Abstract: Based on the conjugate gradient (CG) algorithm, the constrained matrix equation AXB=C and the associate optimal approximation problem are considered for the symmetric arrowhead matrix solutions in the premise of consistency. The convergence results of the method are presented. At last, a numerical example is given to illustrate the efficiency of this method.
Abstract: The conjugate gradient optimization algorithm is combined with the modified back propagation algorithm to yield a computationally efficient algorithm for training multilayer perceptron (MLP) networks (CGFR/AG). The computational efficiency is enhanced by adaptively modifying initial search direction as described in the following steps: (1) Modification on standard back propagation algorithm by introducing a gain variation term in the activation function, (2) Calculation of the gradient descent of error with respect to the weights and gains values and (3) the determination of a new search direction by using information calculated in step (2). The performance of the proposed method is demonstrated by comparing accuracy and computation time with the conjugate gradient algorithm used in MATLAB neural network toolbox. The results show that the computational efficiency of the proposed method was better than the standard conjugate gradient algorithm.
Abstract: The Linear discriminant analysis (LDA) can be
generalized into a nonlinear form - kernel LDA (KLDA) expediently
by using the kernel functions. But KLDA is often referred to a general
eigenvalue problem in singular case. To avoid this complication, this
paper proposes an iterative algorithm for the two-class KLDA. The
proposed KLDA is used as a nonlinear discriminant classifier, and the
experiments show that it has a comparable performance with SVM.
Abstract: According to conjugate gradient algorithm, a new consensus protocol algorithm of discrete-time multi-agent systems is presented, which can achieve finite-time consensus. Finally, a numerical example is given to illustrate our theoretical result.
Abstract: In intensity modulated radiation therapy (IMRT)
treatment planning, beam angles are usually preselected on the basis of
experience and intuition. Therefore, getting an appropriate beam
configuration needs a very long time. Based on the present situation,
the paper puts forward beam orientation optimization using ant colony
optimization (ACO). We use ant colony optimization to select the
beam configurations, after getting the beam configuration using
Conjugate Gradient (CG) algorithm to optimize the intensity profiles.
Combining with the information of the effect of pencil beam, we can
get the global optimal solution accelerating. In order to verify the
feasibility of the presented method, a simulated and clinical case was
tested, compared with dose-volume histogram and isodose line
between target area and organ at risk. The results showed that the
effect was improved after optimizing beam configurations. The
optimization approach could make treatment planning meet clinical
requirements more efficiently, so it had extensive application
perspective.
Abstract: The conjugate gradient optimization algorithm
usually used for nonlinear least squares is presented and is
combined with the modified back propagation algorithm yielding
a new fast training multilayer perceptron (MLP) algorithm
(CGFR/AG). The approaches presented in the paper consist of
three steps: (1) Modification on standard back propagation
algorithm by introducing gain variation term of the activation
function, (2) Calculating the gradient descent on error with
respect to the weights and gains values and (3) the determination
of the new search direction by exploiting the information
calculated by gradient descent in step (2) as well as the previous
search direction. The proposed method improved the training
efficiency of back propagation algorithm by adaptively modifying
the initial search direction. Performance of the proposed method
is demonstrated by comparing to the conjugate gradient algorithm
from neural network toolbox for the chosen benchmark. The
results show that the number of iterations required by the
proposed method to converge is less than 20% of what is required
by the standard conjugate gradient and neural network toolbox
algorithm.