Search results for: support vector regression.

Authors: Süha Yılmaz, Emin Özyılmaz, Melih Turgut, Şuur Nizamoğlu

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In this paper, position vector of a partially null unit speed curve with respect to standard frame of Minkowski space-time is studied. First, it is proven that position vector of every partially null unit speed curve satisfies a vector differential equation of fourth order. In terms of solution of the differential equation, position vector of a partially null unit speed curve is expressed.

Keywords: Frenet Equations, Partially Null Curves, Minkowski Space-time, Vector Differential Equation.

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Authors: Refaat M Mohamed, Ayman El-Baz, Aly A. Farag

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This paper presents a new approach for the prob-ability density function estimation using the Support Vector Ma-chines (SVM) and the Expectation Maximization (EM) algorithms.In the proposed approach, an advanced algorithm for the SVM den-sity estimation which incorporates the Mean Field theory in the learning process is used. Instead of using ad-hoc values for the para-meters of the kernel function which is used by the SVM algorithm,the proposed approach uses the EM algorithm for an automatic optimization of the kernel. Experimental evaluation using simulated data set shows encouraging results.

Keywords: Density Estimation, SVM, Learning Algorithms, Parameters Estimation.

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Authors: Muhammad Awais Shafique, Eiji Hato, Hideki Yaginuma

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Recently GPS data is used in a lot of studies to automatically reconstruct travel patterns for trip survey. The aim is to minimize the use of questionnaire surveys and travel diaries so as to reduce their negative effects. In this paper data acquired from GPS and accelerometer embedded in smart phones is utilized to predict the mode of transportation used by the phone carrier. For prediction, Support Vector Machine (SVM) and Adaptive boosting (AdaBoost) are employed. Moreover a unique method to improve the prediction results from these algorithms is also proposed. Results suggest that the prediction accuracy of AdaBoost after improvement is relatively better than the rest.

Keywords: Accelerometer, AdaBoost, GPS, Mode Prediction, Support vector Machine.

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Authors: K. P. Oyeduntan, K. Oshinubi

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Nigeria is referred as the ‘Giant of Africa’ due to high population, land mass and large economy. However, it still trails far behind many smaller economies in the continent in terms of maritime operations. As we have seen that the maritime industry is the sparkplug for national growth, because it houses the most crucial infrastructure that generates wealth for a nation, it is worrisome that a nation with six seaports lag in maritime activities. In this research, we have studied how the Gross Domestic Product (GDP) of the maritime transport influences the Nigerian economy. To do this, we applied Simple Linear Regression (SLR), Support Vector Machine (SVM), Polynomial Regression Model (PRM), Generalized Additive Model (GAM) and Generalized Linear Mixed Model (GLMM) to model the relationship between the nation’s Total GDP (TGDP) and the Maritime Transport GDP (MGDP) using a time series data of 20 years. The result showed that the MGDP is statistically significant to the Nigerian economy. Amongst the statistical tool applied, the PRM of order 4 describes the relationship better when compared to other methods. The recommendations presented in this study will guide policy makers and help improve the economy of Nigeria.

Keywords: Economy, GDP, maritime transport, port, regression.

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Authors: B. Dora Arul Selvi, .N. Kamaraj

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Transient Stability is an important issue in power systems planning, operation and extension. The objective of transient stability analysis problem is not satisfied with mere transient instability detection or evaluation and it is most important to complement it by defining fast and efficient control measures in order to ensure system security. This paper presents a new Fuzzy Support Vector Machines (FSVM) to investigate the stability status of power systems and a modified generation rescheduling scheme to bring back the identified unstable cases to a more economical and stable operating point. FSVM improves the traditional SVM (Support Vector Machines) by adding fuzzy membership to each training sample to indicate the degree of membership of this sample to different classes. The preventive control based on economic generator rescheduling avoids the instability of the power systems with minimum change in operating cost under disturbed conditions. Numerical results on the New England 39 bus test system show the effectiveness of the proposed method.

Keywords: Fuzzy Support Vector Machine (FSVM), Incremental Cost, Preventive Control, Transient stability

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Authors: Syed Fahad Tahir, Asifullah Khan, Abdul Majid, Anwar M. Mirza

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In this paper, we present an innovative scheme of blindly extracting message bits from an image distorted by an attack. Support Vector Machine (SVM) is used to nonlinearly classify the bits of the embedded message. Traditionally, a hard decoder is used with the assumption that the underlying modeling of the Discrete Cosine Transform (DCT) coefficients does not appreciably change. In case of an attack, the distribution of the image coefficients is heavily altered. The distribution of the sufficient statistics at the receiving end corresponding to the antipodal signals overlap and a simple hard decoder fails to classify them properly. We are considering message retrieval of antipodal signal as a binary classification problem. Machine learning techniques like SVM is used to retrieve the message, when certain specific class of attacks is most probable. In order to validate SVM based decoding scheme, we have taken Gaussian noise as a test case. We generate a data set using 125 images and 25 different keys. Polynomial kernel of SVM has achieved 100 percent accuracy on test data.

Keywords: Bit Correct Ratio (BCR), Grid Search, Intelligent Decoding, Jackknife Technique, Support Vector Machine (SVM), Watermarking.

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Authors: Baljit Singh Khehra, Amar Partap Singh Pharwaha

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Clusters of Microcalcifications (MCCs) are most frequent symptoms of Ductal Carcinoma in Situ (DCIS) recognized by mammography. Least-Square Support Vector Machine (LS-SVM) is a variant of the standard SVM. In the paper, LS-SVM is proposed as a classifier for classifying MCCs as benign or malignant based on relevant extracted features from enhanced mammogram. To establish the credibility of LS-SVM classifier for classifying MCCs, a comparative evaluation of the relative performance of LS-SVM classifier for different kernel functions is made. For comparative evaluation, confusion matrix and ROC analysis are used. Experiments are performed on data extracted from mammogram images of DDSM database. A total of 380 suspicious areas are collected, which contain 235 malignant and 145 benign samples, from mammogram images of DDSM database. A set of 50 features is calculated for each suspicious area. After this, an optimal subset of 23 most suitable features is selected from 50 features by Particle Swarm Optimization (PSO). The results of proposed study are quite promising.

Keywords: Clusters of Microcalcifications, Ductal Carcinoma in Situ, Least-Square Support Vector Machine, Particle Swarm Optimization.

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Authors: Florin Leon, Silvia Curteanu

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Developing complete mechanistic models for polymerization reactors is not easy, because complex reactions occur simultaneously; there is a large number of kinetic parameters involved and sometimes the chemical and physical phenomena for mixtures involving polymers are poorly understood. To overcome these difficulties, empirical models based on sampled data can be used instead, namely regression methods typical of machine learning field. They have the ability to learn the trends of a process without any knowledge about its particular physical and chemical laws. Therefore, they are useful for modeling complex processes, such as the free radical polymerization of methyl methacrylate achieved in a batch bulk process. The goal is to generate accurate predictions of monomer conversion, numerical average molecular weight and gravimetrical average molecular weight. This process is associated with non-linear gel and glass effects. For this purpose, an adaptive sampling technique is presented, which can select more samples around the regions where the values have a higher variation. Several machine learning methods are used for the modeling and their performance is compared: support vector machines, k-nearest neighbor, k-nearest neighbor and random forest, as well as an original algorithm, large margin nearest neighbor regression. The suggested method provides very good results compared to the other well-known regression algorithms.

Keywords: Adaptive sampling, batch bulk methyl methacrylate polymerization, large margin nearest neighbor regression, machine learning.

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Authors: Renju Gangadharan, G. N. Pillai, Indra Gupta

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In this paper a novel method for finding the fault zone on a Thyristor Controlled Series Capacitor (TCSC) incorporated transmission line is presented. The method makes use of the Support Vector Machine (SVM), used in the classification mode to distinguish between the zones, before or after the TCSC. The use of Discrete Wavelet Transform is made to prepare the features which would be given as the input to the SVM. This method was tested on a 400 kV, 50 Hz, 300 Km transmission line and the results were highly accurate.

Keywords: Flexible ac transmission system (FACTS), thyristorcontrolled series-capacitor (TCSC), discrete wavelet transforms(DWT), support vector machine (SVM).

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Authors: Hoon Lee, Soonyoung Park, Kyoungho Choi

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Understanding road features such as lanes, the color of lanes, and sidewalks in a live video captured from a moving vehicle is essential to build video-based navigation systems. In this paper, we present a novel idea to understand the road features using support vector machines. Various feature vectors including color components of road markings and the difference between two regions, i.e., chosen AOIs, and so on are fed into SVM, deciding colors of lanes and sidewalks robustly. Experimental results are provided to show the robustness of the proposed idea.

Keywords: video-based navigation system, lane detection, SVMs, autonomous vehicles

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Authors: Hany Alashwal, Safaai Deris, Razib M. Othman

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Understanding proteins functions is a major goal in the post-genomic era. Proteins usually work in context of other proteins and rarely function alone. Therefore, it is highly relevant to study the interaction partners of a protein in order to understand its function. Machine learning techniques have been widely applied to predict protein-protein interactions. Kernel functions play an important role for a successful machine learning technique. Choosing the appropriate kernel function can lead to a better accuracy in a binary classifier such as the support vector machines. In this paper, we describe a Bayesian kernel for the support vector machine to predict protein-protein interactions. The use of Bayesian kernel can improve the classifier performance by incorporating the probability characteristic of the available experimental protein-protein interactions data that were compiled from different sources. In addition, the probabilistic output from the Bayesian kernel can assist biologists to conduct more research on the highly predicted interactions. The results show that the accuracy of the classifier has been improved using the Bayesian kernel compared to the standard SVM kernels. These results imply that protein-protein interaction can be predicted using Bayesian kernel with better accuracy compared to the standard SVM kernels.

Keywords: Bioinformatics, Protein-protein interactions, Bayesian Kernel, Support Vector Machines.

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Authors: P. Visutsak

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The study of the interaction between humans and computers has been emerging during the last few years. This interaction will be more powerful if computers are able to perceive and respond to human nonverbal communication such as emotions. In this study, we present the image-based approach to emotion classification through lower facial expression. We employ a set of feature points in the lower face image according to the particular face model used and consider their motion across each emotive expression of images. The vector of displacements of all feature points input to the Adaptive Support Vector Machines (A-SVMs) classifier that classify it into seven basic emotions scheme, namely neutral, angry, disgust, fear, happy, sad and surprise. The system was tested on the Japanese Female Facial Expression (JAFFE) dataset of frontal view facial expressions [7]. Our experiments on emotion classification through lower facial expressions demonstrate the robustness of Adaptive SVM classifier and verify the high efficiency of our approach.

Keywords: emotion classification, facial expression, adaptive support vector machines, facial expression classifier.

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Authors: Hamid R. S. Mojaveri, Seyed S. Mousavi, Mojtaba Heydar, Ahmad Aminian

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The aim of this paper is to present a methodology in three steps to forecast supply chain demand. In first step, various data mining techniques are applied in order to prepare data for entering into forecasting models. In second step, the modeling step, an artificial neural network and support vector machine is presented after defining Mean Absolute Percentage Error index for measuring error. The structure of artificial neural network is selected based on previous researchers' results and in this article the accuracy of network is increased by using sensitivity analysis. The best forecast for classical forecasting methods (Moving Average, Exponential Smoothing, and Exponential Smoothing with Trend) is resulted based on prepared data and this forecast is compared with result of support vector machine and proposed artificial neural network. The results show that artificial neural network can forecast more precisely in comparison with other methods. Finally, forecasting methods' stability is analyzed by using raw data and even the effectiveness of clustering analysis is measured.

Keywords: Artificial Neural Networks (ANN), bullwhip effect, demand forecasting, Support Vector Machine (SVM).

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Authors: Nebi Gedik

Abstract:

Regardless of age or gender, cardiovascular illnesses are a serious health concern because of things like poor eating habits, stress, a sedentary lifestyle, hard work schedules, alcohol use, and weight. It tends to happen suddenly and has a high rate of recurrence. Machine learning models can be implemented to assist healthcare systems in the accurate detection and diagnosis of cardiovascular disease (CVD) in patients. Improved heart failure prediction is one of the primary goals of researchers using the heart disease dataset. The purpose of this study is to identify the feature or features that offer the best classification prediction for CVD detection. The support vector machine classifier is used to compare each feature's performance. It has been determined which feature produces the best results.

Keywords: Cardiovascular disease, feature extraction, supervised learning, support vector machine.

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Authors: J. P. Dubois, O. M. Abdul-Latif

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Support Vector Machine (SVM) is a recent class of statistical classification and regression techniques playing an increasing role in applications to detection problems in various engineering problems, notably in statistical signal processing, pattern recognition, image analysis, and communication systems. In this paper, SVM is applied to an infrared (IR) binary communication system with different types of channel models including Ricean multipath fading and partially developed scattering channel with additive white Gaussian noise (AWGN) at the receiver. The structure and performance of SVM in terms of the bit error rate (BER) metric is derived and simulated for these channel stochastic models and the computational complexity of the implementation, in terms of average computational time per bit, is also presented. The performance of SVM is then compared to classical binary signal maximum likelihood detection using a matched filter driven by On-Off keying (OOK) modulation. We found that the performance of SVM is superior to that of the traditional optimal detection schemes used in statistical communication, especially for very low signal-to-noise ratio (SNR) ranges. For large SNR, the performance of the SVM is similar to that of the classical detectors. The implication of these results is that SVM can prove very beneficial to IR communication systems that notoriously suffer from low SNR at the cost of increased computational complexity.

Keywords: Least square-support vector machine, on-off keying, matched filter, maximum likelihood detector, wireless infrared communication.

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Authors: T. Thendral, M. S. Vijaya, S. Karpagavalli

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Tamil handwritten document is taken as a key source of data to identify the writer. Tamil is a classical language which has 247 characters include compound characters, consonants, vowels and special character. Most characters of Tamil are multifaceted in nature. Handwriting is a unique feature of an individual. Writer may change their handwritings according to their frame of mind and this place a risky challenge in identifying the writer. A new discriminative model with pooled features of handwriting is proposed and implemented using support vector machine. It has been reported on 100% of prediction accuracy by RBF and polynomial kernel based classification model.

Keywords: Classification, Feature extraction, Support vector machine, Training, Writer.

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Authors: T. Thendral, M. S. Vijaya, S. Karpagavalli

Abstract:

Tamil handwritten document is taken as a key source of data to identify the writer. Tamil is a classical language which has 247 characters include compound characters, consonants, vowels and special character. Most characters of Tamil are multifaceted in nature. Handwriting is a unique feature of an individual. Writer may change their handwritings according to their frame of mind and this place a risky challenge in identifying the writer. A new discriminative model with pooled features of handwriting is proposed and implemented using support vector machine. It has been reported on 100% of prediction accuracy by RBF and polynomial kernel based classification model.

Keywords: Classification, Feature extraction, Support vector machine, Training, Writer.

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Authors: T. Alghamdi, G. Alaghband

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In this paper we develop a model that couples Two Concurrent Convolution Neural Network with different filters (TC*CNN) for face recognition and compare its performance to an existing sequential CNN (base model). We also test and compare the quality and performance of the models on three datasets with various levels of complexity (easy, moderate, and difficult) and show that for the most complex datasets, edges will produce the most accurate and efficient results. We further show that in such cases while Support Vector Machine (SVM) models are fast, they do not produce accurate results.

Keywords: Convolution neural network, edges, face recognition, support vector machine.

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Authors: Rohit Choudhry, Kumkum Garg

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In this paper, we propose a hybrid machine learning system based on Genetic Algorithm (GA) and Support Vector Machines (SVM) for stock market prediction. A variety of indicators from the technical analysis field of study are used as input features. We also make use of the correlation between stock prices of different companies to forecast the price of a stock, making use of technical indicators of highly correlated stocks, not only the stock to be predicted. The genetic algorithm is used to select the set of most informative input features from among all the technical indicators. The results show that the hybrid GA-SVM system outperforms the stand alone SVM system.

Keywords: Genetic Algorithms, Support Vector Machines, Stock Market Forecasting.

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Authors: Swathi Ganesan, Nalinda Somasiri, Rebecca Jeyavadhanam, Gayathri Karthick

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The COVID-19 crisis presents a substantial and critical hazard to worldwide health. Since the occurrence of the disease in late January 2020 in the UK, the number of infected people confirmed to acquire the illness has increased tremendously across the country, and the number of individuals affected is undoubtedly considerably high. The purpose of this research is to figure out a predictive machine learning (ML) archetypal that could forecast the COVID-19 cases within the UK. This study concentrates on the statistical data collected from 31st January 2020 to 31st March 2021 in the United Kingdom. Information on total COVID-19 cases registered, new cases encountered on a daily basis, total death registered, and patients’ death per day due to Coronavirus is collected from World Health Organization (WHO). Data preprocessing is carried out to identify any missing values, outliers, or anomalies in the dataset. The data are split into 8:2 ratio for training and testing purposes to forecast future new COVID-19 cases. Support Vector Machine (SVM), Random Forest (RF), and linear regression (LR) algorithms are chosen to study the model performance in the prediction of new COVID-19 cases. From the evaluation metrics such as r-squared value and mean squared error, the statistical performance of the model in predicting the new COVID-19 cases is evaluated. RF outperformed the other two ML algorithms with a training accuracy of 99.47% and testing accuracy of 98.26% when n = 30. The mean square error obtained for RF is 4.05e11, which is lesser compared to the other predictive models used for this study. From the experimental analysis, RF algorithm can perform more effectively and efficiently in predicting the new COVID-19 cases, which could help the health sector to take relevant control measures for the spread of the virus.

Keywords: COVID-19, machine learning, supervised learning, unsupervised learning, linear regression, support vector machine, random forest.

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Authors: R. Xu, X. Zhao, X. Li, C. Kwan, C.-I Chang

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An image texture analysis and target recognition approach of using an improved image texture feature coding method (TFCM) and Support Vector Machine (SVM) for target detection is presented. With our proposed target detection framework, targets of interest can be detected accurately. Cascade-Sliding-Window technique was also developed for automated target localization. Application to mammogram showed that over 88% of normal mammograms and 80% of abnormal mammograms can be correctly identified. The approach was also successfully applied to Synthetic Aperture Radar (SAR) and Ground Penetrating Radar (GPR) images for target detection.

Keywords: Image texture analysis, feature extraction, target detection, pattern classification.

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Authors: Mohammad Javadi

Abstract:

Serial hierarchical support vector machine (SHSVM) is proposed to discriminate three brain tissues which are white matter (WM), gray matter (GM), and cerebrospinal fluid (CSF). SHSVM has novel classification approach by repeating the hierarchical classification on data set iteratively. It used Radial Basis Function (rbf) Kernel with different tuning to obtain accurate results. Also as the second approach, segmentation performed with DAGSVM method. In this article eight univariate features from the raw DTI data are extracted and all the possible 2D feature sets are examined within the segmentation process. SHSVM succeed to obtain DSI values higher than 0.95 accuracy for all the three tissues, which are higher than DAGSVM results.

Keywords: Brain segmentation, DTI, hierarchical, SVM.

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Authors: Dursun Aydın

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In this paper, estimation of the linear regression model is made by ordinary least squares method and the partially linear regression model is estimated by penalized least squares method using smoothing spline. Then, it is investigated that differences and similarity in the sum of squares related for linear regression and partial linear regression models (semi-parametric regression models). It is denoted that the sum of squares in linear regression is reduced to sum of squares in partial linear regression models. Furthermore, we indicated that various sums of squares in the linear regression are similar to different deviance statements in partial linear regression. In addition to, coefficient of the determination derived in linear regression model is easily generalized to coefficient of the determination of the partial linear regression model. For this aim, it is made two different applications. A simulated and a real data set are considered to prove the claim mentioned here. In this way, this study is supported with a simulation and a real data example.

Keywords: Partial Linear Regression Model, Linear RegressionModel, Residuals, Deviance, Smoothing Spline.

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Authors: Karina Zaccari, Ernesto Cordeiro Marujo

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This paper presents a Machine Learning (ML) approach to support Meningitis diagnosis in patients at a children’s hospital in Sao Paulo, Brazil. The aim is to use ML techniques to reduce the use of invasive procedures, such as cerebrospinal fluid (CSF) collection, as much as possible. In this study, we focus on predicting the probability of Meningitis given the results of a blood and urine laboratory tests, together with the analysis of pain or other complaints from the patient. We tested a number of different ML algorithms, including: Adaptative Boosting (AdaBoost), Decision Tree, Gradient Boosting, K-Nearest Neighbors (KNN), Logistic Regression, Random Forest and Support Vector Machines (SVM). Decision Tree algorithm performed best, with 94.56% and 96.18% accuracy for training and testing data, respectively. These results represent a significant aid to doctors in diagnosing Meningitis as early as possible and in preventing expensive and painful procedures on some children.

Keywords: Machine learning, medical diagnosis, meningitis detection, gradient boosting.

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Authors: Mei Li, Fahui Zhai

Abstract:

In this paper, the definitions of the quaternion measure and the quaternion vector measure are introduced. The relation between the quaternion measure and the complex vector measure as well as the relation between the quaternion linear functional and the complex linear functional are discussed respectively. By using these relations, the necessary and sufficient condition to determine the quaternion vector measure is given.

Keywords: Quaternion, Quaternion measure, Quaternion vector measure, Quaternion Banach space, Quaternion linear functional.

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Authors: Sae-Rom Pak, Seung Hwan Park, Jeong Ho Cho, Daewoong An, Cheong-Sool Park, Jun Seok Kim, Jun-Geol Baek

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It is important to predict yield in semiconductor test process in order to increase yield. In this study, yield prediction means finding out defective die, wafer or lot effectively. Semiconductor test process consists of some test steps and each test includes various test items. In other world, test data has a big and complicated characteristic. It also is disproportionably distributed as the number of data belonging to FAIL class is extremely low. For yield prediction, general data mining techniques have a limitation without any data preprocessing due to eigen properties of test data. Therefore, this study proposes an under-sampling method using support vector machine (SVM) to eliminate an imbalanced characteristic. For evaluating a performance, randomly under-sampling method is compared with the proposed method using actual semiconductor test data. As a result, sampling method using SVM is effective in generating robust model for yield prediction.

Keywords: Yield Prediction, Semiconductor Test Process, Support Vector Machine, Under Sampling

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Authors: Emin Özyılmaz

Abstract:

In this work, position vector of a time-like dual curve according to standard frame of D31 is investigated. First, it is proven that position vector of a time-like dual curve satisfies a dual vector differential equation of fourth order. The general solution of this dual vector differential equation has not yet been found. Due to this, in terms of special solutions, position vectors of some special time-like dual curves with respect to standard frame of D31 are presented.

Keywords: Classical Differential Geometry, Dual Numbers, DualFrenet Equations, Time-like Dual Curve, Position Vector, DualLorentzian Space.

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Authors: Ju-Hong Lee, Ching-Wei Liao, Kun-Che Lee

Abstract:

This paper deals with the problem of using antenna sensors for adaptive beamforming in the presence of random steering mismatch. We present an efficient adaptive array beamformer with robustness to deal with the considered problem. The robustness of the proposed beamformer comes from the efficient designation of the steering vector. Using the received array data vector, we construct an appropriate correlation matrix associated with the received array data vector and a correlation matrix associated with signal sources. Then, the eigenvector associated with the largest eigenvalue of the constructed signal correlation matrix is designated as an appropriate estimate of the steering vector. Finally, the adaptive weight vector required for adaptive beamforming is obtained by using the estimated steering vector and the constructed correlation matrix of the array data vector. Simulation results confirm the effectiveness of the proposed method.

Keywords: Adaptive beamforming, antenna array, linearly constrained minimum variance, robustness, steering vector.

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Authors: Daniel Morariu, Lucian N. Vintan, Volker Tresp

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Text categorization is the problem of classifying text documents into a set of predefined classes. After a preprocessing step, the documents are typically represented as large sparse vectors. When training classifiers on large collections of documents, both the time and memory restrictions can be quite prohibitive. This justifies the application of feature selection methods to reduce the dimensionality of the document-representation vector. In this paper, three feature selection methods are evaluated: Random Selection, Information Gain (IG) and Support Vector Machine feature selection (called SVM_FS). We show that the best results were obtained with SVM_FS method for a relatively small dimension of the feature vector. Also we present a novel method to better correlate SVM kernel-s parameters (Polynomial or Gaussian kernel).

Keywords: Feature Selection, Learning with Kernels, SupportVector Machine, and Classification.

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Authors: M. Satya Sai Ram, P. Siddaiah, M. Madhavi Latha

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Vector quantization is a powerful tool for speech coding applications. This paper deals with LPC Coding of speech signals which uses a new technique called Multi Switched Split Vector Quantization (MSSVQ), which is a hybrid of Multi, switched, split vector quantization techniques. The spectral distortion performance, computational complexity, and memory requirements of MSSVQ are compared to split vector quantization (SVQ), multi stage vector quantization(MSVQ) and switched split vector quantization (SSVQ) techniques. It has been proved from results that MSSVQ has better spectral distortion performance, lower computational complexity and lower memory requirements when compared to all the above mentioned product code vector quantization techniques. Computational complexity is measured in floating point operations (flops), and memory requirements is measured in (floats).

Keywords: Linear predictive Coding, Multi stage vectorquantization, Switched Split vector quantization, Split vectorquantization, Line Spectral Frequencies (LSF).

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