Search results for: linear regression

Authors: Sotiris B. Kotsiantis

Abstract:

Bagging and boosting are among the most popular re-sampling ensemble methods that generate and combine a diversity of regression models using the same learning algorithm as base-learner. Boosting algorithms are considered stronger than bagging on noise-free data. However, there are strong empirical indications that bagging is much more robust than boosting in noisy settings. For this reason, in this work we built an ensemble using an averaging methodology of bagging and boosting ensembles with 10 sub-learners in each one. We performed a comparison with simple bagging and boosting ensembles with 25 sub-learners on standard benchmark datasets and the proposed ensemble gave better accuracy.

Keywords: Regressors, statistical learning.

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Authors: Wudhichai Assawinchaichote

Abstract:

This paper examines the problem of designing robust H controllers for for HIV/AIDS infection system with dual drug dosages described by a Takagi-Sugeno (S) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop an H controller which guarantees the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value for the system. A sufficient condition of the controller for this system is given in term of Linear Matrix Inequalities (LMIs). The effectiveness of the proposed controller design methodology is finally demonstrated through simulation results. It has been shown that the anti-HIV vaccines are critically important in reducing the infected cells.

Keywords: H∞ Fuzzy control; Takagi-Sugeno (TS) fuzzy model; Linear Matrix Inequalities (LMIs); HIV/AIDS infection system

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Authors: P. Ramana , K. Alice Mary, M. Surya Kalavathi, M. Phani Kumar

Abstract:

This paper discusses two observers, which are used for the estimation of parameters of PMSM. Former one, reduced order observer, which is used to estimate the inaccessible parameters of PMSM. Later one, full order observer, which is used to estimate all the parameters of PMSM even though some of the parameters are directly available for measurement, so as to meet with the insensitivity to the parameter variation. However, the state space model contains some nonlinear terms i.e. the product of different state variables. The asymptotic state observer, which approximately reconstructs the state vector for linear systems without uncertainties, was presented by Luenberger. In this work, a modified form of such an observer is used by including a non-linear term involving the speed. So, both the observers are designed in the framework of nonlinear control; their stability and rate of convergence is discussed.

Keywords: Permanent magnet synchronous motor, Mathematicalmodelling, Rotor reference frame, parameter estimation, Luenbergerobserver, reduced order observer, full order observer

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Authors: Jeng-Wen Lin, Simon Chien-Yuan Chen

Abstract:

Based on assumptions of neo-classical economics and rational choice / public choice theory, this paper investigates the regulation of industrial land use in Taiwan by homeowners associations (HOAs) as opposed to traditional government administration. The comparison, which applies the transaction cost theory and a polynomial regression analysis, manifested that HOAs are superior to conventional government administration in terms of transaction costs and overall efficiency. A case study that compares Taiwan-s commonhold industrial park, NangKang Software Park, to traditional government counterparts using limited data on the costs and returns was analyzed. This empirical study on the relative efficiency of governmental and private institutions justified the important theoretical proposition. Numerical results prove the efficiency of the established model.

Keywords: Homeowners Associations, Institutional Efficiency, Polynomial Regression, Transaction Cost.

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Authors: Débora V. Busman, Venerando E. Amaro, Mattheus da C. Prudêncio

Abstract:

Prognostic studies of the shoreline are of utmost importance for Ponta Negra Beach, located in Natal, Northeastern Brazil, where the infrastructure recently built along the shoreline is severely affected by flooding and erosion. This study compares shoreline predictions using three linear regression methods (LMS, LRR and WLR) and tries to discern the best method for different shoreline position scenarios. The methods have shown erosion on the beach in each of the scenarios tested, even in less intense dynamic conditions. The WLA_A with confidence interval of 95% was the well-adjusted model and calculated a retreat of -1.25 m/yr to -2.0 m/yr in hot spot areas. The change of the shoreline on Ponta Negra Beach can be measured as a negative exponential curve. Analysis of these methods has shown a correlation with the morphodynamic stage of the beach.

Keywords: Coastal Erosion, Prognostic Model, DSAS.

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Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu

Abstract:

This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Keywords: Interpolation, Approximate Solution, Collocation, Differential system, Half step, Converges, Block method, Efficiency.

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Authors: A.F. Salarashayeri, M. Siosemarde

Abstract:

Hydraulic conductivity is one parameter important for predicting the movement of water and contaminants dissolved in the water through the soil. The hydraulic conductivity is measured on soil samples in the lab and sometimes tests carried out in the field. The hydraulic conductivity has been related to soil particle diameter by a number of investigators. In this study, 25 set of soil samples with sand texture. The results show approximately success in predicting hydraulic conductivity from particle diameters data. The following relationship obtained from multiple linear regressions on data (R2 = 0.52): Where d10, d50 and d60, are the soil particle diameter (mm) that 10%, 50% and 60% of all soil particles are finer (smaller) by weight and Ks, saturated hydraulic conductivity is expressed in m/day. The results of regression analysis showed that d10 play a more significant role with respect to Ks, saturated hydraulic conductivity (m/day), and has been named as the effective parameter in Ks calculation.

Keywords: hydraulic conductivity, particle diameter, particle-size distribution and soil

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Authors: M. F. Patricio, P. M. Rosa

Abstract:

In this paper a class of numerical methods to solve linear and nonlinear PDEs and also systems of PDEs is developed. The Differential Transform method associated with the Method of Lines (MoL) is used. The theory for linear problems is extended to the nonlinear case, and a recurrence relation is established. This method can achieve an arbitrary high-order accuracy in time. A variable stepsize algorithm and some numerical results are also presented.

Keywords: Method of Lines, Differential Transform Method.

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Authors: Fadi Awawdeh, H.M. Jaradat

Abstract:

In this paper, we establish existence and uniqueness of solutions for a class of inverse problems of degenerate differential equations. The main tool is the perturbation theory for linear operators.

Keywords: Inverse Problem, Degenerate Differential Equations, Perturbation Theory for Linear Operators

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Authors: Yngvar Berg, Mehdi Azadmehr

Abstract:

In this paper we present a linear autozeroing ultra lowvoltage amplifier. The autozeroing performed by all ULV circuits is important to reduce the impact of noise and especially avoid power supply noise in mixed signal low-voltage CMOS circuits. The simulated data presented is relevant for a 90nm TSMC CMOS process.

Keywords: Low-voltage, trans conductance amplifier, linearity, floating-gate.

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Authors: M. Bohlouli, M. Analoui

Abstract:

For complete support of Quality of Service, it is better that environment itself predicts resource requirements of a job by using special methods in the Grid computing. The exact and correct prediction causes exact matching of required resources with available resources. After the execution of each job, the used resources will be saved in the active database named "History". At first some of the attributes will be exploit from the main job and according to a defined similarity algorithm the most similar executed job will be exploited from "History" using statistic terms such as linear regression or average, resource requirements will be predicted. The new idea in this research is based on active database and centralized history maintenance. Implementation and testing of the proposed architecture results in accuracy percentage of 96.68% to predict CPU usage of jobs and 91.29% of memory usage and 89.80% of the band width usage.

Keywords: Active Database, Grid Computing, ResourceRequirement Prediction, Scheduling,

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Authors: Chaudhuri Manoj Kumar Swain, Susmita Das

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This paper explores a detailed procedure of predicting a path loss (PL) model and its application in estimating the coverage probability in a WiMAX network. For this a hybrid approach is followed in predicting an empirical PL model of a 2.65 GHz WiMAX network deployed in a suburban environment. Data collection, statistical analysis, and regression analysis are the phases of operations incorporated in this approach and the importance of each of these phases has been discussed properly. The procedure of collecting data such as received signal strength indicator (RSSI) through experimental set up is demonstrated. From the collected data set, empirical PL and RSSI models are predicted with regression technique. Furthermore, with the aid of the predicted PL model, essential parameters such as PL exponent as well as the coverage probability of the network are evaluated. This research work may assist in the process of deployment and optimisation of any cellular network significantly.

Keywords: WiMAX, RSSI, path loss, coverage probability, regression analysis.

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Authors: Joe Walsh, Mike Climstein, Ian Timothy Heazlewood, Stephen Burke, Jyrki Kettunen, Kent Adams, Mark DeBeliso

Abstract:

Thousands of masters athletes participate quadrennially in the World Masters Games (WMG), yet this cohort of athletes remains proportionately under-investigated. Due to a growing global obesity pandemic in context of benefits of physical activity across the lifespan, the BMI trends for this unique population was of particular interest. The nexus between health, physical activity and aging is complex and has raised much interest in recent times due to the realization that a multifaceted approach is necessary in order to counteract the obesity pandemic. By investigating age based trends within a population adhering to competitive sport at older ages, further insight might be gleaned to assist in understanding one of many factors influencing this relationship.BMI was derived using data gathered on a total of 6,071 masters athletes (51.9% male, 48.1% female) aged 25 to 91 years ( =51.5, s =±9.7), competing at the Sydney World Masters Games (2009). Using linear and loess regression it was demonstrated that the usual tendency for prevalence of higher BMI increasing with age was reversed in the sample. This trend in reversal was repeated for both male and female only sub-sets of the sample participants, indicating the possibility of improved prevalence of BMI with increasing age for both the sample as a whole and these individual sub-groups.This evidence of improved classification in one index of health (reduced BMI) for masters athletes (when compared to the general population) implies there are either improved levels of this index of health with aging due to adherence to sport or possibly the reduced BMI is advantageous and contributes to this cohort adhering (or being attracted) to masters sport at older ages.

Keywords: Aging, masters athlete, Quetelet Index, sport

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Authors: Chiung-Ju Huang

Abstract:

This study utilizes the quantile regression analysis to examine the impact of governance (including democratic quality and technical quality) on happiness in 101 countries worldwide, classified as “developed countries” and “developing countries”. The empirical results show that the impact of democratic quality and technical quality on happiness is significantly positive for “developed countries”, while is insignificant for “developing countries”. The results suggest that the authorities in developed countries can enhance the level of individual happiness by means of improving the democracy quality and technical quality. However, for developing countries, promoting the quality of governance in order to enhance the level of happiness may not be effective. Policy makers in developed countries may pay more attention on increasing real GDP per capita instead of promoting the quality of governance to enhance individual happiness.

Keywords: Governance, happiness, multiple regression, quantile regression.

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Authors: Mohsen Ziaee

Abstract:

In this paper, a mixed integer linear programming (MILP) model is presented to solve the flexible job shop scheduling problem (FJSP). This problem is one of the hardest combinatorial problems. The objective considered is the minimization of the makespan. The computational results of the proposed MILP model were compared with those of the best known mathematical model in the literature in terms of the computational time. The results show that our model has better performance with respect to all the considered performance measures including relative percentage deviation (RPD) value, number of constraints, and total number of variables. By this improved mathematical model, larger FJS problems can be optimally solved in reasonable time, and therefore, the model would be a better tool for the performance evaluation of the approximation algorithms developed for the problem.

Keywords: Scheduling, flexible job shop, makespan, mixed integer linear programming.

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Authors: N. F. Jamaluddin, N. A. H. Aizam

Abstract:

This paper explains the educational timetabling problem, a type of scheduling problem that is considered as one of the most challenging problem in optimization and operational research. The university examination timetabling problem (UETP), which involves assigning a set number of exams into a set number of timeslots whilst fulfilling all required conditions, has been widely investigated. The limitation of available timeslots and resources with the increasing number of examinations are the main reasons in the difficulty of solving this problem. Dynamical change in the examination scheduling system adds up the complication particularly in coping up with the demand and new requirements by the communities. Our objective is to investigate these demands and requirements with subjects taken from Universiti Malaysia Terengganu (UMT), through questionnaires. Integer linear programming model which reflects the preferences obtained to produce an effective examination timetabling was formed.

Keywords: Demands, educational timetabling, integer linear programming, scheduling, university examination timetabling problem.

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Authors: Tomoaki Hashimoto

Abstract:

Recently, feedback control systems using random dither quantizers have been proposed for linear discrete-time systems. However, the constraints imposed on state and control variables have not yet been taken into account for the design of feedback control systems with random dither quantization. Model predictive control is a kind of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial and terminal time. An important advantage of model predictive control is its ability to handle constraints imposed on state and control variables. Based on the model predictive control approach, the objective of this paper is to present a control method that satisfies probabilistic state constraints for linear discrete-time feedback control systems with random dither quantization. In other words, this paper provides a method for solving the optimal control problems subject to probabilistic state constraints for linear discrete-time feedback control systems with random dither quantization.

Keywords: Optimal control, stochastic systems, discrete-time systems, probabilistic constraints, random dither quantization.

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Authors: Deepthi P.P., P.S. Sathidevi

Abstract:

Proposal for a secure stream cipher based on Linear Feedback Shift Registers (LFSR) is presented here. In this method, shift register structure used for polynomial modular division is combined with LFSR keystream generator to yield a new keystream generator with much higher periodicity. Security is brought into this structure by using the Boolean function to combine state bits of the LFSR keystream generator and taking the output through the Boolean function. This introduces non-linearity and security into the structure in a way similar to the Non-linear filter generator. The security and throughput of the suggested stream cipher is found to be much greater than the known LFSR based structures for the same key length.

Keywords: Linear Feedback Shift Register, Stream Cipher, Filter generator, Keystream generator, Modular division circuit

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Authors: Pierre Kenfack

Abstract:

In this paper we present a contribution for the modelling and control of the inverter voltage of a permanent magnet linear generator with multi air-gap structure. The time domain control method is based on instant comparison of reference signals, in the form of current or voltage, with actual or measured signals. The reference current or voltage must be kept close to the actual signal with a reasonable tolerance. In this work, the time domain control method is used to control tracking signals. The performance evaluation concerns the continuation of reference signal. Simulations validate very well the tracking of reference variables (current, voltage) by measured or actual signals. All is simulated and presented under PSIM Software to show the performance and robustness of the proposed controller.

Keywords: Control, permanent magnet, linear machine, multi air-gap structure.

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Authors: Kazuyoshi MORI

Abstract:

The two-stage compensator designs of linear system are investigated in the framework of the factorization approach. First, we give “full feedback" two-stage compensator design. Based on this result, various types of the two-stage compensator designs with partial feedbacks are derived.

Keywords: Linear System, Factorization Approach, Two-Stage Compensator Design, Parametrization of Stabilizing Controllers.

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Authors: Jiashang Jiang, Hao Liu, Yongxin Yuan

Abstract:

In this paper the gradient based iterative algorithms are presented to solve the following four types linear matrix equations: (a) AXB = F; (b) AXB = F, CXD = G; (c) AXB = F s. t. X = XT ; (d) AXB+CYD = F, where X and Y are unknown matrices, A,B,C,D, F,G are the given constant matrices. It is proved that if the equation considered has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. The numerical results show that the proposed method is reliable and attractive.

Keywords: Matrix equation, iterative algorithm, parameter estimation, minimum norm solution.

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Authors: C. Ardil

Abstract:

This paper introduces a new method for multiplecriteria decision making (MCDM) that avoids order reversal and ensures consistency in decision-making. The proposed method involves range targeting of benefit and cost criteria vectors for range normalization of the initial decision matrix. The Reference Linear Combination (RLC) is used to avoid the rank reversal problem. The preference order generated from the target score matrix does not require relative comparisons between alternatives but relies on a chosen reference solution point after transforming the original decision matrix into an MCDM problem by specifying the minimum and maximum bounds of each criterion. The efficiency and applicability of the proposed RLC method were demonstrated in the selection of commercial passenger aircraft. 

Keywords: Aircraft selection, reference linear combination (RLC), multiple criteria decision-making, MCDM

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Authors: Nicholas D. Assimakis

Abstract:

In linear estimation, the traditional Kalman filter uses the Kalman filter gain in order to produce estimation and prediction of the n-dimensional state vector using the m-dimensional measurement vector. The computation of the Kalman filter gain requires the inversion of an m x m matrix in every iteration. In this paper, a variation of the Kalman filter eliminating the Kalman filter gain is proposed. In the time varying case, the elimination of the Kalman filter gain requires the inversion of an n x n matrix and the inversion of an m x m matrix in every iteration. In the time invariant case, the elimination of the Kalman filter gain requires the inversion of an n x n matrix in every iteration. The proposed Kalman filter gain elimination algorithm may be faster than the conventional Kalman filter, depending on the model dimensions.

Keywords: Discrete time, linear estimation, Kalman filter, Kalman filter gain.

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Authors: Tahseen A. Jilani, Huda Yasin, Madiha Yasin, C. Ardil

Abstract:

In this paper we use data mining techniques to investigate factors that contribute significantly to enhancing the risk of acute coronary syndrome. We assume that the dependent variable is diagnosis – with dichotomous values showing presence or  absence of disease. We have applied binary regression to the factors affecting the dependent variable. The data set has been taken from two different cardiac hospitals of Karachi, Pakistan. We have total sixteen variables out of which one is assumed dependent and other 15 are independent variables. For better performance of the regression model in predicting acute coronary syndrome, data reduction techniques like principle component analysis is applied. Based on results of data reduction, we have considered only 14 out of sixteen factors.

Keywords: Acute coronary syndrome (ACS), binary logistic regression analyses, myocardial ischemia (MI), principle component analysis, unstable angina (U.A.).

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Authors: Chompunut Jantarasorn, Chutima Prommak

Abstract:

The important issue considered in the widespread deployment of Wireless Sensor Networks (WSNs) is an efficiency of the energy consumption. In this paper, we present a study of the optimal relay station planning problems using Binary Integer Linear Programming (BILP) model to minimize the energy consumption in WSNs. Our key contribution is that the proposed model not only ensures the required network lifetime but also guarantees the radio connectivity at high level of communication quality. Specially, we take into account effects of noise, signal quality limitation and bit error rate characteristics. Numerical experiments were conducted in various network scenarios. We analyzed the effects of different sensor node densities and distribution on the energy consumption.

Keywords: Binary Integer Linear Programming, BILP, Energy consumption, Optimal node placement and Wireless sensor networks.

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Authors: Jaharah A. Ghani, Muhammad Rizal, Ahmad Sayuti, Mohd Zaki Nuawi, Mohd Nizam Ab. Rahman, Che Hassan Che Haron

Abstract:

This study presents a new method for detecting the cutting tool wear based on the measured cutting force signals using the regression model and I-kaz method. The detection of tool wear was done automatically using the in-house developed regression model and 3D graphic presentation of I-kaz 3D coefficient during machining process. The machining tests were carried out on a CNC turning machine Colchester Master Tornado T4 in dry cutting condition, and Kistler 9255B dynamometer was used to measure the cutting force signals, which then stored and displayed in the DasyLab software. The progression of the cutting tool flank wear land (VB) was indicated by the amount of the cutting force generated. Later, the I-kaz was used to analyze all the cutting force signals from beginning of the cut until the rejection stage of the cutting tool. Results of the IKaz analysis were represented by various characteristic of I-kaz 3D coefficient and 3D graphic presentation. The I-kaz 3D coefficient number decreases when the tool wear increases. This method can be used for real time tool wear monitoring.

Keywords: mathematical model, I-kaz method, tool wear

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Authors: Sotirios Raptis

Abstract:

Health and Social care (HSc) services planning and scheduling are facing unprecedented challenges, due to the pandemic pressure and also suffer from unplanned spending that is negatively impacted by the global financial crisis. Data-driven approaches can help to improve policies, plan and design services provision schedules using algorithms that assist healthcare managers to face unexpected demands using fewer resources. The paper discusses services packing using statistical significance tests and machine learning (ML) to evaluate demands similarity and coupling. This is achieved by predicting the range of the demand (class) using ML methods such as Classification and Regression Trees (CART), Random Forests (RF), and Logistic Regression (LGR). The significance tests Chi-Squared and Student’s test are used on data over a 39 years span for which data exist for services delivered in Scotland. The demands are associated using probabilities and are parts of statistical hypotheses. These hypotheses, as their NULL part, assume that the target demand is statistically dependent on other services’ demands. This linking is checked using the data. In addition, ML methods are used to linearly predict the above target demands from the statistically found associations and extend the linear dependence of the target’s demand to independent demands forming, thus, groups of services. Statistical tests confirmed ML coupling and made the prediction statistically meaningful and proved that a target service can be matched reliably to other services while ML showed that such marked relationships can also be linear ones. Zero padding was used for missing years records and illustrated better such relationships both for limited years and for the entire span offering long-term data visualizations while limited years periods explained how well patients numbers can be related in short periods of time or that they can change over time as opposed to behaviours across more years. The prediction performance of the associations were measured using metrics such as Receiver Operating Characteristic (ROC), Area Under Curve (AUC) and Accuracy (ACC) as well as the statistical tests Chi-Squared and Student. Co-plots and comparison tables for the RF, CART, and LGR methods as well as the p-value from tests and Information Exchange (IE/MIE) measures are provided showing the relative performance of ML methods and of the statistical tests as well as the behaviour using different learning ratios. The impact of k-neighbours classification (k-NN), Cross-Correlation (CC) and C-Means (CM) first groupings was also studied over limited years and for the entire span. It was found that CART was generally behind RF and LGR but in some interesting cases, LGR reached an AUC = 0 falling below CART, while the ACC was as high as 0.912 showing that ML methods can be confused by zero-padding or by data’s irregularities or by the outliers. On average, 3 linear predictors were sufficient, LGR was found competing well RF and CART followed with the same performance at higher learning ratios. Services were packed only when a significance level (p-value) of their association coefficient was more than 0.05. Social factors relationships were observed between home care services and treatment of old people, low birth weights, alcoholism, drug abuse, and emergency admissions. The work found  that different HSc services can be well packed as plans of limited duration, across various services sectors, learning configurations, as confirmed by using statistical hypotheses.

Keywords: Class, cohorts, data frames, grouping, prediction, probabilities, services.

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Authors: M. B. Meenavathi, K. Rajesh

Abstract:

In this paper, we propose a new class of Volterra series based filters for image enhancement and restoration. Generally the linear filters reduce the noise and cause blurring at the edges. Some nonlinear filters based on median operator or rank operator deal with only impulse noise and fail to cancel the most common Gaussian distributed noise. A class of second order Volterra filters is proposed to optimize the trade-off between noise removal and edge preservation. In this paper, we consider both the Gaussian and mixed Gaussian-impulse noise to test the robustness of the filter. Image enhancement and restoration results using the proposed Volterra filter are found to be superior to those obtained with standard linear and nonlinear filters.

Keywords: Gaussian noise, Image enhancement, Imagerestoration, Linear filters, Nonlinear filters, Volterra series.

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Authors: R. B. Knudsen, O. T. Rasmussen, R. A. Alphinas

Abstract:

The reason for conducting this research is to develop an algorithm that is capable of classifying news articles from the automobile industry, according to the competitive actions that they entail, with the use of Text Mining (TM) methods. It is needed to test how to properly preprocess the data for this research by preparing pipelines which fits each algorithm the best. The pipelines are tested along with nine different classification algorithms in the realm of regression, support vector machines, and neural networks. Preliminary testing for identifying the optimal pipelines and algorithms resulted in the selection of two algorithms with two different pipelines. The two algorithms are Logistic Regression (LR) and Artificial Neural Network (ANN). These algorithms are optimized further, where several parameters of each algorithm are tested. The best result is achieved with the ANN. The final model yields an accuracy of 0.79, a precision of 0.80, a recall of 0.78, and an F1 score of 0.76. By removing three of the classes that created noise, the final algorithm is capable of reaching an accuracy of 94%.

Keywords: Artificial neural network, competitive dynamics, logistic regression, text classification, text mining.

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Authors: Jason Sheng-Hong Tsai, Faezeh Ebrahimzadeh, Min-Ching Chung, Shu-Mei Guo, Leang-San Shieh, Tzong-Jiy Tsai, Li Wang

Abstract:

In this paper, we first construct a new state and disturbance estimator using discrete-time proportional plus integral observer to estimate the system state and the unknown external disturbance for the discrete-time system with an input-to-output direct-feedthrough term. Then, the generalized optimal linear quadratic digital tracker design is applied to construct a proportional plus integral observer-based tracker for the system with an unknown external disturbance to have a desired tracking performance. Finally, a numerical simulation is given to demonstrate the effectiveness of the new application of our proposed approach.

Keywords: Optimal linear quadratic tracker, proportional plus integral observer, state estimator, disturbance estimator.

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