Search results for: generalized regression neural networks

Authors: Mohammad Ali Jabraeil Jamali, Ahmad Khademzadeh, Hasan Asil, Amir Asil

Abstract:

This method decrease usage power (expenditure) in networks on chips (NOC). This method data coding for data transferring in order to reduces expenditure. This method uses data compression reduces the size. Expenditure calculation in NOC occurs inside of NOC based on grown models and transitive activities in entry ports. The goal of simulating is to weigh expenditure for encoding, decoding and compressing in Baseline networks and reduction of switches in this type of networks. KeywordsNetworks on chip, Compression, Encoding, Baseline networks, Banyan networks.

Keywords: Networks on chip, Compression, Encoding, Baseline networks, Banyan networks

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Authors: Kesari Verma, Aniruddha S. Thoke, Pritam Singh

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Automatic face detection is a complex problem in image processing. Many methods exist to solve this problem such as template matching, Fisher Linear Discriminate, Neural Networks, SVM, and MRC. Success has been achieved with each method to varying degrees and complexities. In proposed algorithm we used upright, frontal faces for single gray scale images with decent resolution and under good lighting condition. In the field of face recognition technique the single face is matched with single face from the training dataset. The author proposed a neural network based face detection algorithm from the photographs as well as if any test data appears it check from the online scanned training dataset. Experimental result shows that the algorithm detected up to 95% accuracy for any image.

Keywords: Face Detection, Face Recognition, NN Approach, PCA Algorithm.

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Authors: Marque Adrien, Delahaye Daniel, Marechal Pierre, Berry Isabelle

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Wind direction and uncertainty are crucial in aircraft or unmanned aerial vehicle trajectories. By computing wind covariance matrices on each spatial grid point, these spatial grids can be defined as images with symmetric positive definite matrix elements. A data pre-processing step, a specific convolution, a specific max-pooling, and specific flatten layers are implemented to process such images. Then, the neural network is applied to spatial grids, whose elements are wind covariance matrices, to solve classification problems related to the feasibility of unmanned aerial vehicles based on wind direction and wind uncertainty.

Keywords: Wind direction, uncertainty level, Unmanned Aerial Vehicle, convolution neural network, SPD matrices.

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Authors: R. J. Kuo, W. C. Cheng, W. C. Lien, T. J. Yang

Abstract:

Taiwan is a hyper endemic area for the Hepatitis B virus (HBV). The estimated total number of HBsAg carriers in the general population who are more than 20 years old is more than 3 million. Therefore, a case record review is conducted from January 2003 to June 2007 for all patients with a diagnosis of acute hepatitis who were admitted to the Emergency Department (ED) of a well-known teaching hospital. The cost for the use of medical resources is defined as the total medical fee. In this study, principal component analysis (PCA) is firstly employed to reduce the number of dimensions. Support vector regression (SVR) and artificial neural network (ANN) are then used to develop the forecasting model. A total of 117 patients meet the inclusion criteria. 61% patients involved in this study are hepatitis B related. The computational result shows that the proposed PCA-SVR model has superior performance than other compared algorithms. In conclusion, the Child-Pugh score and echogram can both be used to predict the cost of medical resources for patients with acute hepatitis in the ED.

Keywords: Acute hepatitis, Medical resource cost, Artificial neural network, Support vector regression.

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Authors: Kelong Zheng, Jinsong Hu,

Abstract:

In this paper, numerical solution for the generalized Rosenau-Burgers equation is considered and Crank-Nicolson finite difference scheme is proposed. Existence of the solutions for the difference scheme has been shown. Stability, convergence and priori error estimate of the scheme are proved. Numerical results demonstrate that the scheme is efficient and reliable.

Keywords: Generalized Rosenau-Burgers equation, difference scheme, stability, convergence.

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Authors: Panagiotis Karadimos, Leonidas Anthopoulos

Abstract:

Predicting the actual cost and duration in construction projects concern a continuous and existing problem for the construction sector. This paper addresses this problem with modern methods and data available from past public construction projects. 39 bridge projects, constructed in Greece, with a similar type of available data were examined. Considering each project’s attributes with the actual cost and the actual duration, correlation analysis is performed and the most appropriate predictive project variables are defined. Additionally, the most efficient subgroup of variables is selected with the use of the WEKA application, through its attribute selection function. The selected variables are used as input neurons for neural network models through correlation analysis. For constructing neural network models, the application FANN Tool is used. The optimum neural network model, for predicting the actual cost, produced a mean squared error with a value of 3.84886e-05 and it was based on the budgeted cost and the quantity of deck concrete. The optimum neural network model, for predicting the actual duration, produced a mean squared error with a value of 5.89463e-05 and it also was based on the budgeted cost and the amount of deck concrete.

Keywords: Actual cost and duration, attribute selection, bridge projects, neural networks, predicting models, FANN TOOL, WEKA.

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Authors: Z. Zainuddin, W. K. Lye

Abstract:

In this paper, a clustering algorithm named KHarmonic means (KHM) was employed in the training of Radial Basis Function Networks (RBFNs). KHM organized the data in clusters and determined the centres of the basis function. The popular clustering algorithms, namely K-means (KM) and Fuzzy c-means (FCM), are highly dependent on the initial identification of elements that represent the cluster well. In KHM, the problem can be avoided. This leads to improvement in the classification performance when compared to other clustering algorithms. A comparison of the classification accuracy was performed between KM, FCM and KHM. The classification performance is based on the benchmark data sets: Iris Plant, Diabetes and Breast Cancer. RBFN training with the KHM algorithm shows better accuracy in classification problem.

Keywords: Neural networks, Radial basis functions, Clusteringmethod, K-harmonic means.

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Authors: Vassilis S. Kodogiannis, John N. Lygouras

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In this research study, an intelligent detection system to support medical diagnosis and detection of abnormal lesions by processing endoscopic images is presented. The images used in this study have been obtained using the M2A Swallowable Imaging Capsule - a patented, video color-imaging disposable capsule. Schemes have been developed to extract texture features from the fuzzy texture spectra in the chromatic and achromatic domains for a selected region of interest from each color component histogram of endoscopic images. The implementation of an advanced fuzzy inference neural network which combines fuzzy systems and artificial neural networks and the concept of fusion of multiple classifiers dedicated to specific feature parameters have been also adopted in this paper. The achieved high detection accuracy of the proposed system has provided thus an indication that such intelligent schemes could be used as a supplementary diagnostic tool in endoscopy.

Keywords: Medical imaging, Computer aided diagnosis, Endoscopy, Neuro-fuzzy networks, Fuzzy integral.

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Authors: Shu-Xin Miao

Abstract:

In this note, we discuss the convergence behavior of a modified inexact Uzawa algorithm for solving generalized saddle point problems, which is an extension of the result obtained in a recent paper [Z.H. Cao, Fast Uzawa algorithm for generalized saddle point problems, Appl. Numer. Math., 46 (2003) 157-171].

Keywords: Saddle point problem, inexact Uzawa algorithm, convergence behavior.

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Authors: A.H. Akhaveissy

Abstract:

Nonlinear finite element method and Serendipity eight nodes element are used for determining of ground surface settlement due to tunneling. Linear element with elastic behavior is used for modeling of lining. Modified Generalized plasticity model with nonassociated flow rule is applied for analysis of a tunnel in Sao Paulo – Brazil. The tunnel had analyzed by Lades- model with 16 parameters. In this work modified Generalized Plasticity is used with 10 parameters, also Mohr-Coulomb model is used to analysis the tunnel. The results show good agreement with observed results of field data by modified Generalized Plasticity model than other models. The obtained result by Mohr-Coulomb model shows less settlement than other model due to excavation.

Keywords: Non-associated flow rule, Generalized plasticity, tunnel excavation, Excavation method.

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Authors: Commander Sunil Tyagi

Abstract:

Effectiveness of Artificial Neural Networks (ANN) and Support Vector Machines (SVM) classifiers for fault diagnosis of rolling element bearings are presented in this paper. The characteristic features of vibration signals of rotating driveline that was run in its normal condition and with faults introduced were used as input to ANN and SVM classifiers. Simple statistical features such as standard deviation, skewness, kurtosis etc. of the time-domain vibration signal segments along with peaks of the signal and peak of power spectral density (PSD) are used as features to input the ANN and SVM classifier. The effect of preprocessing of the vibration signal by Discreet Wavelet Transform (DWT) prior to feature extraction is also studied. It is shown from the experimental results that the performance of SVM classifier in identification of bearing condition is better then ANN and pre-processing of vibration signal by DWT enhances the effectiveness of both ANN and SVM classifier

Keywords: ANN, Artificial Intelligence, Fault Diagnosis, Pattern Recognition, Rolling Element Bearing, SVM. Wavelet Transform

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Authors: Rachid Ahdid, Said Safi, Bouzid Manaut

Abstract:

In this paper, we present a comparative study of three methods of 2D face recognition system such as: Iso-Geodesic Curves (IGC), Geodesic Distance (GD) and Geodesic-Intensity Histogram (GIH). These approaches are based on computing of geodesic distance between points of facial surface and between facial curves. In this study we represented the image at gray level as a 2D surface in a 3D space, with the third coordinate proportional to the intensity values of pixels. In the classifying step, we use: Neural Networks (NN), K-Nearest Neighbor (KNN) and Support Vector Machines (SVM). The images used in our experiments are from two wellknown databases of face images ORL and YaleB. ORL data base was used to evaluate the performance of methods under conditions where the pose and sample size are varied, and the database YaleB was used to examine the performance of the systems when the facial expressions and lighting are varied.

Keywords: 2D face recognition, Geodesic distance, Iso-Geodesic Curves, Geodesic-Intensity Histogram, facial surface, Neural Networks, K-Nearest Neighbor, Support Vector Machines.

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Authors: Nadia Hmad, Tony Allen

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This paper presents an ESN-based Arabic phoneme recognition system trained with supervised, forced and combined supervised/forced supervised learning algorithms. Mel-Frequency Cepstrum Coefficients (MFCCs) and Linear Predictive Code (LPC) techniques are used and compared as the input feature extraction technique. The system is evaluated using 6 speakers from the King Abdulaziz Arabic Phonetics Database (KAPD) for Saudi Arabia dialectic and 34 speakers from the Center for Spoken Language Understanding (CSLU2002) database of speakers with different dialectics from 12 Arabic countries. Results for the KAPD and CSLU2002 Arabic databases show phoneme recognition performances of 72.31% and 38.20% respectively.

Keywords: Arabic phonemes recognition, echo state networks (ESNs), neural networks (NNs), supervised learning.

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Authors: Hira Lal Gope, Hidekazu Fukai

Abstract:

The aim of this study is to develop a system which can identify and sort peaberries automatically at low cost for coffee producers in developing countries. In this paper, the focus is on the classification of peaberries and normal coffee beans using image processing and machine learning techniques. The peaberry is not bad and not a normal bean. The peaberry is born in an only single seed, relatively round seed from a coffee cherry instead of the usual flat-sided pair of beans. It has another value and flavor. To make the taste of the coffee better, it is necessary to separate the peaberry and normal bean before green coffee beans roasting. Otherwise, the taste of total beans will be mixed, and it will be bad. In roaster procedure time, all the beans shape, size, and weight must be unique; otherwise, the larger bean will take more time for roasting inside. The peaberry has a different size and different shape even though they have the same weight as normal beans. The peaberry roasts slower than other normal beans. Therefore, neither technique provides a good option to select the peaberries. Defect beans, e.g., sour, broken, black, and fade bean, are easy to check and pick up manually by hand. On the other hand, the peaberry pick up is very difficult even for trained specialists because the shape and color of the peaberry are similar to normal beans. In this study, we use image processing and machine learning techniques to discriminate the normal and peaberry bean as a part of the sorting system. As the first step, we applied Deep Convolutional Neural Networks (CNN) and Support Vector Machine (SVM) as machine learning techniques to discriminate the peaberry and normal bean. As a result, better performance was obtained with CNN than with SVM for the discrimination of the peaberry. The trained artificial neural network with high performance CPU and GPU in this work will be simply installed into the inexpensive and low in calculation Raspberry Pi system. We assume that this system will be used in under developed countries. The study evaluates and compares the feasibility of the methods in terms of accuracy of classification and processing speed.

Keywords: Convolutional neural networks, coffee bean, peaberry, sorting, support vector machine.

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Authors: Nermine Ahmed Hendy, Hania Farag

Abstract:

Emotion recognition is an important research field that finds lots of applications nowadays. This work emphasizes on recognizing different emotions from speech signal. The extracted features are related to statistics of pitch, formants, and energy contours, as well as spectral, perceptual and temporal features, jitter, and shimmer. The Artificial Neural Networks (ANN) was chosen as the classifier. Working on finding a robust and fast ANN classifier suitable for different real life application is our concern. Several experiments were carried out on different ANN to investigate the different factors that impact the classification success rate. Using a database containing 7 different emotions, it will be shown that with a proper and careful adjustment of features format, training data sorting, number of features selected and even the ANN type and architecture used, a success rate of 85% or even more can be achieved without increasing the system complicity and the computation time

Keywords: Classification, emotion recognition, features extraction, feature selection, neural network

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Authors: Fatemeh Mosalman Yazdi

Abstract:

One of the most important requirements for the operation and planning activities of an electrical utility is the prediction of load for the next hour to several days out, known as short term load forecasting. This paper presents the development of an artificial neural network based short-term load forecasting model. The model can forecast daily load profiles with a load time of one day for next 24 hours. In this method can divide days of year with using average temperature. Groups make according linearity rate of curve. Ultimate forecast for each group obtain with considering weekday and weekend. This paper investigates effects of temperature and humidity on consuming curve. For forecasting load curve of holidays at first forecast pick and valley and then the neural network forecast is re-shaped with the new data. The ANN-based load models are trained using hourly historical. Load data and daily historical max/min temperature and humidity data. The results of testing the system on data from Yazd utility are reported.

Keywords: Artificial neural network, Holiday forecasting, pickand valley load forecasting, Short-term load-forecasting.

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Authors: Xiaochuan Chen, Jianguo Yang, Beizhi Li

Abstract:

Design for cost (DFC) is a method that reduces life cycle cost (LCC) from the angle of designers. Multiple domain features mapping (MDFM) methodology was given in DFC. Using MDFM, we can use design features to estimate the LCC. From the angle of DFC, the design features of family cars were obtained, such as all dimensions, engine power and emission volume. At the conceptual design stage, cars- LCC were estimated using back propagation (BP) artificial neural networks (ANN) method and case-based reasoning (CBR). Hamming space was used to measure the similarity among cases in CBR method. Levenberg-Marquardt (LM) algorithm and genetic algorithm (GA) were used in ANN. The differences of LCC estimation model between CBR and artificial neural networks (ANN) were provided. ANN and CBR separately each method has its shortcomings. By combining ANN and CBR improved results accuracy was obtained. Firstly, using ANN selected some design features that affect LCC. Then using LCC estimation results of ANN could raise the accuracy of LCC estimation in CBR method. Thirdly, using ANN estimate LCC errors and correct errors in CBR-s estimation results if the accuracy is not enough accurate. Finally, economically family cars and sport utility vehicle (SUV) was given as LCC estimation cases using this hybrid approach combining ANN and CBR.

Keywords: case-based reasoning, life cycle cost (LCC), artificialneural networks (ANN), family cars

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Authors: Hidehiko Okada

Abstract:

The author proposes an extension of particle swarm optimization (PSO) for solving interval-valued optimization problems and applies the extended PSO to evolutionary training of neural networks (NNs) with interval weights. In the proposed PSO, values in the genotypes are not real numbers but intervals. Experimental results show that interval-valued NNs trained by the proposed method could well approximate hidden target functions despite the fact that no training data was explicitly provided.

Keywords: Evolutionary algorithms, swarm intelligence, particle swarm optimization, neural network, interval arithmetic.

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Authors: Jianmin Xing

Abstract:

Let T,U and V be rings with identity and M be a unitary (T,U)-bimodule, N be a unitary (U, V )- bimodule, D be a unitary (T, V )-bimodule . We characterize homomorphisms and isomorphisms of the generalized matrix ring Γ =  T M D 0 U N 0 0 V .

Keywords: Generalized module homomorphism, ring homomorphism, isomorphisms, triangular matrix rings.

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Authors: Orhan Feyzioğlu, Gülçin Büyüközkan

Abstract:

As a vital activity for companies, new product development (NPD) is also a very risky process due to the high uncertainty degree encountered at every development stage and the inevitable dependence on how previous steps are successfully accomplished. Hence, there is an apparent need to evaluate new product initiatives systematically and make accurate decisions under uncertainty. Another major concern is the time pressure to launch a significant number of new products to preserve and increase the competitive power of the company. In this work, we propose an integrated decision-making framework based on neural networks and fuzzy logic to make appropriate decisions and accelerate the evaluation process. We are especially interested in the two initial stages where new product ideas are selected (go/no go decision) and the implementation order of the corresponding projects are determined. We show that this two-staged intelligent approach allows practitioners to roughly and quickly separate good and bad product ideas by making use of previous experiences, and then, analyze a more shortened list rigorously.

Keywords: Decision Making, Neural Networks, Fuzzy Theory and Systems, Choquet Integral, New Product Development.

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Authors: Inam Shamsher, Zaheer Ahmad, Jehanzeb Khan Orakzai, Awais Adnan

Abstract:

This paper deals with an Optical Character Recognition system for printed Urdu, a popular Pakistani/Indian script and is the third largest understandable language in the world, especially in the subcontinent but fewer efforts are made to make it understandable to computers. Lot of work has been done in the field of literature and Islamic studies in Urdu, which has to be computerized. In the proposed system individual characters are recognized using our own proposed method/ algorithms. The feature detection methods are simple and robust. Supervised learning is used to train the feed forward neural network. A prototype of the system has been tested on printed Urdu characters and currently achieves 98.3% character level accuracy on average .Although the system is script/ language independent but we have designed it for Urdu characters only.

Keywords: Algorithm, Feed Forward Neural Networks, Supervised learning, Pattern Matching.

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Authors: Sandeep Chandana, Rene V. Mayorga

Abstract:

The paper presents a new hybridization methodology involving Neural, Fuzzy and Rough Computing. A Rough Sets based approximation technique has been proposed based on a certain Neuro – Fuzzy architecture. A New Rough Neuron composition consisting of a combination of a Lower Bound neuron and a Boundary neuron has also been described. The conventional convergence of error in back propagation has been given away for a new framework based on 'Output Excitation Factor' and an inverse input transfer function. The paper also presents a brief comparison of performances, of the existing Rough Neural Networks and ANFIS architecture against the proposed methodology. It can be observed that the rough approximation based neuro-fuzzy architecture is superior to its counterparts.

Keywords: Boundary neuron, neuro-fuzzy, output excitation factor, RANFIS, rough approximation, rough neural computing.

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Authors: Atena Sajedin, Shokoufeh Zakernejad, Soheil Faridi, Mehrdad Javadi, Reza Ebrahimpour

Abstract:

This paper illustrates the use of a combined neural network model for classification of electrocardiogram (ECG) beats. We present a trainable neural network ensemble approach to develop customized electrocardiogram beat classifier in an effort to further improve the performance of ECG processing and to offer individualized health care. We process a three stage technique for detection of premature ventricular contraction (PVC) from normal beats and other heart diseases. This method includes a denoising, a feature extraction and a classification. At first we investigate the application of stationary wavelet transform (SWT) for noise reduction of the electrocardiogram (ECG) signals. Then feature extraction module extracts 10 ECG morphological features and one timing interval feature. Then a number of multilayer perceptrons (MLPs) neural networks with different topologies are designed. The performance of the different combination methods as well as the efficiency of the whole system is presented. Among them, Stacked Generalization as a proposed trainable combined neural network model possesses the highest recognition rate of around 95%. Therefore, this network proves to be a suitable candidate in ECG signal diagnosis systems. ECG samples attributing to the different ECG beat types were extracted from the MIT-BIH arrhythmia database for the study.

Keywords: ECG beat Classification; Combining Classifiers;Premature Ventricular Contraction (PVC); Multi Layer Perceptrons;Wavelet Transform

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Authors: Daniela Matei, Radu Matei

Abstract:

In this paper a class of analog algorithms based on the concept of Cellular Neural Network (CNN) is applied in some processing operations of some important medical images, namely retina images, for detecting various symptoms connected with diabetic retinopathy. Some specific processing tasks like morphological operations, linear filtering and thresholding are proposed, the corresponding template values are given and simulations on real retina images are provided.

Keywords: Diabetic retinopathy, pathology detection, cellular neural networks, analog algorithms.

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Authors: Samia Salah, M’hamed Hadj Sadok, Abderrezak Guessoum

Abstract:

In this paper, we propose a new modular approach called neuroglial consisting of two neural networks slow and fast which emulates a biological reality recently discovered. The implementation is based on complex multi-time scale systems; validation is performed on the model of the asynchronous machine. We applied the geometric approach based on the Gerschgorin circles for the decoupling of fast and slow variables, and the method of singular perturbations for the development of reductions models.

This new architecture allows for smaller networks with less complexity and better performance in terms of mean square error and convergence than the single network model.

Keywords: Gerschgorin’s Circles, Neuroglial Network, Multi time scales systems, Singular perturbation method.

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Authors: A. M. Pashayev, D. D. Askerov, C. Ardil, R. A. Sadiqov, P. S. Abdullayev

Abstract:

Researches show that probability-statistical methods application, especially at the early stage of the aviation Gas Turbine Engine (GTE) technical condition diagnosing, when the flight information has property of the fuzzy, limitation and uncertainty is unfounded. Hence the efficiency of application of new technology Soft Computing at these diagnosing stages with the using of the Fuzzy Logic and Neural Networks methods is considered. According to the purpose of this problem training with high accuracy of fuzzy multiple linear and non-linear models (fuzzy regression equations) which received on the statistical fuzzy data basis is made. For GTE technical condition more adequate model making dynamics of skewness and kurtosis coefficients- changes are analysed. Researches of skewness and kurtosis coefficients values- changes show that, distributions of GTE work parameters have fuzzy character. Hence consideration of fuzzy skewness and kurtosis coefficients is expedient. Investigation of the basic characteristics changes- dynamics of GTE work parameters allows drawing conclusion on necessity of the Fuzzy Statistical Analysis at preliminary identification of the engines' technical condition. Researches of correlation coefficients values- changes shows also on their fuzzy character. Therefore for models choice the application of the Fuzzy Correlation Analysis results is offered. At the information sufficiency is offered to use recurrent algorithm of aviation GTE technical condition identification (Hard Computing technology is used) on measurements of input and output parameters of the multiple linear and non-linear generalised models at presence of noise measured (the new recursive Least Squares Method (LSM)). The developed GTE condition monitoring system provides stageby- stage estimation of engine technical conditions. As application of the given technique the estimation of the new operating aviation engine technical condition was made.

Keywords: aviation gas turbine engine, technical condition, fuzzy logic, neural networks, fuzzy statistics

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Authors: Jihan Abdulazeez Ahmed, Adnan Mohsin Abdulazeez Brifcani

Abstract:

This paper suggests a new internal architecture of holon based on feature selection model using the combination of Bees Algorithm (BA) and Artificial Neural Network (ANN). BA is used to generate features while ANN is used as a classifier to evaluate the produced features. Proposed system is applied on the Wine dataset, the statistical result proves that the proposed system is effective and has the ability to choose informative features with high accuracy.

Keywords: Artificial Neural Networks, Holonic Approach, Feature Selection, Bee Algorithm.

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Authors: Thejaswi H. Raya, Vineetha Bettaiah, Heggere S. Ranganath

Abstract:

For over a decade, the Pulse Coupled Neural Network (PCNN) based algorithms have been successfully used in image interpretation applications including image segmentation. There are several versions of the PCNN based image segmentation methods, and the segmentation accuracy of all of them is very sensitive to the values of the network parameters. Most methods treat PCNN parameters like linking coefficient and primary firing threshold as global parameters, and determine them by trial-and-error. The automatic determination of appropriate values for linking coefficient, and primary firing threshold is a challenging problem and deserves further research. This paper presents a method for obtaining global as well as local values for the linking coefficient and the primary firing threshold for neurons directly from the image statistics. Extensive simulation results show that the proposed approach achieves excellent segmentation accuracy comparable to the best accuracy obtainable by trial-and-error for a variety of images.

Keywords: Automatic Selection of PCNN Parameters, Image Segmentation, Neural Networks, Pulse Coupled Neural Network

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Authors: Debabrata Mandal

Abstract:

The aim of this paper is to define several operations such as Intersection, Union, OR, AND operations of intuitionistic (resp. generalized) neutrosophic soft sets in the sense of Maji and compare these with intuitionistic (resp. generalized) neutrosophic soft sets in the sense of Said et al via examples. At the end of the paper, a new concept - extension is introduced, which can be used to refine our choices in case of decision making.

Keywords: AND, OR, Union, Intersection, Extension, Decision making.

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Authors: Yahya H. Zweiri

Abstract:

The back-propagation algorithm calculates the weight changes of an artificial neural network, and a two-term algorithm with a dynamically optimal learning rate and a momentum factor is commonly used. Recently the addition of an extra term, called a proportional factor (PF), to the two-term BP algorithm was proposed. The third term increases the speed of the BP algorithm. However, the PF term also reduces the convergence of the BP algorithm, and optimization approaches for evaluating the learning parameters are required to facilitate the application of the three terms BP algorithm. This paper considers the optimization of the new back-propagation algorithm by using derivative information. A family of approaches exploiting the derivatives with respect to the learning rate, momentum factor and proportional factor is presented. These autonomously compute the derivatives in the weight space, by using information gathered from the forward and backward procedures. The three-term BP algorithm and the optimization approaches are evaluated using the benchmark XOR problem.

Keywords: Neural Networks, Backpropagation, Optimization.

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