Search results for: features engineering methods for forecasting

Authors: A.Tajaddini

Abstract:

In this paper, two matrix iterative methods are presented to solve the matrix equation A1X1B1 + A2X2B2 + ... + AlXlBl = C the minimum residual problem l i=1 AiXiBi−CF = minXi∈BRni×ni l i=1 AiXiBi−CF and the matrix nearness problem [X1, X2, ..., Xl] = min[X1,X2,...,Xl]∈SE [X1,X2, ...,Xl] − [X1, X2, ..., Xl]F , where BRni×ni is the set of bisymmetric matrices, and SE is the solution set of above matrix equation or minimum residual problem. These matrix iterative methods have faster convergence rate and higher accuracy than former methods. Paige’s algorithms are used as the frame method for deriving these matrix iterative methods. The numerical example is used to illustrate the efficiency of these new methods.

Keywords: Bisymmetric matrices, Paige’s algorithms, Least square.

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Authors: S. Kotsiantis, A. Kostoulas, S. Lykoudis, A. Argiriou, K. Menagias

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Estimates of temperature values at a specific time of day, from daytime and daily profiles, are needed for a number of environmental, ecological, agricultural and technical applications, ranging from natural hazards assessments, crop growth forecasting to design of solar energy systems. The scope of this research is to investigate the efficiency of data mining techniques in estimating minimum, maximum and mean temperature values. For this reason, a number of experiments have been conducted with well-known regression algorithms using temperature data from the city of Patras in Greece. The performance of these algorithms has been evaluated using standard statistical indicators, such as Correlation Coefficient, Root Mean Squared Error, etc.

Keywords: regression algorithms, supervised machine learning.

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Authors: S. Sendilkumar, B. L. Mathur, Joseph Henry

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A new approach for protection of power transformer is presented using a time-frequency transform known as Wavelet transform. Different operating conditions such as inrush, Normal, load, External fault and internal fault current are sampled and processed to obtain wavelet coefficients. Different Operating conditions provide variation in wavelet coefficients. Features like energy and Standard deviation are calculated using Parsevals theorem. These features are used as inputs to PNN (Probabilistic neural network) for fault classification. The proposed algorithm provides more accurate results even in the presence of noise inputs and accurately identifies inrush and fault currents. Overall classification accuracy of the proposed method is found to be 96.45%. Simulation of the fault (with and without noise) was done using MATLAB AND SIMULINK software taking 2 cycles of data window (40 m sec) containing 800 samples. The algorithm was evaluated by using 10 % Gaussian white noise.

Keywords: Power Transformer, differential Protection, internalfault, inrush current, Wavelet Energy, Db9.

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Authors: Yue Zhao, Jianping Li

Abstract:

This paper covers the present situation and problem of experimental teaching of mathematics specialty in recent years, puts forward and demonstrates experimental teaching methods for different education. From the aspects of content and experimental teaching approach, uses as an example the course “Experiment for Program Designing & Algorithmic Language" and discusses teaching practice and laboratory course work. In addition a series of successful methods and measures are introduced in experimental teaching.

Keywords: Differentiated teaching, experimental teaching, program design and algorithmic language, teaching method.

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Authors: G. Venkata Hari Prasad, P. Rajesh Kumar

Abstract:

Phonocardiography is important in appraisal of congenital heart disease and pulmonary hypertension as it reflects the duration of right ventricular systoles. The systolic murmur in patients with intra-cardiac shunt decreases as pulmonary hypertension develops and may eventually disappear completely as the pulmonary pressure reaches systemic level. Phonocardiography and auscultation are non-invasive, low-cost, and accurate methods to assess heart disease. In this work an objective signal processing tool to extract information from phonocardiography signal using Wavelet is proposed to classify the murmur as normal or abnormal. Since the feature vector is large, a Binary Particle Swarm Optimization (PSO) with mutation for feature selection is proposed. The extracted features improve the classification accuracy and were tested across various classifiers including Naïve Bayes, kNN, C4.5, and SVM.

Keywords: Phonocardiography, Coiflet, Feature selection, Particle Swarm Optimization.

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Authors: Tatiana A. Dolenko, Sergey A. Burikov, Alexander O. Efitorov, Sergey A. Dolenko

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In this study, a comparative analysis of the approaches associated with the use of neural network algorithms for effective solution of a complex inverse problem – the problem of identifying and determining the individual concentrations of inorganic salts in multicomponent aqueous solutions by the spectra of Raman scattering of light – is performed. It is shown that application of artificial neural networks provides the average accuracy of determination of concentration of each salt no worse than 0.025 M. The results of comparative analysis of input data compression methods are presented. It is demonstrated that use of uniform aggregation of input features allows decreasing the error of determination of individual concentrations of components by 16-18% on the average.

Keywords: Inverse problems, multi-component solutions, neural networks, Raman spectroscopy.

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Authors: R. Sridevi, G. Jagajothi

Abstract:

Artificial Immune Systems (AIS), inspired by the human immune system, are algorithms and mechanisms which are self-adaptive and self-learning classifiers capable of recognizing and classifying by learning, long-term memory and association. Unlike other human system inspired techniques like genetic algorithms and neural networks, AIS includes a range of algorithms modeling on different immune mechanism of the body. In this paper, a mechanism of a human immune system based on apoptosis is adopted to build an Intrusion Detection System (IDS) to protect computer networks. Features are selected from network traffic using Fisher Score. Based on the selected features, the record/connection is classified as either an attack or normal traffic by the proposed methodology. Simulation results demonstrates that the proposed AIS based on apoptosis performs better than existing AIS for intrusion detection.

Keywords: Apoptosis, Artificial Immune System (AIS), Fisher Score, KDD dataset, Network intrusion detection.

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Authors: Qiu Chen, Koji Kotani, Feifei Lee, Tadahiro Ohmi

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In this paper, we propose an improved face recognition algorithm using histogram-based features in spatial and frequency domains. For adding spatial information of the face to improve recognition performance, a region-division (RD) method is utilized. The facial area is firstly divided into several regions, then feature vectors of each facial part are generated by Binary Vector Quantization (BVQ) histogram using DCT coefficients in low frequency domains, as well as Local Binary Pattern (LBP) histogram in spatial domain. Recognition results with different regions are first obtained separately and then fused by weighted averaging. Publicly available ORL database is used for the evaluation of our proposed algorithm, which is consisted of 40 subjects with 10 images per subject containing variations in lighting, posing, and expressions. It is demonstrated that face recognition using RD method can achieve much higher recognition rate.

Keywords: Face recognition, Binary vector quantization (BVQ), Local Binary Patterns (LBP), DCT coefficients.

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Authors: Shiann-Shiun Jeng, Chen-Wan Tsung, Hong-You Liou, Chun-Chieh Chang, Jia-Ming Chen

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The coverage probability and range of IEEE 802.16 systems depend on different wireless scenarios. Evaluating the performance of IEEE 802.16 systems over Stanford University Interim (SUI) channels is suggested by IEEE 802.16 specifications. In order to derive an effective method for forecasting the coverage probability and range, this study uses the SUI channel model to analyze the coverage probability with Rayleigh fading for an IEEE 802.16 system. The BER of the IEEE 802.16 system is shown in the simulation results. Then, the maximum allowed path loss can be calculated and substituted into the coverage analysis. Therefore, simulation results show the coverage range with and without Rayleigh fading.

Keywords: OFDM, coverage, SUI channel, IEEE 802.16

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Authors: Alemu Moges Belay

Abstract:

In the 1980s, companies began to feel the effect of three major influences on their product development: newer and innovative technologies, increasing product complexity and larger organizations. And therefore companies were forced to look for new product development methods. This paper tries to focus on the two of new product development methods (DFM and CE). The aim of this paper is to see and analyze different product development methods specifically on Design for Manufacturability and Concurrent Engineering. Companies can achieve and be benefited by minimizing product life cycle, cost and meeting delivery schedule. This paper also presents simplified models that can be modified and used by different companies based on the companies- objective and requirements. Methodologies that are followed to do this research are case studies. Two companies were taken and analysed on the product development process. Historical data, interview were conducted on these companies in addition to that, Survey of literatures and previous research works on similar topics has been done during this research. This paper also tries to show the implementation cost benefit analysis and tries to calculate the implementation time. From this research, it has been found that the two companies did not achieve the delivery time to the customer. Some of most frequently coming products are analyzed and 50% to 80 % of their products are not delivered on time to the customers. The companies are following the traditional way of product development that is sequentially design and production method, which highly affect time to market. In the case study it is found that by implementing these new methods and by forming multi disciplinary team in designing and quality inspection; the company can reduce the workflow steps from 40 to 30.

Keywords: Design for manufacturability, Concurrent Engineering, Time-to-Market, Product development

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Authors: Manasjyoti Bhuyan, Kandarpa Kumar Sarma, Hirendra Das

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Signature represents an individual characteristic of a person which can be used for his / her validation. For such application proper modeling is essential. Here we propose an offline signature recognition and verification scheme which is based on extraction of several features including one hybrid set from the input signature and compare them with the already trained forms. Feature points are classified using statistical parameters like mean and variance. The scanned signature is normalized in slant using a very simple algorithm with an intention to make the system robust which is found to be very helpful. The slant correction is further aided by the use of an Artificial Neural Network (ANN). The suggested scheme discriminates between originals and forged signatures from simple and random forgeries. The primary objective is to reduce the two crucial parameters-False Acceptance Rate (FAR) and False Rejection Rate (FRR) with lesser training time with an intension to make the system dynamic using a cluster of ANNs forming a multiple classifier system.

Keywords: offline, algorithm, FAR, FRR, ANN.

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Authors: Mohammad Rostami Mehr, Seyed Arya Mir Rashed, Arndt Lueder, Magdalena Mißler-Behr

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This paper represents the conception that complex problems do not necessary need similar complex solutions in order to cope with the complexity. Furthermore, a simple solution based on established methods can provide a sufficient way dealing with the complexity. To verify this conception, the presented paper focuses on the field of change management as a part of new product development process in automotive sector. In the field of complexity management, dealing with increasing complexity is essential, while, only non-flexible rigid processes that are not designed to handle complexity are available. The basic methodology of this paper can be divided in four main sections: 1) analyzing the complexity of the change management, 2) literature review in order to identify potential solutions and methods, 3) capturing and implementing expertise of experts from change management filed of an automobile manufacturing company and 4) systematical comparison of the identified methods from literature and connecting these with defined requirements of the complexity of the change management in order to develop a solution. As a practical outcome, this paper provides a method to capture the complexity of engineering changes (EC) and includes it within the EC evaluation process, following case-related process guidance to cope with the complexity. Furthermore, this approach supports the conception that dealing with complexity is possible while utilizing rather simple and established methods by combining them in to a powerful tool.

Keywords: complexity management, new product development, engineering change management, flexibility

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Authors: M. Guillard, M. Philippe, F. Laurent, J. Martinerie, J. P. Lachaux, G. Florence

Abstract:

One approach to assess neural networks underlying the cognitive processes is to study Electroencephalography (EEG). It is relevant to detect various mental states and characterize the physiological changes that help to discriminate two situations. That is why an EEG (amplitude, synchrony) classification procedure is described, validated. The two situations are "eyes closed" and "eyes opened" in order to study the "alpha blocking response" phenomenon in the occipital area. The good classification rate between the two situations is 92.1 % (SD = 3.5%) The spatial distribution of a part of amplitude features that helps to discriminate the two situations are located in the occipital regions that permit to validate the localization method. Moreover amplitude features in frontal areas, "short distant" synchrony in frontal areas and "long distant" synchrony between frontal and occipital area also help to discriminate between the two situations. This procedure will be used for mental fatigue detection.

Keywords: Classification, EEG Synchrony, alpha, resting situation.

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Authors: Mohamad Mahdavi

Abstract:

Most of the real queuing systems include special properties and constraints, which can not be analyzed directly by using the results of solved classical queuing models. Lack of Markov chains features, unexponential patterns and service constraints, are the mentioned conditions. This paper represents an applied general algorithm for analysis and optimizing the queuing systems. The algorithm stages are described through a real case study. It is consisted of an almost completed non-Markov system with limited number of customers and capacities as well as lots of common exception of real queuing networks. Simulation is used for optimizing this system. So introduced stages over the following article include primary modeling, determining queuing system kinds, index defining, statistical analysis and goodness of fit test, validation of model and optimizing methods of system with simulation.

Keywords: Estimation, queuing system, simulation model, probability distribution, non-Markov chain.

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Authors: Guangbin Wang, Ning Zhang, Fuping Tan

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In this paper, we present parallel alternating two-stage methods for solving linear system Ax = b, where A is a monotone matrix or an H-matrix. And we give some convergence results of these methods for nonsingular linear system.

Keywords: Parallel, alternating two-stage, convergence, linear system.

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Authors: Wen Po Cheng, Chia Yun Chung, Ruey Fang Yu, Chao Feng Chen

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The main objective of this research was to study the differences of aluminum hydrolytic products between two PACl preparation methods. These two methods were the acidification process of freshly formed amorphous Al(OH)₃ and the conventional alkalization process of aluminum chloride solution. According to Ferron test and ²⁷Al NMR analysis of those two PACl preparation procedures, the reaction rate constant (k) values and Al₁₃ percentage of acid addition process at high basicity value were both lower than those values of the alkaline addition process. The results showed that the molecular structure and size distribution of the aluminum species in both preparing methods were suspected to be significantly different at high basicity value.

Keywords: Polyaluminum chloride, Al13, amorphous aluminum hydroxide, Ferron test.

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Authors: Xinyue Zhao, Yutaka Satoh, Hidenori Takauji, Shun'ichi Kaneko

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A hybrid feature based adaptive particle filter algorithm is presented for object tracking in real scenarios with static camera. The hybrid feature is combined by two effective features: the Grayscale Arranging Pairs (GAP) feature and the color histogram feature. The GAP feature has high discriminative ability even under conditions of severe illumination variation and dynamic background elements, while the color histogram feature has high reliability to identify the detected objects. The combination of two features covers the shortage of single feature. Furthermore, we adopt an updating target model so that some external problems such as visual angles can be overcame well. An automatic initialization algorithm is introduced which provides precise initial positions of objects. The experimental results show the good performance of the proposed method.

Keywords: Hybrid feature, adaptive Particle Filter, robust Object Tracking, Grayscale Arranging Pairs (GAP) feature.

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Authors: Homayoon Zarshenas, Mahdi Bamdad, Hadi Grailu, Akbar A. Shakoori

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In this study we focus on improvement performance of a cue based Motor Imagery Brain Computer Interface (BCI). For this purpose, data fusion approach is used on results of different classifiers to make the best decision. At first step Distinction Sensitive Learning Vector Quantization method is used as a feature selection method to determine most informative frequencies in recorded signals and its performance is evaluated by frequency search method. Then informative features are extracted by packet wavelet transform. In next step 5 different types of classification methods are applied. The methodologies are tested on BCI Competition II dataset III, the best obtained accuracy is 85% and the best kappa value is 0.8. At final step ordered weighted averaging (OWA) method is used to provide a proper aggregation classifiers outputs. Using OWA enhanced system accuracy to 95% and kappa value to 0.9. Applying OWA just uses 50 milliseconds for performing calculation.

Keywords: BCI, EEG, Classifier, Fuzzy operator, OWA.

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Authors: R.Sukesh Kumar, Abhisek Verma, Jasprit Singh

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In this work a novel approach for color image segmentation using higher order entropy as a textural feature for determination of thresholds over a two dimensional image histogram is discussed. A similar approach is applied to achieve multi-level thresholding in both grayscale and color images. The paper discusses two methods of color image segmentation using RGB space as the standard processing space. The threshold for segmentation is decided by the maximization of conditional entropy in the two dimensional histogram of the color image separated into three grayscale images of R, G and B. The features are first developed independently for the three ( R, G, B ) spaces, and combined to get different color component segmentation. By considering local maxima instead of the maximum of conditional entropy yields multiple thresholds for the same image which forms the basis for multilevel thresholding.

Keywords: conditional entropy, multi-level thresholding, segmentation, two dimensional image histogram

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Authors: Jia-Hong Lee, Mei-Yi Wu, Hsien-Tsung Kuo

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Texture is an important characteristic in real and synthetic scenes. Texture analysis plays a critical role in inspecting surfaces and provides important techniques in a variety of applications. Although several descriptors have been presented to extract texture features, the development of object recognition is still a difficult task due to the complex aspects of texture. Recently, many robust and scaling-invariant image features such as SIFT, SURF and ORB have been successfully used in image retrieval and object recognition. In this paper, we have tried to compare the performance for texture classification using these feature descriptors with k-means clustering. Different classifiers including K-NN, Naive Bayes, Back Propagation Neural Network , Decision Tree and Kstar were applied in three texture image sets － UIUCTex, KTH-TIPS and Brodatz, respectively. Experimental results reveal SIFTS as the best average accuracy rate holder in UIUCTex, KTH-TIPS and SURF is advantaged in Brodatz texture set. BP neuro network works best in the test set classification among all used classifiers.

Keywords: Texture classification, texture descriptor, SIFT, SURF, ORB.

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Authors: Miljan B. Petrović, Dušan B. Petrović, Goran S. Nikolić

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This paper describes a method for AWGN (Additive White Gaussian Noise) variance estimation in noisy stochastic signals, referred to as Multiplicative-Noising Variance Estimation (MNVE). The aim was to develop an estimation algorithm with minimal number of assumptions on the original signal structure. The provided MATLAB simulation and results analysis of the method applied on speech signals showed more accuracy than standardized AR (autoregressive) modeling noise estimation technique. In addition, great performance was observed on very low signal-to-noise ratios, which in general represents the worst case scenario for signal denoising methods. High execution time appears to be the only disadvantage of MNVE. After close examination of all the observed features of the proposed algorithm, it was concluded it is worth of exploring and that with some further adjustments and improvements can be enviably powerful.

Keywords: Noise, signal-to-noise ratio, stochastic signals, variance estimation.

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Authors: B. Q. Huang, Tarik Rashid, M-T. Kechadi

Abstract:

this paper presents a multi-context recurrent network for time series analysis. While simple recurrent network (SRN) are very popular among recurrent neural networks, they still have some shortcomings in terms of learning speed and accuracy that need to be addressed. To solve these problems, we proposed a multi-context recurrent network (MCRN) with three different learning algorithms. The performance of this network is evaluated on some real-world application such as handwriting recognition and energy load forecasting. We study the performance of this network and we compared it to a very well established SRN. The experimental results showed that MCRN is very efficient and very well suited to time series analysis and its applications.

Keywords: Gradient descent method, recurrent neural network, learning algorithms, time series, BP

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Authors: P. Řehoř, D. Holátová, V. Doležalová

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Paper deals with analysis of strategic management methods in non-profit making organization in the Czech Republic. Strategic management represents an aggregate of methods and approaches that can be applied for managing organizations - in this article the organizations which associate owners and keepers of nonstate forest properties. Authors use these methods of strategic management: analysis of stakeholders, SWOT analysis and questionnaire inquiries. The questionnaire was distributed electronically via e-mail. In October 2013 we obtained data from a total of 84 questionnaires. Based on the results the authors recommend the using of confrontation strategy which improves the competitiveness of non-profit making organizations.

Keywords: Strategic management, non-profit making organization, strategy analysis, SWOT analysis, strategy, competitiveness.

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Authors: Chothmal, Basant Agarwal

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Sentiment analysis means to classify a given review document into positive or negative polar document. Sentiment analysis research has been increased tremendously in recent times due to its large number of applications in the industry and academia. Sentiment analysis models can be used to determine the opinion of the user towards any entity or product. E-commerce companies can use sentiment analysis model to improve their products on the basis of users’ opinion. In this paper, we propose a new One-class Support Vector Machine (One-class SVM) based sentiment analysis model for movie review documents. In the proposed approach, we initially extract features from one class of documents, and further test the given documents with the one-class SVM model if a given new test document lies in the model or it is an outlier. Experimental results show the effectiveness of the proposed sentiment analysis model.

Keywords: Feature selection methods, Machine learning, NB, One-class SVM, Sentiment Analysis, Support Vector Machine.

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Authors: Khalil Monfaredi, Hassan Faraji Baghtash, Majid Abbasi

Abstract:

In this paper a novel high output impedance, low input impedance, wide bandwidth, very simple current mirror with input and output voltage requirements less than that of a simple current mirror is presented. These features are achieved with very simple structure avoiding extra large node impedances to ensure high bandwidth operation. The circuit's principle of operation is discussed and compared to simple and low voltage cascode (LVC) current mirrors. Such outstanding features of this current mirror as high output impedance ~384K, low input impedance~6.4, wide bandwidth~178MHz, low input voltage ~ 362mV, low output voltage ~ 38mV and low current transfer error ~4% (all at 50μA) makes it an outstanding choice for high performance applications. Simulation results in BSIM 0.35μm CMOS technology with HSPICE are given in comparison with simple, and LVC current mirrors to verify and validate the performance of the proposed current mirror.

Keywords: Analog circuits, Current mirror, high frequency, Low power, Low voltage.

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Authors: Belkacem Brahmi, Mohand Ouamer Bibi

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In this paper, we present a new method for solving quadratic programming problems, not strictly convex. Constraints of the problem are linear equalities and inequalities, with bounded variables. The suggested method combines the active-set strategies and support methods. The algorithm of the method and numerical experiments are presented, while comparing our approach with the active set method on randomly generated problems.

Keywords: Convex quadratic programming, dual support methods, active set methods.

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Authors: Brian A. Smith, Ronald W. McClendon, Gerrit Hoogenboom

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The mitigation of crop loss due to damaging freezes requires accurate air temperature prediction models. An improved model for temperature prediction in Georgia was developed by including information on seasonality and modifying parameters of an existing artificial neural network model. Alternative models were compared by instantiating and training multiple networks for each model. The inclusion of up to 24 hours of prior weather information and inputs reflecting the day of year were among improvements that reduced average four-hour prediction error by 0.18°C compared to the prior model. Results strongly suggest model developers should instantiate and train multiple networks with different initial weights to establish appropriate model parameters.

Keywords: Time-series forecasting, weather modeling.

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Authors: N. W. U. D. Chathurani, Shlomo Geva, Vinod Chandran, Proboda Rajapaksha

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Selecting an appropriate image representation is the most important factor in implementing an effective Content-Based Image Retrieval (CBIR) system. This paper presents a multi-feature fusion approach for efficient CBIR, based on the distance distribution of features and relative feature weights at the time of query processing. It is a simple yet effective approach, which is free from the effect of features' dimensions, ranges, internal feature normalization and the distance measure. This approach can easily be adopted in any feature combination to improve retrieval quality. The proposed approach is empirically evaluated using two benchmark datasets for image classification (a subset of the Corel dataset and Oliva and Torralba) and compared with existing approaches. The performance of the proposed approach is confirmed with the significantly improved performance in comparison with the independently evaluated baseline of the previously proposed feature fusion approaches.

Keywords: Feature fusion, image retrieval, membership function, normalization.

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Authors: R. B. Ibrahim, M. S. Argungu, I. M. Mungadi

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It is obvious in this present time, internet has become an indispensable part of human life since its inception. The Internet has provided diverse opportunities to make life so easy for human beings, through the adoption of various channels. Among these channels are email, internet banking, video conferencing, and the like. Email is one of the easiest means of communication hugely accepted among individuals and organizations globally. But over decades the security integrity of this platform has been challenged with malicious activities like Phishing. Email phishing is designed by phishers to fool the recipient into handing over sensitive personal information such as passwords, credit card numbers, account credentials, social security numbers, etc. This activity has caused a lot of financial damage to email users globally which has resulted in bankruptcy, sudden death of victims, and other health-related sicknesses. Although many methods have been proposed to detect email phishing, in this research, the results of multiple machine-learning methods for predicting email phishing have been compared with the use of filter-wrapper feature selection. It is worth noting that all three models performed substantially but one outperformed the other. The dataset used for these models is obtained from Kaggle online data repository, while three classifiers: decision tree, Naïve Bayes, and Logistic regression are ensemble (Bagging) respectively. Results from the study show that the Decision Tree (CART) bagging ensemble recorded the highest accuracy of 98.13% using PEF (Phishing Essential Features). This result further demonstrates the dependability of the proposed model.

Keywords: Ensemble, hybrid, filter-wrapper, phishing.

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Authors: Ioannis N. Koukoulis, Clio G. Vossou, Christopher G. Provatidis

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The aim of the current work is to present a comparison among three popular optimization methods in the inverse elastostatics problem (IESP) of flaw detection within a solid. In more details, the performance of a simulated annealing, a Hooke & Jeeves and a sequential quadratic programming algorithm was studied in the test case of one circular flaw in a plate solved by both the boundary element (BEM) and the finite element method (FEM). The proposed optimization methods use a cost function that utilizes the displacements of the static response. The methods were ranked according to the required number of iterations to converge and to their ability to locate the global optimum. Hence, a clear impression regarding the performance of the aforementioned algorithms in flaw identification problems was obtained. Furthermore, the coupling of BEM or FEM with these optimization methods was investigated in order to track differences in their performance.

Keywords: Elastostatic, inverse problem, optimization.

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