A comparison on classical-hybrid conjugate gradient method under exact line search

One of the popular approaches in modifying the Conjugate Gradient (CG) Method is hybridization. In this paper, a new hybrid CG is introduced and its performance is compared to the classical CG method which are Rivaie-Mustafa-Ismail-Leong (RMIL) and Syarafina-Mustafa-Rivaie (SMR) methods. The proposed hybrid CG is evaluated as a convex combination of RMIL and SMR method. Their performance are analyzed under the exact line search. The comparison performance showed that the hybrid CG is promising and has outperformed the classical CG of RMIL and SMR in terms of the number of iterations and central processing unit per time

Identification of rainfall patterns on hydrological simulation using robust principal component analysis

A robust dimension reduction method in Principal Component Analysis (PCA) was used to rectify the issue of unbalanced clusters in rainfall patterns due to the skewed nature of rainfall data. A robust measure in PCA using Tukey’s biweight correlation to downweigh observations was introduced and the optimum breakdown point to extract the number of components in PCA using this approach is proposed. A set of simulated data matrix that mimicked the real data set was used to determine an appropriate breakdown point for robust PCA and compare the performance of the both approaches. The simulated data indicated a breakdown point of 70% cumulative percentage of variance gave a good balance in extracting the number of components. The results showed a more significant and substantial improvement with the robust PCA than the PCA based Pearson correlation in terms of the average number of clusters obtained and its cluster quality

Accelerated Proximal Iterative re-Weighted ℓ1\ell_1 Alternating Minimization for Image Deblurring

The quadratic penalty alternating minimization (AM) method is widely used for solving the convex $\ell_1$ total variation (TV) image deblurring problem. However, quadratic penalty AM for solving the nonconvex nonsmooth $\ell_p$, $0 < p < 1$ TV image deblurring problems is less studied. In this paper, we propose two algorithms, namely proximal iterative re-weighted $\ell_1$ AM (PIRL1-AM) and its accelerated version, accelerated proximal iterative re-weighted $\ell_1$ AM (APIRL1-AM) for solving the nonconvex nonsmooth $\ell_p$ TV image deblurring problem. The proposed algorithms are derived from the proximal iterative re-weighted $\ell_1$ (IRL1) algorithm and the proximal gradient algorithm. Numerical results show that PIRL1-AM is effective in retaining sharp edges in image deblurring while APIRL1-AM can further provide convergence speed up in terms of the number of algorithm iterations and computational time

Personality traits and its relationship with work performance for majority group of farmers in Malaysia

Paddy is regarded as the third most widely planted crop in Malaysia that covers an area of 686,050 hectares in total. Although a large scale rice cultivation is practiced in this country, it still falls short in meeting the demand for its ever growing population. According to Rogers’ theory, the majority group (early and late majority) influence most of the paddy production in Malaysia and they form 68% of the paddy farmers. In this regard, it suffices to say that most of the rice supply in this country came from this group of farmers. The objective of the study was to determine the relationship between personality traits and work performance among the paddy farmers in the majority group. A face to face survey was carried out using a questionnaire where the respondents were chosen using the cluster sampling technique. Descriptive analysis was used to describe the demographics of the respondents, while correlation and multiple regressions were used to examine the strength and relationship between personality traits and work performance. The correlation coefficients showed that six personal trait variables were positively correlated with work performance, and only one personal trait variable was negatively correlated with work performance at 0.05 level of significance. Specifically, discipline was found moderately correlated with work performance. Moreover, the results also showed that, the ability to solve problems, network information, and discipline were found to significantly predict work performance of the paddy farmers. Overall, these three variables explained 44% variance of the work performance. Respectively, it is recommended that extension programmes should focus on these three variables in order to increase the work performance of the majority groups of paddy farmers

Prediction of student’s academic performance during online learning based on regression in support vector machine

Since the Movement Control Order (MCO) was adopted, all the universities have implemented and modified the principle of online learning and teaching in consequence of Covid-19. This situation has relatively affected the students’ academic performance. Therefore, this paper employs the regression method in Support Vector Machine (SVM) to investigate the prediction of students’ academic performance in online learning during the Covid-19 pandemic. The data was collected from undergraduate students of the Department of Mathematics, Faculty of Science and Mathematics, Sultan Idris Education University (UPSI). Students’ Cumulative Grade Point Average (CGPA) during online learning indicates their academic performance. The algorithm of Support Vector Machine (SVM) as a machine learning was employed to construct a prediction model of students’ academic performance., Two parameters, namely C (cost) and epsilon of the Support Vector Machine (SVM) algorithm should be identified first prior to further analysis. The best parameter C (cost) and epsilon in SVM regression are 4 and 0.8. The parameters then were used for four kernels, i.e., radial basis function kernel, linear kernel, polynomial kernel, and sigmoid kernel. from the findings, the finest type of kernel is the radial basis function kernel, with the lowest support vector value and the lowest Root Mean Square Error (RMSE) which are 27 and 0.2557. Based on the research, the results show that the pattern of prediction of students’ academic performance is similar to the current CGPA. Therefore, Support Vector Machine regression can predict students’ academic performance

Performance analysis and validation of modified singular spectrum analysis based on simulation torrential rainfall data

A popular method for time series analysis to extract the components of noise and trend from the time series data is called the singular spectrum analysis (SSA). However, the drawback of SSA is its problem in determining the appropriate window length, L for certain data set in confirming patent separation of the components of trend and noise. Another issue that crops up when using SSA is that, over time, the sum of day-to-day rainfall becomes nearly comparable. In this case, disjoints sets of singular values and distinctive series components could essentially be intermixed, resulting in poor separability between trend and noise components. The introduction of modified SSA is to mitigate the problems efficiently. The performance of modified SSA is measured by using wcorrelation and RMSE based on simulated data. These results show that the parameter L = T/5 was suitable to use in short time series rainfall data. It can be proved by the plot of the extracted trend for modified SSA that appears to conform to the original data configuration for time series rainfall however there is the omission of components of noise predominantly for L = T/5 in detecting the uncharacteristically heavy downpour which could potentially initiate the occurrence of torrential rainfall. In addition, the result shows that average RMSE for reconstructed time series components of modified SSA is much smaller than SSA for each L

Global Convergence of a New Coefficient Nonlinear Conjugate Gradient Method

Nonlinear conjugate gradient (CG) methods are widely used in optimization field due to its efficiency for solving a large scale unconstrained optimization problems. Many studies and modifications have been developed in order to improve the method. The method is known to possess sufficient descend condition and its global convergence properties under strong Wolfe-Powell search direction. In this paper, the new coefficient of CG method is presented. The global convergence and sufficient descend properties of the new coefficient are established by using strong Wolfe-Powell line search direction. Results show that the new coefficient is able to globally converge under certain assumptions and theories

Performance Analysis and Validation of Modified Singular Spectrum Analysis based on Simulation Torrential Rainfall Data

A popular method for time series analysis to extract the components of noise and trend from the time series data is called the singular spectrum analysis (SSA). However, the drawback of SSA is its problem in determining the appropriate window length, L for certain data set in confirming patent separation of the components of trend and noise. Another issue that crops up when using SSA is that, over time, the sum of day-to-day rainfall becomes nearly comparable. In this case, disjoints sets of singular values and distinctive series components could essentially be intermixed, resulting in poor separability between trend and noise components. The introduction of modified SSA is to mitigate the problems efficiently. The performance of modified SSA is measured by using w-correlation and RMSE based on simulated data. These results show that the parameter L = T/5 was suitable to use in short time series rainfall data. It can be proved by the plot of the extracted trend for modified SSA that appears to conform to the original data configuration for time series rainfall however there is the omission of components of noise predominantly for L = T/5 in detecting the uncharacteristically heavy downpour which could potentially initiate the occurrence of torrential rainfall. In addition, the result shows that average RMSE for reconstructed time series components of modified SSA is much smaller than SSA for each

Pattern analysis of corona virus disease (COVID-19) - outbreak in Malaysia

The ongoing Corona Virus Disease (COVID-19) outbreak is now declared as the pandemic by World Health Organization (WHO). This disease began in Wuhan, China in late 2019 and is widely spread now all over the world. Progressively, Malaysia has been the leading country in Southeast Asia for this outbreak with cases more than 2000 as on 26th March 2020. This article highlights the analysis of the outbreak pattern which follows the exponential growth regression line. Data is collected daily for 66 days starting from the 1st case defined on 25th January 2020. Regression line is used because it can describe the relationship between predictors and the outcome within the datasets that can be used for prediction purposes. Fitting the real data to the graph, an equation which follows the exponential growth model is obtained. The calculation of the relative error between the exact and the approximate data shows that the pattern follows the exponential growth model as it is compared with the quadratic regression line. This analysis can be particularly beneficial for the health authorities in preparing immediate and effective strategies to flatten the curve. Malaysia government is currently working hard in flattening the curve by implementing Restricted Movement Order (RMO)