This paper presents two novel algorithms for feature extraction-Subpattern Complete Two Dimensional Linear Discriminant Principal Component Analysis (SpC2DLDPCA) and Subpattern Complete Two Dimensional Locality Preser...This paper presents two novel algorithms for feature extraction-Subpattern Complete Two Dimensional Linear Discriminant Principal Component Analysis (SpC2DLDPCA) and Subpattern Complete Two Dimensional Locality Preserving Principal Component Analysis (SpC2DLPPCA). The modified SpC2DLDPCA and SpC2DLPPCA algorithm over their non-subpattern version and Subpattern Complete Two Dimensional Principal Component Analysis (SpC2DPCA) methods benefit greatly in the following four points: (1) SpC2DLDPCA and SpC2DLPPCA can avoid the failure that the larger dimension matrix may bring about more consuming time on computing their eigenvalues and eigenvectors. (2) SpC2DLDPCA and SpC2DLPPCA can extract local information to implement recognition. (3)The idea of subblock is introduced into Two Dimensional Principal Component Analysis (2DPCA) and Two Dimensional Linear Discriminant Analysis (2DLDA). SpC2DLDPCA combines a discriminant analysis and a compression technique with low energy loss. (4) The idea is also introduced into 2DPCA and Two Dimensional Locality Preserving projections (2DLPP), so SpC2DLPPCA can preserve local neighbor graph structure and compact feature expressions. Finally, the experiments on the CASIA(B) gait database show that SpC2DLDPCA and SpC2DLPPCA have higher recognition accuracies than their non-subpattern versions and SpC2DPCA.展开更多
A multilayer flow is a stratified fluid composed of a finite number of layers with densities homogeneous within one layer but different from each other. It is an intermediate system between the single-layer barotropic...A multilayer flow is a stratified fluid composed of a finite number of layers with densities homogeneous within one layer but different from each other. It is an intermediate system between the single-layer barotropic model and the continuously stratified baroclinic model. Since this system can simulate the baroclinic effect simply, it is widely used to study the large-scale dynamic process in atmosphere and ocean. The present paper is concerned with the linear stability of the multilayer quasi-geostrophic flow, and the associated linear stability criteria are established. Firstly, the nonlinear model is turned into the form of a Hamiltonian system, and a basic flow is defined. But it cannot be an extreme point of the Hamiltonian function since the system is an infinite-dimensional one. Therefore, it is necessary to reconstruct a new Hamiltonian function so that the basic flow becomes an extreme point of it. Secondly, the linearized equations of disturbances in the multilayer quasi-geostrophic flow are derived by introducing infinitesimal disturbances superposed on the basic flows. Finally, the properties of the linearized system are discussed, and the linear stability criteria in the sense of Liapunov are derived under two different conditions with respect to certain norms.展开更多
An algorithm for calculating gravity effect of three-dimensional (3D) linear density distribution is presented in this paper. The linear continuous density distribution is represented with 3D grid model, which has a ...An algorithm for calculating gravity effect of three-dimensional (3D) linear density distribution is presented in this paper. The linear continuous density distribution is represented with 3D grid model, which has a resemblance to the velocity model used in some seismic tomography codes. The consensus in representation method of density model and velocity model facilitates the seismic-gravity-integrated interpretation or simultaneous inversion. The numerical test of synthetic data shows that although the analytical gravity formula for linear density distribution is more complex than that for piecewise constant density distribution, it takes less time to calculate the gravity effect with linear density model than that with piecewise constant density model. In addition, this method is used in the integrated interpretation of 3D seismological tomography and gravity data in Dabie Mountain area.展开更多
This paper addresses the new algebraic test to check the aperiodic stability of two dimensional linear time invariant discrete systems. Initially, the two dimensional characteristics equations are converted into equiv...This paper addresses the new algebraic test to check the aperiodic stability of two dimensional linear time invariant discrete systems. Initially, the two dimensional characteristics equations are converted into equivalent one-dimensional equation. Further Fuller’s idea is applied on the equivalent one-dimensional characteristics equation. Then using the co-efficient of the characteristics equation, the routh table is formed to ascertain the aperiodic stability of the given two-dimensional linear discrete system. The illustrations were presented to show the applicability of the proposed technique.展开更多
The Ablowitz-Ladik equation is a very important model in nonlinear mathematical physics. In this paper, the hyper- bolic function solitary wave solutions, the trigonometric function periodic wave solutions, and the ra...The Ablowitz-Ladik equation is a very important model in nonlinear mathematical physics. In this paper, the hyper- bolic function solitary wave solutions, the trigonometric function periodic wave solutions, and the rational wave solutions with more arbitrary parameters of two-dimensional Ablowitz-Ladik equation are derived by using the （GI/G）-expansion method, and the effects of the parameters （including the coupling constant and other parameters） on the linear stability of the exact solutions are analysed and numerically simulated.展开更多
In this paper,the k major cone and strict k major cone in real infinite dimensional linear space are introduced,through which the k major order is defined,and their properties are also discussed.Therefore,with the ...In this paper,the k major cone and strict k major cone in real infinite dimensional linear space are introduced,through which the k major order is defined,and their properties are also discussed.Therefore,with the help of them any two elements in real infinite dimensional linear space can be compared.展开更多
This paper deals with a new higher order compact difference scheme, which is, O(h4) using coupled approach on the 19-point 3D stencil for the solution of three dimensional nonlinear biharmonic equations. At each inter...This paper deals with a new higher order compact difference scheme, which is, O(h4) using coupled approach on the 19-point 3D stencil for the solution of three dimensional nonlinear biharmonic equations. At each internal grid point, the solution u(x,y,z) and its Laplacian Δ4u are obtained. The resulting stencil algo-rithm is presented and hence this new algorithm can be easily incorporated to solve many problems. The present discretization allows us to use the Dirichlet boundary conditions only and there is no need to discretize the derivative boundary conditions near the boundary. We also show that special treatment is required to handle the boundary conditions. Convergence analysis for a model problem is briefly discussed. The method is tested on three problems and compares very favourably with the corresponding second order approximation which we also discuss using coupled approach.展开更多
This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an e...This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an equivalent single dimensional characteristic equation is formed from the two dimensional characteristic equation then the stability formulation in the left half of Z-plane, where the roots of characteristic equation f(Z) = 0 should lie within the shifted unit circle. The coefficient of the unit shifted characteristic equation is suitably arranged in the form of matrix and the inner determinants are evaluated using proposed Jury’s concept. The proposed stability technique is simple and direct. It reduces the computational cost. An illustrative example shows the applicability of the proposed scheme.展开更多
<strong>Purpose:</strong><span style="font-family:;" "=""><span style="font-family:Verdana;"> This study sought to review the characteristics, strengths, weak...<strong>Purpose:</strong><span style="font-family:;" "=""><span style="font-family:Verdana;"> This study sought to review the characteristics, strengths, weaknesses variants, applications areas and data types applied on the various </span><span><span style="font-family:Verdana;">Dimension Reduction techniques. </span><b><span style="font-family:Verdana;">Methodology: </span></b><span style="font-family:Verdana;">The most commonly used databases employed to search for the papers were ScienceDirect, Scopus, Google Scholar, IEEE Xplore and Mendeley. An integrative review was used for the study where </span></span></span><span style="font-family:Verdana;">341</span><span style="font-family:;" "=""><span style="font-family:Verdana;"> papers were reviewed. </span><b><span style="font-family:Verdana;">Results:</span></b><span style="font-family:Verdana;"> The linear techniques considered were Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), Singular Value Decomposition (SVD), Latent Semantic Analysis (LSA), Locality Preserving Projections (LPP), Independent Component Analysis (ICA) and Project Pursuit (PP). The non-linear techniques which were developed to work with applications that ha</span></span><span style="font-family:Verdana;">ve</span><span style="font-family:Verdana;"> complex non-linear structures considered were Kernel Principal Component Analysis (KPC</span><span style="font-family:Verdana;">A), Multi</span><span style="font-family:Verdana;">-</span><span style="font-family:;" "=""><span style="font-family:Verdana;">dimensional Scaling (MDS), Isomap, Locally Linear Embedding (LLE), Self-Organizing Map (SOM), Latent Vector Quantization (LVQ), t-Stochastic </span><span style="font-family:Verdana;">neighbor embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP). DR techniques can further be categorized into supervised, unsupervised and more recently semi-supervised learning methods. The supervised versions are the LDA and LVQ. All the other techniques are unsupervised. Supervised variants of PCA, LPP, KPCA and MDS have </span><span style="font-family:Verdana;">been developed. Supervised and semi-supervised variants of PP and t-SNE have also been developed and a semi supervised version of the LDA has been developed. </span><b><span style="font-family:Verdana;">Conclusion:</span></b><span style="font-family:Verdana;"> The various application areas, strengths, weaknesses and variants of the DR techniques were explored. The different data types that have been applied on the various DR techniques were also explored.</span></span>展开更多
基金Sponsored by the National Science Foundation of China( Grant No. 61201370,61100103)the Independent Innovation Foundation of Shandong University( Grant No. 2012DX07)
文摘This paper presents two novel algorithms for feature extraction-Subpattern Complete Two Dimensional Linear Discriminant Principal Component Analysis (SpC2DLDPCA) and Subpattern Complete Two Dimensional Locality Preserving Principal Component Analysis (SpC2DLPPCA). The modified SpC2DLDPCA and SpC2DLPPCA algorithm over their non-subpattern version and Subpattern Complete Two Dimensional Principal Component Analysis (SpC2DPCA) methods benefit greatly in the following four points: (1) SpC2DLDPCA and SpC2DLPPCA can avoid the failure that the larger dimension matrix may bring about more consuming time on computing their eigenvalues and eigenvectors. (2) SpC2DLDPCA and SpC2DLPPCA can extract local information to implement recognition. (3)The idea of subblock is introduced into Two Dimensional Principal Component Analysis (2DPCA) and Two Dimensional Linear Discriminant Analysis (2DLDA). SpC2DLDPCA combines a discriminant analysis and a compression technique with low energy loss. (4) The idea is also introduced into 2DPCA and Two Dimensional Locality Preserving projections (2DLPP), so SpC2DLPPCA can preserve local neighbor graph structure and compact feature expressions. Finally, the experiments on the CASIA(B) gait database show that SpC2DLDPCA and SpC2DLPPCA have higher recognition accuracies than their non-subpattern versions and SpC2DPCA.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.41575026,41275113,and 41475021)
文摘A multilayer flow is a stratified fluid composed of a finite number of layers with densities homogeneous within one layer but different from each other. It is an intermediate system between the single-layer barotropic model and the continuously stratified baroclinic model. Since this system can simulate the baroclinic effect simply, it is widely used to study the large-scale dynamic process in atmosphere and ocean. The present paper is concerned with the linear stability of the multilayer quasi-geostrophic flow, and the associated linear stability criteria are established. Firstly, the nonlinear model is turned into the form of a Hamiltonian system, and a basic flow is defined. But it cannot be an extreme point of the Hamiltonian function since the system is an infinite-dimensional one. Therefore, it is necessary to reconstruct a new Hamiltonian function so that the basic flow becomes an extreme point of it. Secondly, the linearized equations of disturbances in the multilayer quasi-geostrophic flow are derived by introducing infinitesimal disturbances superposed on the basic flows. Finally, the properties of the linearized system are discussed, and the linear stability criteria in the sense of Liapunov are derived under two different conditions with respect to certain norms.
文摘An algorithm for calculating gravity effect of three-dimensional (3D) linear density distribution is presented in this paper. The linear continuous density distribution is represented with 3D grid model, which has a resemblance to the velocity model used in some seismic tomography codes. The consensus in representation method of density model and velocity model facilitates the seismic-gravity-integrated interpretation or simultaneous inversion. The numerical test of synthetic data shows that although the analytical gravity formula for linear density distribution is more complex than that for piecewise constant density distribution, it takes less time to calculate the gravity effect with linear density model than that with piecewise constant density model. In addition, this method is used in the integrated interpretation of 3D seismological tomography and gravity data in Dabie Mountain area.
文摘This paper addresses the new algebraic test to check the aperiodic stability of two dimensional linear time invariant discrete systems. Initially, the two dimensional characteristics equations are converted into equivalent one-dimensional equation. Further Fuller’s idea is applied on the equivalent one-dimensional characteristics equation. Then using the co-efficient of the characteristics equation, the routh table is formed to ascertain the aperiodic stability of the given two-dimensional linear discrete system. The illustrations were presented to show the applicability of the proposed technique.
基金Project supported by the Basic Science and the Front Technology Research Foundation of Henan Province,China(Grant Nos.092300410179 and122102210427)the Doctoral Scientific Research Foundation of Henan University of Science and Technology,China(Grant No.09001204)+1 种基金the Scientific Research Innovation Ability Cultivation Foundation of Henan University of Science and Technology,China(Grant No.011CX011)the Scientific Research Foundation of Henan University of Science and Technology(Grant No.2012QN011)
文摘The Ablowitz-Ladik equation is a very important model in nonlinear mathematical physics. In this paper, the hyper- bolic function solitary wave solutions, the trigonometric function periodic wave solutions, and the rational wave solutions with more arbitrary parameters of two-dimensional Ablowitz-Ladik equation are derived by using the （GI/G）-expansion method, and the effects of the parameters （including the coupling constant and other parameters） on the linear stability of the exact solutions are analysed and numerically simulated.
文摘In this paper,the k major cone and strict k major cone in real infinite dimensional linear space are introduced,through which the k major order is defined,and their properties are also discussed.Therefore,with the help of them any two elements in real infinite dimensional linear space can be compared.
文摘This paper deals with a new higher order compact difference scheme, which is, O(h4) using coupled approach on the 19-point 3D stencil for the solution of three dimensional nonlinear biharmonic equations. At each internal grid point, the solution u(x,y,z) and its Laplacian Δ4u are obtained. The resulting stencil algo-rithm is presented and hence this new algorithm can be easily incorporated to solve many problems. The present discretization allows us to use the Dirichlet boundary conditions only and there is no need to discretize the derivative boundary conditions near the boundary. We also show that special treatment is required to handle the boundary conditions. Convergence analysis for a model problem is briefly discussed. The method is tested on three problems and compares very favourably with the corresponding second order approximation which we also discuss using coupled approach.
文摘This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an equivalent single dimensional characteristic equation is formed from the two dimensional characteristic equation then the stability formulation in the left half of Z-plane, where the roots of characteristic equation f(Z) = 0 should lie within the shifted unit circle. The coefficient of the unit shifted characteristic equation is suitably arranged in the form of matrix and the inner determinants are evaluated using proposed Jury’s concept. The proposed stability technique is simple and direct. It reduces the computational cost. An illustrative example shows the applicability of the proposed scheme.
文摘<strong>Purpose:</strong><span style="font-family:;" "=""><span style="font-family:Verdana;"> This study sought to review the characteristics, strengths, weaknesses variants, applications areas and data types applied on the various </span><span><span style="font-family:Verdana;">Dimension Reduction techniques. </span><b><span style="font-family:Verdana;">Methodology: </span></b><span style="font-family:Verdana;">The most commonly used databases employed to search for the papers were ScienceDirect, Scopus, Google Scholar, IEEE Xplore and Mendeley. An integrative review was used for the study where </span></span></span><span style="font-family:Verdana;">341</span><span style="font-family:;" "=""><span style="font-family:Verdana;"> papers were reviewed. </span><b><span style="font-family:Verdana;">Results:</span></b><span style="font-family:Verdana;"> The linear techniques considered were Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), Singular Value Decomposition (SVD), Latent Semantic Analysis (LSA), Locality Preserving Projections (LPP), Independent Component Analysis (ICA) and Project Pursuit (PP). The non-linear techniques which were developed to work with applications that ha</span></span><span style="font-family:Verdana;">ve</span><span style="font-family:Verdana;"> complex non-linear structures considered were Kernel Principal Component Analysis (KPC</span><span style="font-family:Verdana;">A), Multi</span><span style="font-family:Verdana;">-</span><span style="font-family:;" "=""><span style="font-family:Verdana;">dimensional Scaling (MDS), Isomap, Locally Linear Embedding (LLE), Self-Organizing Map (SOM), Latent Vector Quantization (LVQ), t-Stochastic </span><span style="font-family:Verdana;">neighbor embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP). DR techniques can further be categorized into supervised, unsupervised and more recently semi-supervised learning methods. The supervised versions are the LDA and LVQ. All the other techniques are unsupervised. Supervised variants of PCA, LPP, KPCA and MDS have </span><span style="font-family:Verdana;">been developed. Supervised and semi-supervised variants of PP and t-SNE have also been developed and a semi supervised version of the LDA has been developed. </span><b><span style="font-family:Verdana;">Conclusion:</span></b><span style="font-family:Verdana;"> The various application areas, strengths, weaknesses and variants of the DR techniques were explored. The different data types that have been applied on the various DR techniques were also explored.</span></span>
