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.
Conjugate gradient (CG) methods are widely used in solving nonlinear unconstrained optimization problems such as designs, economics, physics and engineering due to its low computational memory requirement. In this paper, a new modifications of CG coefficient ( ) which possessed global convergence properties is proposed by using exact line search. Based on the number of iterations and central processing unit (CPU) time, the numerical results show that the new performs better than some other well known CG methods under some standard test functions.
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.
<p><span>Hybridization is one of the popular approaches in modifying the conjugate gradient method. In this paper, a new hybrid conjugate gradient is suggested and analyzed in which the parameter <!--[if gte mso 9]><xml>
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</xml><![endif]--> while using exact line search. The proposed method is shown to possess both sufficient descent and global convergence properties. Numerical performances show that the proposed method is promising and has overpowered other hybrid conjugate gradient methods in its number of iterations and central processing unit per time. </span></p>
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