the boundary problem. For the numerical solution, we use hybrid procedures which are a connection of the multiple shooting method with that of collocation.
5
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KIS: An automated attribute induction method for classification of DNA sequences

100%
Biedrzycki R., Arabas J.
International Journal of Applied Mathematics and Computer Science
|
2012
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tom 22
|
nr 3
711-721
EN
This paper presents an application of methods from the machine learning domain to solving the task of DNA sequence recognition. We present an algorithm that learns to recognize groups of DNA sequences sharing common features such as sequence functionality. We demonstrate application of the algorithm to find splice sites, i.e., to properly detect donor and acceptor sequences. We compare the results with those of reference methods that have been designed and tuned to detect splice sites. We also show how to use the algorithm to find a human readable model of the IRE (Iron-Responsive Element) and to find IRE sequences. The method, although universal, yields results which are of quality comparable to those obtained by reference methods. In contrast to reference methods, this approach uses models that operate on sequence patterns, which facilitates interpretation of the results by humans.
6
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The "Thirty-seven Percent Rule" and the secretary problem with relative ranks

100%
Bajnok B., Semov S.
Discussiones Mathematicae Probability and Statistics
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2014
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tom 34
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nr 1-2
5-21
EN
We revisit the problem of selecting an item from n choices that appear before us in random sequential order so as to minimize the expected rank of the item selected. In particular, we examine the stopping rule where we reject the first k items and then select the first subsequent item that ranks lower than the l-th lowest-ranked item among the first k. We prove that the optimal rule has k ~ n/e, as in the classical secretary problem where our sole objective is to select the item of lowest rank; however, with the optimally chosen l, here we can get the expected rank of the item selected to be less than any positive power of n (as n approaches infinity). We also introduce a common generalization where our goal is to minimize the expected rank of the item selected, but this rank must be within the lowest d.
7
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Quasi-hierarchical evolution algorithm for flow assignment in survivable connection-oriented networks

100%
Przewozniczek M., Walkowiak K.
International Journal of Applied Mathematics and Computer Science
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2006
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tom 16
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nr 4
487-502
EN
The main objective of this paper is to develop an effective evolutionary algorithm (EA) for the path-assignment problem in survivable connection-oriented networks. We assume a single-link failure scenario, which is the most common and frequently reported failure event. Since the network flow is modeled as a non-bifurcated multicommodity flow, the discussed optimization problem is NP-complete. Thus, we develop an effective heuristic algorithm based on an evolutionary algorithm. The main novelty of this work is that the proposed evolutionary algorithm consists of two levels. The "high" level applies typical EA operators. The "low" level is based on the idea of a hierarchical algorithm. However, the presented approach is not a classical hierarchical algorithm. Therefore, we call the algorithm quasi-hierarchical. We present its description and the results of simulation runs over various networks.
8
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Gradient flow optimization for reducing blocking effects of transform coding

100%
Gao F., Li X., Wang X., Wee W. G.
International Journal of Applied Mathematics and Computer Science
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2004
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tom 14
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nr 1
105-111
EN
This paper addresses the problem of reducing blocking effects in transform coding. A novel optimization approach using the gradient flow is proposed. Using some properties of the gradient flow on a manifold, an optimized filter design method for reducing the blocking effects is presented. Based on this method, an image reconstruction algorithm is derived. The algorithm maintains the fidelity of images while reducing the blocking effects. Experimental tests demonstrate that the presented algorithm is effective.
9
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Optimization of the service strategy in a queueing system with energy harvesting and customers' impatience

100%
Dudin A., Lee M., Dudin S.
International Journal of Applied Mathematics and Computer Science
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2016
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tom 26
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nr 2
367-378
EN
A single-server queueing system with an infinite buffer is considered. The service of a customer is possible only in the presence of at least one unit of energy, and during the service the number of available units decreases by one. New units of energy arrive in the system at random instants of time if the finite buffer for maintenance of energy is not full. Customers are impatient and leave the system without service after a random amount of waiting time. Such a queueing system describes, e.g., the operation of a sensor node which harvests energy necessary for information transmission from the environment. Aiming to minimize the loss of customers due to their impatience (and maximize the throughput of the system), a new strategy of control by providing service is proposed. This strategy suggests that service temporarily stops if the number of customers or units of energy in the system becomes zero. The server is switched off (is in sleep mode) for some time. This time finishes (the server wakes up) if both the number of customers in the buffer and the number of energy units reach some fixed threshold values or when the number of energy units reaches some threshold value and there are customers in the buffer. Arrival flows of customers and energy units are assumed to be described by an independent Markovian arrival process. The service time has a phase-type distribution. The system behavior is described by a multi-dimensional Markov chain. The generator of this Markov chain is derived. The ergodicity condition is presented. Expressions for key performance measures are given. Numerical results illustrating the dependence of a customer's loss probability on the thresholds defining the discipline of waking up the server are provided. The importance of the account of correlation in arrival processes is numerically illustrated.
10
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Content available

New lower bounds on the weighted chromatic number of a graph

100%
Caramia M., Fiala J.
Discussiones Mathematicae Graph Theory
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2004
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tom 24
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nr 2
183-195
EN
In this paper we present theoretical and algorithmic results for the computation of lower bounds on the chromatic number of a weighted graph. In particular, we study different ways of a possible improvement of the lower bound offered by a maximum weighted clique. Based on our findings we devise new algorithms and show their performance on random graphs.
11
Content available remote

An application of the Fourier transform to optimization of continuous 2-D systems

88%
Dymkou V., Dymkov M.
International Journal of Applied Mathematics and Computer Science
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2003
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tom 13
|
nr 1
45-54
EN
This paper uses the theory of entire functions to study the linear quadratic optimization problem for a class of continuous 2D systems. We show that in some cases optimal control can be given by an analytical formula. A simple method is also proposed to find an approximate solution with preassigned accuracy. Some application to the 1D optimization problem is presented, too. The obtained results form a theoretical background for the design problem of optimal controllers for relevant processes.
12
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Content available

Analysis of an MAP/PH/1 queue with flexible group service

88%
Brugno A., D'Apice C., Dudin A., Manzo R.
International Journal of Applied Mathematics and Computer Science
|
2017
|
tom 27
|
nr 1
119-131
EN
A novel customer batch service discipline for a single server queue is introduced and analyzed. Service to customers is offered in batches of a certain size. If the number of customers in the system at the service completion moment is less than this size, the server does not start the next service until the number of customers in the system reaches this size or a random limitation of the idle time of the server expires, whichever occurs first. Customers arrive according to a Markovian arrival process. An individual customer's service time has a phase-type distribution. The service time of a batch is defined as the maximum of the individual service times of the customers which form the batch. The dynamics of such a system are described by a multi-dimensional Markov chain. An ergodicity condition for this Markov chain is derived, a stationary probability distribution of the states is computed, and formulas for the main performance measures of the system are provided. The Laplace-Stieltjes transform of the waiting time is obtained. Results are numerically illustrated.
13
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A homotopy approach to rational covariance extension with degree constraint

88%
Enqvist P.
International Journal of Applied Mathematics and Computer Science
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2001
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tom 11
|
nr 5
1173-1201
EN
The solutions to the Rational Covariance Extension Problem (RCEP) are parameterized by the spectral zeros. The rational filter with a specified numerator solving the RCEP can be determined from a known convex optimization problem. However, this optimization problem may become ill-conditioned for some parameter values. A modification of the optimization problem to avoid the ill-conditioning is proposed and the modified problem is solved efficiently by a continuation method.
14
Content available remote

Application of agent-based simulated annealing and tabu search procedures to solving the data reduction problem

88%
Czarnowski I., Jędrzejowicz P.
International Journal of Applied Mathematics and Computer Science
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2011
|
tom 21
|
nr 1
57-68
EN
The problem considered concerns data reduction for machine learning. Data reduction aims at deciding which features and instances from the training set should be retained for further use during the learning process. Data reduction results in increased capabilities and generalization properties of the learning model and a shorter time of the learning process. It can also help in scaling up to large data sources. The paper proposes an agent-based data reduction approach with the learning process executed by a team of agents (A-Team). Several A-Team architectures with agents executing the simulated annealing and tabu search procedures are proposed and investigated. The paper includes a detailed description of the proposed approach and discusses the results of a validating experiment.
15
Content available remote

Integrated design of observer based fault detection for a class of uncertain nonlinear systems

88%
Chen W., Khan A., Abid M., Ding S.
International Journal of Applied Mathematics and Computer Science
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2011
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tom 21
|
nr 3
423-430
EN
Integrated design of observer based Fault Detection (FD) for a class of uncertain nonlinear systems with Lipschitz nonlinearities is studied. In the context of norm based residual evaluation, the residual generator and evaluator are designed together in an integrated form, and, based on it, a trade-off FD system is finally achieved in the sense that, for a given Fault Detection Rate (FDR), the False Alarm Rate (FAR) is minimized. A numerical example is given to illustrate the effectiveness of the proposed design method.
16
Content available remote

Internet shopping optimization problem

88%
Błażewicz J., Kovalyov M., Musiał J., Urbański A., Wojciechowski A.
International Journal of Applied Mathematics and Computer Science
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2010
|
tom 20
|
nr 2
385-390
EN
A high number of Internet shops makes it difficult for a customer to review manually all the available offers and select optimal outlets for shopping. A partial solution to the problem is brought by price comparators which produce price rankings from collected offers. However, their possibilities are limited to a comparison of offers for a single product requested by the customer. The issue we investigate in this paper is a multiple-item multiple-shop optimization problem, in which total expenses of a customer to buy a given set of items should be minimized over all available offers. In this paper, the Internet Shopping Optimization Problem (ISOP) is defined in a formal way and a proof of its strong NP-hardness is provided. We also describe polynomial time algorithms for special cases of the problem.
17
Content available remote

A numerical procedure for filtering and efficient high-order signal differentiation

88%
Ibrir S., Diop S.
International Journal of Applied Mathematics and Computer Science
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2004
|
tom 14
|
nr 2
201-208
EN
In this paper, we propose a numerical algorithm for filtering and robust signal differentiation. The numerical procedure is based on the solution of a simplified linear optimization problem. A compromise between smoothing and fidelity with respect to the measurable data is achieved by the computation of an optimal regularization parameter that minimizes the Generalized Cross Validation criterion (GCV). Simulation results are given to highlight the effectiveness of the proposed procedure.
18
Content available remote

Heuristic algorithms for optimization of task allocation and result distribution in peer-to-peer computing systems

88%
Chmaj G., Walkowiak K., Tarnawski M., Kucharzak M.
International Journal of Applied Mathematics and Computer Science
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2012
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tom 22
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nr 3
733-748
EN
Recently, distributed computing system have been gaining much attention due to a growing demand for various kinds of effective computations in both industry and academia. In this paper, we focus on Peer-to-Peer (P2P) computing systems, also called public-resource computing systems or global computing systems. P2P computing systems, contrary to grids, use personal computers and other relatively simple electronic equipment (e.g., the PlayStation console) to process sophisticated computational projects. A significant example of the P2P computing idea is the BOINC (Berkeley Open Infrastructure for Network Computing) project. To improve the performance of the computing system, we propose to use the P2P approach to distribute results of computational projects, i.e., results are transmitted in the system like in P2P file sharing systems (e.g., BitTorrent). In this work, we concentrate on offline optimization of the P2P computing system including two elements: scheduling of computations and data distribution. The objective is to minimize the system OPEX cost related to data processing and data transmission. We formulate an Integer Linear Problem (ILP) to model the system and apply this formulation to obtain optimal results using the CPLEX solver. Next, we propose two heuristic algorithms that provide results very close to an optimum and can be used for larger problem instances than those solvable by CPLEX or other ILP solvers.
19
Content available remote

Anycasting in connection-oriented computer networks: Models, algorithms and results

88%
Walkowiak K.
International Journal of Applied Mathematics and Computer Science
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2010
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tom 20
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nr 1
207-220
EN
Our discussion in this article centers around various issues related to the use of anycasting in connection-oriented computer networks. Anycast is defined as a one-to-one-of-many transmission to deliver a packet to one of many hosts. Anycasting can be applied if the same content is replicated over many locations in the network. Examples of network techniques that apply anycasting are Content Delivery Networks (CDNs), Domain Name Service (DNS), Peer-to-Peer (P2P) systems. The role of anycasting is growing concurrently with the popularity of electronic music, movies, and other content required by Internet users. In this work we focus on the optimization of anycast flows in connection-oriented networks. We formulate a model of anycast connections and next propose a heuristic algorithm based on the Lagrangean relaxation aimed to optimize jointly routes for anycast and unicast connections. Results of numerical experiments are presented and evaluated. Finally, we analyze briefly problems related to anycasting in dynamic routing and multi-layer networks.
20
Content available remote

Evolutionary computation based on Bayesian classifiers

75%
Miquélez T., Bengoetxea E., Larrañaga P.
International Journal of Applied Mathematics and Computer Science
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2004
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tom 14
|
nr 3
335-349
EN
Evolutionary computation is a discipline that has been emerging for at least 40 or 50 years. All methods within this discipline are characterized by maintaining a set of possible solutions (individuals) to make them successively evolve to fitter solutions generation after generation. Examples of evolutionary computation paradigms are the broadly known Genetic Algorithms (GAs) and Estimation of Distribution Algorithms (EDAs). This paper contributes to the further development of this discipline by introducing a new evolutionary computation method based on the learning and later simulation of a Bayesian classifier in every generation. In the method we propose, at each iteration the selected group of individuals of the population is divided into different classes depending on their respective fitness value. Afterwards, a Bayesian classifier-either naive Bayes, seminaive Bayes, tree augmented naive Bayes or a similar one-is learned to model the corresponding supervised classification problem. The simulation of the latter Bayesian classifier provides individuals that form the next generation. Experimental results are presented to compare the performance of this new method with different types of EDAs and GAs. The problems chosen for this purpose are combinatorial optimization problems which are commonly used in the literature.
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