Search results for: least square support vector machine.

Authors: Esther T. Akinlabi, Stephen A. Akinlabi

Abstract:

The design of temperature measuring approach for a re-configured milling machine to produce friction stir welds is reported in this paper. The product design specifications for the redesigning of a milling machine were first outlined and the ranking criteria were determined. Three different concepts were generated for the temperature measurement on the reconfigured system and the preferred or the best concept was selected based on the set design ranking criteria. Further simulation and performance analysis was then conducted on the concept. The Infrared Thermography (IRT) concept was selected for the temperature measurement among other concepts generated because it is an ideal and most effective system of measurement in this regard.

Keywords: Clamping system, Friction Stir Welding, Reconfiguration, Support systems.

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Authors: J. S. Kim, N. P. Hong

Abstract:

In this paper, a CMOS vector modulator designed for wireless backhaul system based on 802.11ac is presented. A poly phase filter and sign select switches yield two orthogonal signal paths. Two variable gain amplifiers with strongly reduced phase shift of only ±5 ° are used to weight these paths. It has a phase control range of 360 ° and a gain range of -10 dB to 10 dB. The current drawn from a 1.2 V supply amounts 20.4 mA. Using a 0.13 mm technology, the chip die area amounts 1.47x0.75 mm².

Keywords: CMOS, vector modulator, backhaul, 802.11ac.

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Authors: Kanda Runapongsa Saikaew, Chaluemwut Noyunsan

Abstract:

Nowadays social media information, such as news, links, images, or VDOs, is shared extensively. However, the effectiveness of disseminating information through social media lacks in quality: less fact checking, more biases, and several rumors. Many researchers have investigated about credibility on Twitter, but there is no the research report about credibility information on Facebook. This paper proposes features for measuring credibility on Facebook information. We developed the system for credibility on Facebook. First, we have developed FB credibility evaluator for measuring credibility of each post by manual human’s labelling. We then collected the training data for creating a model using Support Vector Machine (SVM). Secondly, we developed a chrome extension of FB credibility for Facebook users to evaluate the credibility of each post. Based on the usage analysis of our FB credibility chrome extension, about 81% of users’ responses agree with suggested credibility automatically computed by the proposed system.

Keywords: Facebook, social media, credibility measurement.

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Authors: Roman Graf, Sergiu Gordea, Heather M. Ryan

Abstract:

This paper presents an approach for easy creation and classification of institutional risk profiles supporting endangerment analysis of file formats. The main contribution of this work is the employment of data mining techniques to support set up of the most important risk factors. Subsequently, risk profiles employ risk factors classifier and associated configurations to support digital preservation experts with a semi-automatic estimation of endangerment group for file format risk profiles. Our goal is to make use of an expert knowledge base, accuired through a digital preservation survey in order to detect preservation risks for a particular institution. Another contribution is support for visualisation of risk factors for a requried dimension for analysis. Using the naive Bayes method, the decision support system recommends to an expert the matching risk profile group for the previously selected institutional risk profile. The proposed methods improve the visibility of risk factor values and the quality of a digital preservation process. The presented approach is designed to facilitate decision making for the preservation of digital content in libraries and archives using domain expert knowledge and values of file format risk profiles. To facilitate decision-making, the aggregated information about the risk factors is presented as a multidimensional vector. The goal is to visualise particular dimensions of this vector for analysis by an expert and to define its profile group. The sample risk profile calculation and the visualisation of some risk factor dimensions is presented in the evaluation section.

Keywords: linked open data, information integration, digital libraries, data mining.

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Authors: Mais Nijim, Rama Devi Chennuboyina, Waseem Al Aqqad

Abstract:

Advances in spatial and spectral resolution of satellite images have led to tremendous growth in large image databases. The data we acquire through satellites, radars, and sensors consists of important geographical information that can be used for remote sensing applications such as region planning, disaster management. Spatial data classification and object recognition are important tasks for many applications. However, classifying objects and identifying them manually from images is a difficult task. Object recognition is often considered as a classification problem, this task can be performed using machine-learning techniques. Despite of many machine-learning algorithms, the classification is done using supervised classifiers such as Support Vector Machines (SVM) as the area of interest is known. We proposed a classification method, which considers neighboring pixels in a region for feature extraction and it evaluates classifications precisely according to neighboring classes for semantic interpretation of region of interest (ROI). A dataset has been created for training and testing purpose; we generated the attributes by considering pixel intensity values and mean values of reflectance. We demonstrated the benefits of using knowledge discovery and data-mining techniques, which can be on image data for accurate information extraction and classification from high spatial resolution remote sensing imagery.

Keywords: Remote sensing, object recognition, classification, data mining, waterbody identification, feature extraction.

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Authors: Randhir Singh Baghel

Abstract:

In this study, the fundamental ideas guiding the dynamic area of machine learning—where models thrive and algorithms change over time—are rooted in an innate mathematical link. This study explores the fundamental ideas that drive the development of intelligent systems, providing light on the mutually beneficial link between mathematics and machine learning.

Keywords: Machine Learning, deep learning, Neural Network, optimization.

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Authors: Laila Y. Fannas, Ahmed Y. Ben Sasi

Abstract:

This research presents a handwritten signature recognition based on angle feature vector using Artificial Neural Network (ANN). Each signature image will be represented by an Angle vector. The feature vector will constitute the input to the ANN. The collection of signature images will be divided into two sets. One set will be used for training the ANN in a supervised fashion. The other set which is never seen by the ANN will be used for testing. After training, the ANN will be tested for recognition of the signature. When the signature is classified correctly, it is considered correct recognition otherwise it is a failure.

Keywords: Signature Recognition, Artificial Neural Network, Angle Features.

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Authors: Mihaela Popescu, Alexandru Bitoleanu, Mircea Dobriceanu

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This paper deals with the current space-vector decomposition in three-phase, three-wire systems on the basis of some case studies. We propose four components of the current spacevector in terms of DC and AC components of the instantaneous active and reactive powers. The term of supplementary useless current vector is also pointed out. The analysis shows that the current decomposition which respects the definition of the instantaneous apparent power vector is useful for compensation reasons only if the supply voltages are sinusoidal. A modified definition of the components of the current is proposed for the operation under nonsinusoidal voltage conditions.

Keywords: Active current, Active filtering, p–q theory, Reactive current.

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Authors: Ahmad Tariq Sheikh, Shahzad Amin Sheikh

Abstract:

A new distance-adjusted approach is proposed in which static square contours are defined around an estimated symbol in a QAM constellation, which create regions that correspond to fixed step sizes and weighting factors. As a result, the equalizer tap adjustment consists of a linearly weighted sum of adaptation criteria that is scaled by a variable step size. This approach is the basis of two new algorithms: the Variable step size Square Contour Algorithm (VSCA) and the Variable step size Square Contour Decision-Directed Algorithm (VSDA). The proposed schemes are compared with existing blind equalization algorithms in the SCA family in terms of convergence speed, constellation eye opening and residual ISI suppression. Simulation results for 64-QAM signaling over empirically derived microwave radio channels confirm the efficacy of the proposed algorithms. An RTL implementation of the blind adaptive equalizer based on the proposed schemes is presented and the system is configured to operate in VSCA error signal mode, for square QAM signals up to 64-QAM.

Keywords: Adaptive filtering, Blind Equalization, Square Contour Algorithm.

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Authors: Hani M. Aburas

Abstract:

“Dengue" is an African word meaning “bone breaking" because it causes severe joint and muscle pain that feels like bones are breaking. It is an infectious disease mainly transmitted by female mosquito, Aedes aegypti, and causes four serotypes of dengue viruses. In recent years, a dramatic increase in the dengue fever confirmed cases around the equator-s belt has been reported. Several conventional indices have been designed so far to monitor the transmitting vector populations known as House Index (HI), Container Index (CI), Breteau Index (BI). However, none of them describes the adult mosquito population size which is important to direct and guide comprehensive control strategy operations since number of infected people has a direct relationship with the vector density. Therefore, it is crucial to know the population size of the transmitting vector in order to design a suitable and effective control program. In this context, a study is carried out to report a new statistical index, ABURAS Index, using Poisson distribution based on the collection of vector population in Jeddah Governorate, Saudi Arabia.

Keywords: Poisson distribution, statistical index, prediction, Aedes aegypti.

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Authors: Kanthida Kusonmano, Michael Netzer, Bernhard Pfeifer, Christian Baumgartner, Klaus R. Liedl, Armin Graber

Abstract:

Availability of high dimensional biological datasets such as from gene expression, proteomic, and metabolic experiments can be leveraged for the diagnosis and prognosis of diseases. Many classification methods in this area have been studied to predict disease states and separate between predefined classes such as patients with a special disease versus healthy controls. However, most of the existing research only focuses on a specific dataset. There is a lack of generic comparison between classifiers, which might provide a guideline for biologists or bioinformaticians to select the proper algorithm for new datasets. In this study, we compare the performance of popular classifiers, which are Support Vector Machine (SVM), Logistic Regression, k-Nearest Neighbor (k-NN), Naive Bayes, Decision Tree, and Random Forest based on mock datasets. We mimic common biological scenarios simulating various proportions of real discriminating biomarkers and different effect sizes thereof. The result shows that SVM performs quite stable and reaches a higher AUC compared to other methods. This may be explained due to the ability of SVM to minimize the probability of error. Moreover, Decision Tree with its good applicability for diagnosis and prognosis shows good performance in our experimental setup. Logistic Regression and Random Forest, however, strongly depend on the ratio of discriminators and perform better when having a higher number of discriminators.

Keywords: Classification, High dimensional data, Machine learning

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Authors: A. Biran, P. Sobhe Bidari, A. Almazroe V. Lakshminarayanan, K. Raahemifar

Abstract:

Diabetic Retinopathy (DR) is a severe retinal disease which is caused by diabetes mellitus. It leads to blindness when it progress to proliferative level. Early indications of DR are the appearance of microaneurysms, hemorrhages and hard exudates. In this paper, an automatic algorithm for detection of DR has been proposed. The algorithm is based on combination of several image processing techniques including Circular Hough Transform (CHT), Contrast Limited Adaptive Histogram Equalization (CLAHE), Gabor filter and thresholding. Also, Support Vector Machine (SVM) Classifier is used to classify retinal images to normal or abnormal cases including non-proliferative or proliferative DR. The proposed method has been tested on images selected from Structured Analysis of the Retinal (STARE) database using MATLAB code. The method is perfectly able to detect DR. The sensitivity specificity and accuracy of this approach are 90%, 87.5%, and 91.4% respectively.

Keywords: Diabetic retinopathy, fundus images, STARE, Gabor filter, SVM.

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Authors: Abdelwahed Echchatbi, Adil Rizki, Ali Haddi, Nabil Mrani, Noureddine Elalami

Abstract:

In this note, the robust static output feedback stabilisation of an induction machine is addressed. The machine is described by a non homogenous bilinear model with structural uncertainties, and the feedback gain is computed via an iterative LMI (ILMI) algorithm.

Keywords: Induction machine, Static output feedback, robust stabilisation.

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Authors: A. Niknejad, G. H. Liaghat, A. H. Behravesh, H. Moslemi Naeini

Abstract:

In this paper, a semi empirical formula is presented based on the experimental results to predict the first pick (maximum force) value in the instantaneous folding force- axial distance diagram of a square column. To achieve this purpose, the maximum value of the folding force was assumed to be a function of the average folding force. Using the experimental results, the maximum value of the force necessary to initiate the first fold in a square column was obtained with respect to the geometrical quantities and material properties. Finally, the results obtained from the semi empirical relation in this paper, were compared to the experimental results which showed a good correlation.

Keywords: Honeycomb, folding force, square column, aluminum, axial loading.

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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: Pradeep Singh, Sukhwinder Singh, Gurjinder Kaur

Abstract:

In recent years, rapid advances in software and hardware in the field of information technology along with a digital imaging revolution in the medical domain facilitate the generation and storage of large collections of images by hospitals and clinics. To search these large image collections effectively and efficiently poses significant technical challenges, and it raises the necessity of constructing intelligent retrieval systems. Content-based Image Retrieval (CBIR) consists of retrieving the most visually similar images to a given query image from a database of images[5]. Medical CBIR (content-based image retrieval) applications pose unique challenges but at the same time offer many new opportunities. On one hand, while one can easily understand news or sports videos, a medical image is often completely incomprehensible to untrained eyes.

Keywords: Classification, clustering, content-based image retrieval (CBIR), relevance feedback (RF), statistical similarity matching, support vector machine (SVM).

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Authors: Xin H. Zou, Qiang Wang

Abstract:

The comparisons of two typical fluidic thrust vectoring exhaust nozzles including two-dimensional(2-D) nozzle and axisymmetric nozzle on aerodynamic characteristics was presented by numerical simulation. The results show: the thrust vector angles increased with the increasing secondary flow but decreased with the nozzle pressure ratio (NPR) increasing. With the same secondary flow and NPR, the thrust vector angles of 2-D nozzle were higher than the axisymmetric nozzle-s. So with the lower NPR and more secondary weight flow, the much higher thrust vector angle was caused by 2-D fluidic nozzle. And with the higher NPR and less secondary weight flow, there was not much difference in angular dimension between two nozzles.

Keywords: Aerodynamic characteristics, fluidic nozzle, vector angle, thrust coefficient comparison.

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Authors: P. Sawatnatee, S. Udomsuk, K-N. Areerak, K-L. Areerak, A. Srikaew

Abstract:

The paper presents how to design the indirect vector control of three-phase induction motor drive systems using the artificial intelligence technique called the adaptive tabu search. The results from the simulation and the experiment show that the drive system with the controller designed from the proposed method can provide the best output speed response compared with those of the conventional method. The controller design using the proposed technique can be used to create the software package for engineers to achieve the optimal controller design of the induction motor speed control based on the indirect vector concept.

 

Keywords: Indirect Vector Control, Induction Motor, Adaptive Tabu Search, Control Design, Artificial Intelligence.

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Authors: Abdul Amir Hazbavi

Abstract:

The present study is an attempt to provide a relatively comprehensive preview of the Iranian English translators’ perception on Machine Translation. Furthermore, the study tries to shed light on the status of implementation of Machine Translation among the Iranian English Translators. To reach the aforementioned objectives, the Localization Industry Standards Association’s questioner for measuring perceptions with regard to the adoption of a technology innovation was adapted and used to investigate the perception and implementation of Machine Translation applications by the Iranian English language translators. The participants of the study were 224 last-year undergraduate Iranian students of English translation at 10 universities across the country. The study revealed a very low level of adoption and a very high level of willingness to get familiar with and learn about Machine Translation, as well as a positive perception of and attitude toward Machine Translation by the Iranian English translators.

Keywords: Translation Technology, Machine Translation, Perception and Implementation.

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Authors: M. Aghili, S. Tabarestani, C. Freytes, M. Shojaie, M. Cabrerizo, A. Barreto, N. Rishe, R. E. Curiel, D. Loewenstein, R. Duara, M. Adjouadi

Abstract:

A major challenge in medical studies, especially those that are longitudinal, is the problem of missing measurements which hinders the effective application of many machine learning algorithms. Furthermore, recent Alzheimer's Disease studies have focused on the delineation of Early Mild Cognitive Impairment (EMCI) and Late Mild Cognitive Impairment (LMCI) from cognitively normal controls (CN) which is essential for developing effective and early treatment methods. To address the aforementioned challenges, this paper explores the potential of using the eXtreme Gradient Boosting (XGBoost) algorithm in handling missing values in multiclass classification. We seek a generalized classification scheme where all prodromal stages of the disease are considered simultaneously in the classification and decision-making processes. Given the large number of subjects (1631) included in this study and in the presence of almost 28% missing values, we investigated the performance of XGBoost on the classification of the four classes of AD, NC, EMCI, and LMCI. Using 10-fold cross validation technique, XGBoost is shown to outperform other state-of-the-art classification algorithms by 3% in terms of accuracy and F-score. Our model achieved an accuracy of 80.52%, a precision of 80.62% and recall of 80.51%, supporting the more natural and promising multiclass classification.

Keywords: eXtreme Gradient Boosting, missing data, Alzheimer disease, early mild cognitive impairment, late mild cognitive impairment, multiclass classification, ADNI, support vector machine, random forest.

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Authors: Jixin Liu, Zheming Lu

Abstract:

In this paper, a novel multipurpose audio watermarking algorithm is proposed based on Vector Quantization (VQ) in Discrete Cosine Transform (DCT) domain using the codeword labeling and index-bit constrained method. By using this algorithm, it can fulfill the requirements of both the copyright protection and content integrity authentication at the same time for the multimedia artworks. The robust watermark is embedded in the middle frequency coefficients of the DCT transform during the labeled codeword vector quantization procedure. The fragile watermark is embedded into the indices of the high frequency coefficients of the DCT transform by using the constrained index vector quantization method for the purpose of integrity authentication of the original audio signals. Both the robust and the fragile watermarks can be extracted without the original audio signals, and the simulation results show that our algorithm is effective with regard to the transparency, robustness and the authentication requirements

Keywords: Copyright Protection, Discrete Cosine Transform, Integrity Authentication, Multipurpose Audio Watermarking, Vector Quantization.

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Authors: K.Somasundaram, S.Domnic

Abstract:

A low bit rate still image compression scheme by compressing the indices of Vector Quantization (VQ) and generating residual codebook is proposed. The indices of VQ are compressed by exploiting correlation among image blocks, which reduces the bit per index. A residual codebook similar to VQ codebook is generated that represents the distortion produced in VQ. Using this residual codebook the distortion in the reconstructed image is removed, thereby increasing the image quality. Our scheme combines these two methods. Experimental results on standard image Lena show that our scheme can give a reconstructed image with a PSNR value of 31.6 db at 0.396 bits per pixel. Our scheme is also faster than the existing VQ variants.

Keywords: Image compression, Vector Quantization, Residual Codebook.

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Authors: Mrs.K.Kavitha, S.Arivazhagan

Abstract:

A spatial classification technique incorporating a State of Art Feature Extraction algorithm is proposed in this paper for classifying a heterogeneous classes present in hyper spectral images. The classification accuracy can be improved if and only if both the feature extraction and classifier selection are proper. As the classes in the hyper spectral images are assumed to have different textures, textural classification is entertained. Run Length feature extraction is entailed along with the Principal Components and Independent Components. A Hyperspectral Image of Indiana Site taken by AVIRIS is inducted for the experiment. Among the original 220 bands, a subset of 120 bands is selected. Gray Level Run Length Matrix (GLRLM) is calculated for the selected forty bands. From GLRLMs the Run Length features for individual pixels are calculated. The Principle Components are calculated for other forty bands. Independent Components are calculated for next forty bands. As Principal & Independent Components have the ability to represent the textural content of pixels, they are treated as features. The summation of Run Length features, Principal Components, and Independent Components forms the Combined Features which are used for classification. SVM with Binary Hierarchical Tree is used to classify the hyper spectral image. Results are validated with ground truth and accuracies are calculated.

Keywords: Multi-class, Run Length features, PCA, ICA, classification and Support Vector Machines.

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Authors: Hsian Ming Goo

Abstract:

The paper concerns a special approximate algorithm of the square root of the specific positive integer, which is built by the use of the property of positive integer solution of the Pell’s equation, together with using some elementary theorems of matrices, and then takes it to compare with general used the Newton’s method and give a practical numerical example and error analysis; it is unexpected to find its special property: the significant figure of the approximation value of the square root of positive integer will increase one digit by one. It is well useful in some occasions.

Keywords: Special approximate algorithm, square root, Pell’s equation, Newton’s method, error analysis.

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Authors: A. Tellaeche, X. P. Burgos-Artizzu, G. Pajares, A. Ribeiro

Abstract:

One important objective in Precision Agriculture is to minimize the volume of herbicides that are applied to the fields through the use of site-specific weed management systems. In order to reach this goal, two major factors need to be considered: 1) the similar spectral signature, shape and texture between weeds and crops; 2) the irregular distribution of the weeds within the crop's field. This paper outlines an automatic computer vision system for the detection and differential spraying of Avena sterilis, a noxious weed growing in cereal crops. The proposed system involves two processes: image segmentation and decision making. Image segmentation combines basic suitable image processing techniques in order to extract cells from the image as the low level units. Each cell is described by two area-based attributes measuring the relations among the crops and the weeds. From these attributes, a hybrid decision making approach determines if a cell must be or not sprayed. The hybrid approach uses the Support Vector Machines and the Fuzzy k-Means methods, combined through the fuzzy aggregation theory. This makes the main finding of this paper. The method performance is compared against other available strategies.

Keywords: Fuzzy k-Means, Precision agriculture, SupportVectors Machines, Weed detection.

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Authors: Irtaza M. Syed, Kaamran Raahemifar

Abstract:

In this paper, we present a comparative assessment of Space Vector Pulse Width Modulation (SVPWM) and Model Predictive Control (MPC) for two-level three phase (2L-3P) Voltage Source Inverter (VSI). VSI with associated system is subjected to both control techniques and the results are compared. Matlab/Simulink was used to model, simulate and validate the control schemes. Findings of this study show that MPC is superior to SVPWM in terms of total harmonic distortion (THD) and implementation.

Keywords: Model Predictive Control, Space Vector Pulse Width Modulation, Voltage Source Inverter.

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Authors: S. Esakkirajan, T. Veerakumar, V. Senthil Murugan, P. Navaneethan

Abstract:

The existing image coding standards generally degrades at low bit-rates because of the underlying block based Discrete Cosine Transform scheme. Over the past decade, the success of wavelets in solving many different problems has contributed to its unprecedented popularity. Due to implementation constraints scalar wavelets do not posses all the properties such as orthogonality, short support, linear phase symmetry, and a high order of approximation through vanishing moments simultaneously, which are very much essential for signal processing. New class of wavelets called 'Multiwavelets' which posses more than one scaling function overcomes this problem. This paper presents a new image coding scheme based on non linear approximation of multiwavelet coefficients along with multistage vector quantization. The performance of the proposed scheme is compared with the results obtained from scalar wavelets.

Keywords: Image compression, Multiwavelets, Multi-stagevector quantization.

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Authors: Quratulain N. Rajput, Sajjad Haider

Abstract:

This paper applies Bayesian Networks to support information extraction from unstructured, ungrammatical, and incoherent data sources for semantic annotation. A tool has been developed that combines ontologies, machine learning, and information extraction and probabilistic reasoning techniques to support the extraction process. Data acquisition is performed with the aid of knowledge specified in the form of ontology. Due to the variable size of information available on different data sources, it is often the case that the extracted data contains missing values for certain variables of interest. It is desirable in such situations to predict the missing values. The methodology, presented in this paper, first learns a Bayesian network from the training data and then uses it to predict missing data and to resolve conflicts. Experiments have been conducted to analyze the performance of the presented methodology. The results look promising as the methodology achieves high degree of precision and recall for information extraction and reasonably good accuracy for predicting missing values.

Keywords: Information Extraction, Bayesian Network, ontology, Machine Learning

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Authors: A. Larabi, M. S. Boucherit

Abstract:

In this paper, we show that the association of the PI regulators for the speed and stator currents with a control strategy using the linearization by state feedback for an induction machine without speed sensor, and with an adaptation of the rotor resistance. The rotor speed is estimated by using the model reference adaptive system approach (MRAS). This method consists of using two models: The first is the reference model and the second is an adjustable one in which two components of the stator flux, obtained from the measurement of the currents and stator voltages are estimated. The estimated rotor speed is then obtained by canceling the difference between stator-flux of the reference model and those of the adjustable one. Satisfactory results of simulation are obtained and discussed in this paper to highlight the proposed approach.

Keywords: Asynchronous actuator, PI Regulator, adaptivemethod with reference model, Vector control.

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Authors: Marian Gaiceanu, Emil Rosu

Abstract:

In this paper the optimal control strategy for Permanent Magnet Synchronous Motor (PMSM) based drive system is presented. The designed full optimal control is available for speed operating range up to base speed. The optimal voltage space-vector assures input energy reduction and stator loss minimization, maintaining the output energy in the same limits with the conventional PMSM electrical drive. The optimal control with three components is based on the energetically criteria and it is applicable in numerical version, being a nonrecursive solution. The simulation results confirm the increased efficiency of the optimal PMSM drive. The properties of the optimal voltage space vector are shown.

Keywords: Matlab/Simulink, optimal control, permanent magnet synchronous motor, Riccati equation, space vector PWM

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