Kun Zhu¹, Nana Zhang¹, Qing Zhang², Shi Ying^{1, *}, Xu Wang³

CMC-Computers, Materials & Continua, Vol.65, No.2, pp. 1467-1486, 2020, DOI:10.32604/cmc.2020.011415

Abstract Software defect prediction plays a very important role in software quality assurance, which aims to inspect as many potentially defect-prone software modules as possible. However, the performance of the prediction model is susceptible to high dimensionality of the dataset that contains irrelevant and redundant features. In addition, software metrics for software defect prediction are almost entirely traditional features compared to the deep semantic feature representation from deep learning techniques. To address these two issues, we propose the following two solutions in this paper: (1) We leverage a novel non-linear manifold learning method - SOINN Landmark… More >

Ligang Zheng^1,*, Chao Song²

CMC-Computers, Materials & Continua, Vol.56, No.3, pp. 529-539, 2018, DOI:10.3970/cmc.2018.03780

Abstract There is a steep increase in data encoded as symmetric positive definite (SPD) matrix in the past decade. The set of SPD matrices forms a Riemannian manifold that constitutes a half convex cone in the vector space of matrices, which we sometimes call SPD manifold. One of the fundamental problems in the application of SPD manifold is to find the nearest neighbor of a queried SPD matrix. Hashing is a popular method that can be used for the nearest neighbor search. However, hashing cannot be directly applied to SPD manifold due to its non-Euclidean intrinsic More >

Muhammad Shoaib Arif¹, Mairaj Bibi², Adnan Jhangir³

CMC-Computers, Materials & Continua, Vol.54, No.2, pp. 181-195, 2018, DOI:10.3970/cmc.2018.054.181

Abstract This communique is opted to study the approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices. We choose the geodesic distance between -AHX - XA and P as the cost function, and put forward the Extended Hamiltonian algorithm (EHA) and Natural gradient algorithm (NGA) for the solution. Finally, several numerical experiments give you an idea about the effectiveness of the proposed algorithms. We also show the comparison between these two algorithms EHA and NGA. Obtained results are provided and analyzed graphically. We also conclude that the extended Hamiltonian algorithm has More >

Chein-Shan Liu¹

CMC-Computers, Materials & Continua, Vol.39, No.2, pp. 153-178, 2014, DOI:10.3970/cmc.2014.039.153

Abstract For the numerical solution of an ill-posed positive linear system we combine the methods from invariant manifold theory and sliding mode control theory, developing an affine nonlinear dynamical system with a positive control force and with the residual vector as being a gain vector. This system is proven asymptotically stable to the zero residual vector by using an argument from the Lyapunov stability theory. We find that the system fast tends to the sliding surface and then moves with a sliding mode, such that the resultant sliding mode control algorithm (SMCA) is robust against large More >

Chein-Shan Liu ¹

CMC-Computers, Materials & Continua, Vol.33, No.2, pp. 175-198, 2013, DOI:10.3970/cmc.2013.033.175

Abstract An optimal m-vector descent iterative algorithm in a Krylov subspace is developed, of which the m weighting parameters are optimized from a properly defined objective function to accelerate the convergence rate in solving an ill-posed linear problem. The optimal multi-vector iterative algorithm (OMVIA) is convergent fast and accurate, which is verified by numerical tests of several linear inverse problems, including the backward heat conduction problem, the heat source identification problem, the inverse Cauchy problem, and the external force recovery problem. Because the OMVIA has a good filtering effect, the numerical results recovered are quite smooth More >

C. Delprete¹, F. Freschi², M. Repetto², C. Rosso¹

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.5, pp. 397-420, 2013, DOI:10.3970/cmes.2013.094.397

Abstract The growing necessity of accuracy in analyzing engineering problems requires more detailed and sophisticated models. Those models can include multiphysics interactions, that, sometimes, are highly nonlinear and the application of the superposition principle is then not possible. The cell method can be suitably used to study nonlinear multiphysics problems, because its theoretical framework for the physical laws is intrinsically multiphysics. In this way it is possible to take into account the mutual effects between different physics. Within the cell method framework, the coupling terms can be directly formulated in terms of the global variables used More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.3, pp. 241-269, 2013, DOI:10.32604/cmes.2013.092.241

Abstract In order to solve an ill-posed linear problem, we propose an innovative Jacobian type iterative method by presetting a conditioner before the steepest descent direction. The preconditioner is derived from an invariant manifold approach, which includes two parameters α and γ to be determined. When the weighting parameter α is optimized by minimizing a properly defined objective function, the relaxation parameter γ can be derived to accelerate the convergence speed under a switching criterion. When the switch is turned-on, by using the derived value of γ it can pull back the iterative orbit to the fast manifold. More >

Y.C. Cai^1,2,3, J. Wu², S.N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.1, pp. 63-85, 2013, DOI:10.3970/cmes.2013.092.063

Abstract The numerical manifold method (NMM), based on the finite covers, unifies the continuum analyses and discontinuum analyses without changing a predefined mathematical mesh of the uncracked solid, and has the advantages of being concise in theory as well as being clear in concept. It provides a natural method to analyze complex shaped strong discontinuities as well as weak discontinuities such as multiple cracks, intersecting cracks, and branched cracks. However, the absence of an effective algorithm for cover generation, to date, is still a bottle neck in the research and application in the NMM. To address… More >

Chih-Wen Chang^1,2, Chein-Shan Liu³

CMC-Computers, Materials & Continua, Vol.34, No.2, pp. 143-175, 2013, DOI:10.3970/cmc.2013.034.143

Abstract The nonlinear Poisson problems in heat diffusion governed by elliptic type partial differential equations are solved by a modified globally optimal iterative algorithm (MGOIA). The MGOIA is a purely iterative method for searching the solution vector x without using the invert of the Jacobian matrix D. Moreover, we reveal the weighting parameter αc in the best descent vector w = αcE + DTE and derive the convergence rate and find a criterion of the parameter γ. When utilizing αc and γ, we can further accelerate the convergence speed several times. Several numerical experiments are carefully More >

Chih-Wen Chang^1,2, Chein-Shan Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.4, pp. 269-292, 2012, DOI:10.3970/cmes.2012.088.269

Abstract In this article, we utilize an optimal vector driven algorithm (OVDA) to cope with the nonlinear heat conduction problems (HCPs). From this set of nonlinear ordinary differential equations, we propose a purely iterative scheme and the spatial-discretization of finite difference method for revealing the solution vector x, without having to invert the Jacobian matrix D. Furthermore, we introduce three new ideas of bifurcation, attracting set and optimal combination, which are restrained by two parameters g and a. Several numerical instances of nonlinear systems under noise are examined, finding that the OVDA has a fast convergence More >