Search results for: Artificial Bee Colony (ABC) algorithm

Authors: Shashank N. Mathur, Anil K. Ahlawat, Virendra P. Vishwakarma

Abstract:

In this paper, a comparative study of application of supervised and unsupervised learning algorithms on illumination invariant face recognition has been carried out. The supervised learning has been carried out with the help of using a bi-layered artificial neural network having one input, two hidden and one output layer. The gradient descent with momentum and adaptive learning rate back propagation learning algorithm has been used to implement the supervised learning in a way that both the inputs and corresponding outputs are provided at the time of training the network, thus here is an inherent clustering and optimized learning of weights which provide us with efficient results.. The unsupervised learning has been implemented with the help of a modified Counterpropagation network. The Counterpropagation network involves the process of clustering followed by application of Outstar rule to obtain the recognized face. The face recognition system has been developed for recognizing faces which have varying illumination intensities, where the database images vary in lighting with respect to angle of illumination with horizontal and vertical planes. The supervised and unsupervised learning algorithms have been implemented and have been tested exhaustively, with and without application of histogram equalization to get efficient results.

Keywords: Artificial Neural Networks, back propagation, Counterpropagation networks, face recognition, learning algorithms.

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Authors: Keqin Li

Abstract:

Given a parallel program to be executed on a heterogeneous computing system, the overall execution time of the program is determined by a schedule. In this paper, we analyze the worst-case performance of the list scheduling algorithm for scheduling tasks of a parallel program in a mixed-machine heterogeneous computing system such that the total execution time of the program is minimized. We prove tight lower and upper bounds for the worst-case performance ratio of the list scheduling algorithm. We also examine the average-case performance of the list scheduling algorithm. Our experimental data reveal that the average-case performance of the list scheduling algorithm is much better than the worst-case performance and is very close to optimal, except for large systems with large heterogeneity. Thus, the list scheduling algorithm is very useful in real applications.

Keywords: Average-case performance, list scheduling algorithm, mixed-machine heterogeneous computing system, worst-case performance.

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Authors: Seung-Won Jung, Hye-Soo Kim, Le Thanh Ha, Seung-Jin Baek, Sung-Jea Ko

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In this paper, a novel deinterlacing algorithm is proposed. The proposed algorithm approximates the distribution of the luminance into a polynomial function. Instead of using one polynomial function for all pixels, different polynomial functions are used for the uniform, texture, and directional edge regions. The function coefficients for each region are computed by matrix multiplications. Experimental results demonstrate that the proposed method performs better than the conventional algorithms.

Keywords: Deinterlacing, polynomial interpolation.

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Authors: Wayne Goodridge, Alexander Nikov, Ashok Sahai

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Multi criteria decision making (MCDM) methods like analytic hierarchy process, ELECTRE and multi-attribute utility theory are critically studied. They have irregularities in terms of the reliability of ranking of the best alternatives. The Routing Decision Support (RDS) algorithm is trying to improve some of their deficiencies. This paper gives a mathematical verification that the RDS algorithm conforms to the test criteria for an effective MCDM method when a linear preference function is considered.

Keywords: Decision support systems, linear preference function, multi-criteria decision-making algorithm, analytic hierarchy process.

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Authors: Parham Azimi, Hamid Reza Charmchi

Abstract:

In this research, we have developed a new efficient heuristic algorithm for the dynamic facility layout problem with budget constraint (DFLPB). This heuristic algorithm combines two mathematical programming methods such as discrete event simulation and linear integer programming (IP) to obtain a near optimum solution. In the proposed algorithm, the non-linear model of the DFLP has been changed to a pure integer programming (PIP) model. Then, the optimal solution of the PIP model has been used in a simulation model that has been designed in a similar manner as the DFLP for determining the probability of assigning a facility to a location. After a sufficient number of runs, the simulation model obtains near optimum solutions. Finally, to verify the performance of the algorithm, several test problems have been solved. The results show that the proposed algorithm is more efficient in terms of speed and accuracy than other heuristic algorithms presented in previous works found in the literature.

Keywords: Budget constraint, Dynamic facility layout problem, Integer programming, Simulation

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Authors: S. Abdourraziq, R. El Bachtiri

Abstract:

The use of solar energy as a source for pumping water is one of the promising areas in the photovoltaic (PV) application. The energy of photovoltaic pumping systems (PVPS) can be widely improved by employing an MPPT algorithm. This will lead consequently to maximize the electrical motor speed of the system. This paper presents a modified incremental conductance (IncCond) MPPT algorithm with direct control method applied to a standalone PV pumping system. The influence of the algorithm parameters on system behavior is investigated and compared with the traditional (INC) method. The studied system consists of a PV panel, a DC-DC boost converter, and a PMDC motor-pump. The simulation of the system by MATLAB-SIMULINK is carried out. Simulation results found are satisfactory.

Keywords: Photovoltaic pumping system (PVPS), incremental conductance (INC), MPPT algorithm, boost converter.

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Authors: Taehyun Yoon, Keechul Jung

Abstract:

There are many researches to detect collision between real object and virtual object in 3D space. In general, these techniques are need to huge computing power. So, many research and study are constructed by using cloud computing, network computing, and distribute computing. As a reason of these, this paper proposed a novel fast 3D collision detection algorithm between real and virtual object using 2D intersection area. Proposed algorithm uses 4 multiple cameras and coarse-and-fine method to improve accuracy and speed performance of collision detection. In the coarse step, this system examines the intersection area between real and virtual object silhouettes from all camera views. The result of this step is the index of virtual sensors which has a possibility of collision in 3D space. To decide collision accurately, at the fine step, this system examines the collision detection in 3D space by using the visual hull algorithm. Performance of the algorithm is verified by comparing with existing algorithm. We believe proposed algorithm help many other research, study and application fields such as HCI, augmented reality, intelligent space, and so on.

Keywords: Collision Detection, Computer Vision, Human Computer Interaction, Visual Hull

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Authors: Vahid Hajipour, Samira V. Noshafagh, Reza Tavakkoli-Moghaddam

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This article proposes a novel Pareto-based multiobjective meta-heuristic algorithm named non-dominated ranking genetic algorithm (NRGA) to solve multi-facility location-allocation problem. In NRGA, a fitness value representing rank is assigned to each individual of the population. Moreover, two features ranked based roulette wheel selection including select the fronts and choose solutions from the fronts, are utilized. The proposed solving methodology is validated using several examples taken from the specialized literature. The performance of our approach shows that NRGA algorithm is able to generate true and well distributed Pareto optimal solutions.

Keywords: Non-dominated ranking genetic algorithm, Pareto solutions, Multi-facility location-allocation problem.

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Authors: Sana Ktata, Kaïs Ouni, Noureddine Ellouze

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Electrocardiogram (ECG) data compression algorithm is needed that will reduce the amount of data to be transmitted, stored and analyzed, but without losing the clinical information content. A wavelet ECG data codec based on the Set Partitioning In Hierarchical Trees (SPIHT) compression algorithm is proposed in this paper. The SPIHT algorithm has achieved notable success in still image coding. We modified the algorithm for the one-dimensional (1-D) case and applied it to compression of ECG data. By this compression method, small percent root mean square difference (PRD) and high compression ratio with low implementation complexity are achieved. Experiments on selected records from the MIT-BIH arrhythmia database revealed that the proposed codec is significantly more efficient in compression and in computation than previously proposed ECG compression schemes. Compression ratios of up to 48:1 for ECG signals lead to acceptable results for visual inspection.

Keywords: Discrete Wavelet Transform, ECG compression, SPIHT.

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Authors: A. Andreasyan, C. Connors

Abstract:

The Elliptic Curve Digital Signature algorithm-based X509v3 certificates are becoming more popular due to their short public and private key sizes. Moreover, these certificates can be stored in Internet of Things (IoT) devices, with limited resources, using less memory and transmitted in network security protocols, such as Internet Key Exchange (IKE), Transport Layer Security (TLS) and Secure Shell (SSH) with less bandwidth. The proposed method gives another advantage, in that it increases the performance of the above-mentioned protocols in terms of key exchange by saving one scalar multiplication operation.

Keywords: Cryptography, elliptic curve digital signature algorithm, key exchange, network security protocols.

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Authors: Ioannis P. Panapakidis, Marios N. Moschakis

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With the continuous increment of smart meter installations across the globe, the need for processing of the load data is evident. Clustering-based load profiling is built upon the utilization of unsupervised machine learning tools for the purpose of formulating the typical load curves or load profiles. The most commonly used algorithm in the load profiling literature is the K-means. While the algorithm has been successfully tested in a variety of applications, its drawback is the strong dependence in the initialization phase. This paper proposes a novel modified form of the K-means that addresses the aforementioned problem. Simulation results indicate the superiority of the proposed algorithm compared to the K-means.

Keywords: Clustering, load profiling, load modeling, machine learning, energy efficiency and quality.

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Authors: Hichem Sassi, Tawfik Najeh, Noureddine Liouane

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Information of nodes’ locations is an important criterion for lots of applications in Wireless Sensor Networks. In the hop-based range-free localization methods, anchors transmit the localization messages counting a hop count value to the whole network. Each node receives this message and calculates its own distance with anchor in hops and then approximates its own position. However the estimative distances can provoke large error, and affect the localization precision. To solve the problem, this paper proposes an algorithm, which makes the unknown nodes fix the nearest anchor as a reference and select two other anchors which are the most accurate to achieve the estimated location. Compared to the DV-Hop algorithm, experiment results illustrate that proposed algorithm has less average localization error and is more effective.

Keywords: Wireless Sensors Networks, Localization problem, localization average error, DV–Hop Algorithm, MATLAB.

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Authors: S. Karabulut, A. Güllü, A. Güldas, R. Gürbüz

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This study investigates the effects of the lead angle and chip thickness variation on surface roughness during the machining of compacted graphite iron using ceramic cutting tools under dry cutting conditions. Analytical models were developed for predicting the surface roughness values of the specimens after the face milling process. Experimental data was collected and imported to the artificial neural network model. A multilayer perceptron model was used with the back propagation algorithm employing the input parameters of lead angle, cutting speed and feed rate in connection with chip thickness. Furthermore, analysis of variance was employed to determine the effects of the cutting parameters on surface roughness. Artificial neural network and regression analysis were used to predict surface roughness. The values thus predicted were compared with the collected experimental data, and the corresponding percentage error was computed. Analysis results revealed that the lead angle is the dominant factor affecting surface roughness. Experimental results indicated an improvement in the surface roughness value with decreasing lead angle value from 88° to 45°.

Keywords: CGI, milling, surface roughness, ANN, regression, modeling, analysis.

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Authors: Y. Wang

Abstract:

The Traveling salesman problem (TSP) is NP-hard in combinatorial optimization. The research shows the algorithms for TSP on the sparse graphs have the shorter computation time than those for TSP according to the complete graphs. We present an improved iterative algorithm to compute the sparse graphs for TSP by frequency graphs computed with frequency quadrilaterals. The iterative algorithm is enhanced by adjusting two parameters of the algorithm. The computation time of the algorithm is O(CN_maxn²) where C is the iterations, N_max is the maximum number of frequency quadrilaterals containing each edge and n is the scale of TSP. The experimental results showed the computed sparse graphs generally have less than 5n edges for most of these Euclidean instances. Moreover, the maximum degree and minimum degree of the vertices in the sparse graphs do not have much difference. Thus, the computation time of the methods to resolve the TSP on these sparse graphs will be greatly reduced.

Keywords: Frequency quadrilateral, iterative algorithm, sparse graph, traveling salesman problem.

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Authors: Buntara Sthenly Gan, Naohiro Kawada

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A simple and easy algorithm is presented for a fast calculation of kernel functions which required in fluid simulations using the Smoothed Particle Hydrodynamic (SPH) method. Present proposed algorithm improves the Linked-list algorithm and adopts the Pair-Wise Interaction technique, which are widely used for evaluating kernel functions in fluid simulations using the SPH method. The algorithm is easy to be implemented without any complexities in programming. Some benchmark examples are used to show the simulation time saved by using the proposed algorithm. Parametric studies on the number of divisions for sub-domains, smoothing length and total amount of particles are conducted to show the effectiveness of the present technique. A compact formulation is proposed for practical usage.

Keywords: Technique, fluid simulation, smoothing particle hydrodynamic (SPH), particle interaction.

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Authors: Rajkishore Prasad, Hiroshi Saruwatari, Kiyohiro Shikano

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This paper describes Independent Component Analysis (ICA) based fixed-point algorithm for the blind separation of the convolutive mixture of speech, picked-up by a linear microphone array. The proposed algorithm extracts independent sources by non- Gaussianizing the Time-Frequency Series of Speech (TFSS) in a deflationary way. The degree of non-Gaussianization is measured by negentropy. The relative performances of algorithm under random initialization and Null beamformer (NBF) based initialization are studied. It has been found that an NBF based initial value gives speedy convergence as well as better separation performance

Keywords: Blind signal separation, independent component analysis, negentropy, convolutive mixture.

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Authors: Mariyam Arif, Ye Liu, Israr Ul Haq, Ahsan Ashfaq

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High cost of fossil fuels and intensifying installations of alternate energy generation sources are intimidating main challenges in power systems. Making accurate load forecasting an important and challenging task for optimal energy planning and management at both distribution and generation side. There are many techniques to forecast load but each technique comes with its own limitation and requires data to accurately predict the forecast load. Artificial Neural Network (ANN) is one such technique to efficiently forecast the load. Comparison between two different ranges of input datasets has been applied to dynamic ANN technique using MATLAB Neural Network Toolbox. It has been observed that selection of input data on training of a network has significant effects on forecasted results. Day-wise input data forecasted the load accurately as compared to year-wise input data. The forecasted load is then distributed among the six generators by using the linear programming to get the optimal point of generation. The algorithm is then verified by comparing the results of each generator with their respective generation limits.

Keywords: Artificial neural networks, demand-side management, economic dispatch, linear programming, power generation dispatch.

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Authors: Fernanda M. Assef, Maria Teresinha A. Steiner

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The aim of this paper is to compare and discuss better classifier algorithm options for credit risk assessment by applying different Machine Learning techniques. Using records from a Brazilian financial institution, this study uses a database of 5,432 companies that are clients of the bank, where 2,600 clients are classified as non-defaulters, 1,551 are classified as defaulters and 1,281 are temporarily defaulters, meaning that the clients are overdue on their payments for up 180 days. For each case, a total of 15 attributes was considered for a one-against-all assessment using four different techniques: Artificial Neural Networks Multilayer Perceptron (ANN-MLP), Artificial Neural Networks Radial Basis Functions (ANN-RBF), Logistic Regression (LR) and finally Support Vector Machines (SVM). For each method, different parameters were analyzed in order to obtain different results when the best of each technique was compared. Initially the data were coded in thermometer code (numerical attributes) or dummy coding (for nominal attributes). The methods were then evaluated for each parameter and the best result of each technique was compared in terms of accuracy, false positives, false negatives, true positives and true negatives. This comparison showed that the best method, in terms of accuracy, was ANN-RBF (79.20% for non-defaulter classification, 97.74% for defaulters and 75.37% for the temporarily defaulter classification). However, the best accuracy does not always represent the best technique. For instance, on the classification of temporarily defaulters, this technique, in terms of false positives, was surpassed by SVM, which had the lowest rate (0.07%) of false positive classifications. All these intrinsic details are discussed considering the results found, and an overview of what was presented is shown in the conclusion of this study.

Keywords: Artificial Neural Networks, ANNs, classifier algorithms, credit risk assessment, logistic regression, machine learning, support vector machines.

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Authors: Belkacem Selma, Boumediene Selma, Samira Chouraqui, Hanifi Missoum, Tourkia Guerzou

Abstract:

Natural disasters have occurred and will continue to cause human and material damage. Therefore, the idea of "preventing" natural disasters will never be possible. However, their prediction is possible with the advancement of technology. Even if natural disasters are effectively inevitable, their consequences may be partly controlled. The rapid growth and progress of artificial intelligence (AI) had a major impact on the prediction of natural disasters and risk assessment which are necessary for effective disaster reduction. Earthquake prediction to prevent the loss of human lives and even property damage is an important factor; that, is why it is crucial to develop techniques for predicting this natural disaster. This study aims to analyze the ability of artificial neural networks (ANNs) to predict earthquakes that occur in a given area. The used data describe the problem of high energy (higher than 104 J) seismic bumps forecasting in a coal mine using two long walls as an example. For this purpose, seismic bumps data obtained from mines have been analyzed. The results obtained show that the ANN is able to predict earthquake parameters with  high accuracy; the classification accuracy through neural networks is more than 94%, and the models developed are efficient and robust and depend only weakly on the initial database.

Keywords: Earthquake prediction, artificial intelligence, AI, Artificial Neural Network, ANN, seismic bumps.

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Authors: Avishai Sintov, Roland Menassa, Amir Shapiro

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Industrial robotic arms utilize multiple end-effectors, each for a specific part and for a specific task. We propose a novel algorithm which will define a single end-effector’s configuration able to grasp a given set of objects with different geometries. The algorithm will have great benefit in production lines allowing a single robot to grasp various parts. Hence, reducing the number of endeffectors needed. Moreover, the algorithm will reduce end-effector design and manufacturing time and final product cost. The algorithm searches for a common grasp over the set of objects. The search algorithm maps all possible grasps for each object which satisfy a quality criterion and takes into account possible external wrenches (forces and torques) applied to the object. The mapped grasps are- represented by high-dimensional feature vectors which describes the shape of the gripper. We generate a database of all possible grasps for each object in the feature space. Then we use a search and classification algorithm for intersecting all possible grasps over all parts and finding a single common grasp suitable for all objects. We present simulations of planar and spatial objects to validate the feasibility of the approach.

Keywords: Common Grasping, Search Algorithm, Robotic End-Effector.

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Authors: Mohamed E. Salem Abozaed

Abstract:

Detection and classification of power quality (PQ) disturbances is an important consideration to electrical utilities and many industrial customers so that diagnosis and mitigation of such disturbance can be implemented quickly. S-transform algorithm and continuous wavelet transforms (CWT) are time-frequency algorithms, and both of them are powerful in detection and classification of PQ disturbances. This paper presents detection and classification of PQ disturbances using S-transform and CWT algorithms. The results of detection and classification, provides that S-transform is more accurate in detection and classification for most PQ disturbance than CWT algorithm, where as CWT algorithm more powerful in detection in some disturbances like notching

Keywords: CWT, Disturbances classification, Disturbances detection, Power quality, S-transform.

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Authors: Thomas Fuhrmann

Abstract:

A new fast correlation algorithm for calibrating the wavelength of Optical Spectrum Analyzers (OSAs) was introduced in [1]. The minima of acetylene gas spectra were measured and correlated with saved theoretical data [2]. So it is possible to find the correct wavelength calibration data using a noisy reference spectrum. First tests showed good algorithmic performance for gas line spectra with high noise. In this article extensive performance tests were made to validate the noise resistance of this algorithm. The filter and correlation parameters of the algorithm were optimized for improved noise performance. With these parameters the performance of this wavelength calibration was simulated to predict the resulting wavelength error in real OSA systems. Long term simulations were made to evaluate the performance of the algorithm over the lifetime of a real OSA.

Keywords: correlation, gas reference, optical spectrum analyzer, wavelength calibration

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Authors: Lokendra Singh Umrao, Ravi Shankar Singh

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This paper presents an optimal broadcast algorithm for the hypercube networks. The main focus of the paper is the effectiveness of the algorithm in the presence of many node faults. For the optimal solution, our algorithm builds with spanning tree connecting the all nodes of the networks, through which messages are propagated from source node to remaining nodes. At any given time, maximum n − 1 nodes may fail due to crashing. We show that the hypercube networks are strongly fault-tolerant. Simulation results analyze to accomplish algorithm characteristics under many node faults. We have compared our simulation results between our proposed method and the Fu’s method. Fu’s approach cannot tolerate n − 1 faulty nodes in the worst case, but our approach can tolerate n − 1 faulty nodes.

Keywords: Fault tolerance, hypercube, broadcasting, link/node faults, routing.

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Authors: Mattheos K. Protopapas, Elias B. Kosmatopoulos

Abstract:

An iterative algorithm is proposed and tested in Cournot Game models, which is based on the convergence of sequential best responses and the utilization of a genetic algorithm for determining each player-s best response to a given strategy profile of its opponents. An extra outer loop is used, to address the problem of finite accuracy, which is inherent in genetic algorithms, since the set of feasible values in such an algorithm is finite. The algorithm is tested in five Cournot models, three of which have convergent best replies sequence, one with divergent sequential best replies and one with “local NE traps"[14], where classical local search algorithms fail to identify the Nash Equilibrium. After a series of simulations, we conclude that the algorithm proposed converges to the Nash Equilibrium, with any level of accuracy needed, in all but the case where the sequential best replies process diverges.

Keywords: Best response, Cournot oligopoly, genetic algorithms, Nash equilibrium.

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Authors: Wissem Saidani, Yacine Morsly, Mohand Saïd Djouadi

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In this paper, we consider the problem of tracking multiple maneuvering targets using switching multiple target motion models. With this paper, we aim to contribute in solving the problem of model-based body motion estimation by using data coming from visual sensors. The Interacting Multiple Model (IMM) algorithm is specially designed to track accurately targets whose state and/or measurement (assumed to be linear) models changes during motion transition. However, when these models are nonlinear, the IMM algorithm must be modified in order to guarantee an accurate track. In this paper we propose to avoid the Extended Kalman filter because of its limitations and substitute it with the Unscented Kalman filter which seems to be more efficient especially according to the simulation results obtained with the nonlinear IMM algorithm (IMMUKF). To resolve the problem of data association, the JPDA approach is combined with the IMM-UKF algorithm, the derived algorithm is noted JPDA-IMM-UKF.

Keywords: Estimation, Kalman filtering, Multi-Target Tracking, Visual servoing, data association.

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Authors: Nnamdi I. Nwulu, Shola G. Oroja

Abstract:

It has become crucial over the years for nations to improve their credit scoring methods and techniques in light of the increasing volatility of the global economy. Statistical methods or tools have been the favoured means for this; however artificial intelligence or soft computing based techniques are becoming increasingly preferred due to their proficient and precise nature and relative simplicity. This work presents a comparison between Support Vector Machines and Artificial Neural Networks two popular soft computing models when applied to credit scoring. Amidst the different criteria-s that can be used for comparisons; accuracy, computational complexity and processing times are the selected criteria used to evaluate both models. Furthermore the German credit scoring dataset which is a real world dataset is used to train and test both developed models. Experimental results obtained from our study suggest that although both soft computing models could be used with a high degree of accuracy, Artificial Neural Networks deliver better results than Support Vector Machines.

Keywords: Artificial Neural Networks, Credit Scoring, SoftComputing Models, Support Vector Machines.

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Authors: Tesnim Charrad, Kaouther Nouira, Ahmed Ferchichi

Abstract:

In order to reduce the number of deaths due to heart problems, we propose the use of Hierarchical Temporal Memory Algorithm (HTM) which is a real time anomaly detection algorithm. HTM is a cortical learning algorithm based on neocortex used for anomaly detection. In other words, it is based on a conceptual theory of how the human brain can work. It is powerful in predicting unusual patterns, anomaly detection and classification. In this paper, HTM have been implemented and tested on ECG datasets in order to detect cardiac anomalies. Experiments showed good performance in terms of specificity, sensitivity and execution time.

Keywords: HTM, Real time anomaly detection, ECG, Cardiac Anomalies.

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Authors: M. Sinecen, M. Makinacı

Abstract:

The purpose of this paper is to assess the value of neural networks for classification of cancer and noncancer prostate cells. Gauss Markov Random Fields, Fourier entropy and wavelet average deviation features are calculated from 80 noncancer and 80 cancer prostate cell nuclei. For classification, artificial neural network techniques which are multilayer perceptron, radial basis function and learning vector quantization are used. Two methods are utilized for multilayer perceptron. First method has single hidden layer and between 3-15 nodes, second method has two hidden layer and each layer has between 3-15 nodes. Overall classification rate of 86.88% is achieved.

Keywords: Artificial neural networks, texture classification, cancer diagnosis.

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Authors: Farhad Hadinejad, Hasan Saberi, Saeed Kazem

Abstract:

Support vector clustering (SVC) is an important kernelbased clustering algorithm in multi applications. It has got two main bottle necks, the high computation price and labeling piece. In this paper, we presented a modified SVC method, named Grid–SVC, to improve the original algorithm computationally. First we normalized and then we parted the interval, where the SVC is processing, using a novel Grid–based clustering algorithm. The algorithm parts the intervals, based on the density function of the data set and then applying the cartesian multiply makes multi-dimensional grids. Eliminating many outliers and noise in the preprocess, we apply an improved SVC method to each parted grid in a parallel way. The experimental results show both improvement in time complexity order and the accuracy.

Keywords: Grid–based clustering, SVC, Density function, Radial basis function.

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Authors: Zohreh O. Akbari

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In this paper a deterministic polynomial-time algorithm is presented for the Clique problem. The case is considered as the problem of omitting the minimum number of vertices from the input graph so that none of the zeroes on the graph-s adjacency matrix (except the main diagonal entries) would remain on the adjacency matrix of the resulting subgraph. The existence of a deterministic polynomial-time algorithm for the Clique problem, as an NP-complete problem will prove the equality of P and NP complexity classes.

Keywords: Clique problem, Deterministic Polynomial-time Algorithm, Equality of P and NP Complexity Classes.

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