连续超松弛支持向量机回归算法应用研究

支持向量回归问题的研究,对函数拟合(回归逼近)具有重要的理论和应用意义.借鉴分类问题的有效算法,将其推广到回归问题中来,针对用于分类问题的SOR支持向量机有效算法,提出了SORR支持向量回归算法.在若干不同维数的数据集上,对SORR算法、ASVR算法和LibSVM算法进行数值试验,并进行比较分析.数值实验结果表明,SORR算法是有效的,与当前流行的支持向量机回归算法相比,在回归精度和学习速度上都有一定的优势.     

A modified symmetric successive overrelaxation method for augmented systems

In this paper, we establish a modified symmetric successive overrelaxation (MSSOR) method, to solve augmented systems of linear equations, which uses two relaxation parameters. This method is an extension of the symmetric SOR (SSOR) iterative method. The convergence of the MSSOR method for augmented systems is studied. Numerical examples show that the new method is an efficient method.     

Critical slowing-down in SU(2) Landau-gauge-fixing algorithms at β=∞

We evaluate numerically and analytically the dynamic critical exponent z for five gauge-fixing algorithms in SU(2) lattice Landau-gauge theory by considering the case β=∞. Numerical data are obtained in two, three and four dimensions. Results are in agreement with those obtained previously at finite β in two dimensions. The theoretical analysis, valid for any dimension d, helps us clarify the tuning of these algorithms. We also study generalizations of the overrelaxation algorithm and of the stochastic overrelaxation algorithm and verify that we cannot have a dynamic critical exponent z smaller than 1 with these local algorithms. Finally, the analytic approach is applied to the so-called λ-gauges, again at β=∞, and verified numerically for the two-dimensional case.     

A novel global optimization technique for high dimensional functions

Several types of line search methods are documented in the literature and are well known for unconstraint optimization problems. This paper proposes a modified line search method, which makes use of partial derivatives and restarts the search process after a given number of iterations by modifying the boundaries based on the best solution obtained at the previous iteration (or set of iterations). Using several high‐dimensional benchmark functions, we illustrate that the proposed line search restart (LSRS) approach is very suitable for high‐dimensional global optimization problems. Performance of the proposed algorithm is compared with two popular global optimization approaches, namely, genetic algorithm and particle swarm optimization method. Empirical results for up to 2000 dimensions clearly illustrate that the proposed approach performs very well for the tested high‐dimensional functions. © 2009 Wiley Periodicals, Inc.     

一种基于二维隐马尔可夫模型的图像分类算法

针对图像分块之间的相互依赖关系,提出一种基于二维隐马尔可夫模型的图像分类算 法。该算法将一维隐马尔可夫模型扩展成二维隐马尔可夫模型,模型中相邻的图像分块在平面两个 方向上按条件转移概率进行状态转换,反应出两个维上的依赖关系。隐马尔可夫模型参数通过期望 最大化算法(EM)来估计。同时,本文利用二维Viterbi算法,在训练隐马尔可夫模型的基础上,实现 对图像进行最优分类。文件图像分割的应用表明,隐马尔可夫算法优于CART算法。     

A Java extension with support for dimensions

We present an extension to the Java language with support for physical dimensions and units of measurement. This should reduce programming errors in scientific and technological areas. We discuss various aspects of dimensions and units, and then design principles for support in programming languages. An overview of earlier work shows that some language extensions focused on units, whereas we argue that dimensions are a better starting point; units can then simply be treated as constants. Then we present the Java extension, and show how to define and use dimensions and units. The communication between the program and the outer world gets special attention. The programmer can still make dimensional errors there, but we claim the risk is reduced. It has been simple to build support for this extension into an existing Java compiler. We outline the applied technique. Copyright © 1999 John Wiley & Sons, Ltd.     

Multi‐dimensional asymptotic waveform evaluation method and adaptive hopping technique

The multi‐dimensional asymptotic waveform evaluation (MD‐AWE) method is proposed as an extension of the conventional one dimensional asymptotic waveform evaluation (1D‐AWE) method. It can be applied in parameter analysis of structures, particularly with multiple variables, at which repeated calculations are required. The MD‐AWE is proposed at first, and then an adaptive hopping technique similar to the complex frequency hopping (CFH) technique to expand the approximation region of MD‐AWE is delivered, and this technique also helps to reduce the memory usage by taking lower order of MD‐AWE. In the end, two examples are given with good results, which show the efficiency and accuracy of the proposed method. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2008.     

Alternating splitting waveform relaxation method and its successive overrelaxation acceleration

For the large sparse implicit linear initial value problem, we present a block successive overrelaxation scheme for the alternating direction implicit waveform relaxation method to further accelerate its convergence speed, and discuss the convergence property of the resulting iteration method in detail. Numerical implementations about several non-Hermitian implicit linear initial value problems show that the alternating direction implicit waveform relaxation method is very effective, and the block successive overrelaxation technique really accelerates its convergence speed.     

Accelerating spectral atomic and molecular collisions methods with graphics processing units

We present a computation method to accelerate the calculation of the Hamiltonian of a three-body time independent Schrödinger equation for collisions. The Hamiltonian is constructed with one dimensional (basis overlaps) and two dimensional (interparticle interaction) integrals that are mapped into a computational grid in a Graphics Processing Unit (GPU). We illustrate the method for the case of an electron impact single ionization of a two electron atom. This proposal makes use of a Generalized Sturmian Basis set for each electron, which are obtained numerically on a quadrature grid that is used to compute the integrals in the GPU. The optimal computation is more than twenty times faster in the GPU than the calculation in CPU. The method can be easily scaled to computers with several Graphics Processing Units or clusters.     

Enhancing subspace clustering based on dynamic prediction

In high dimensional data, many dimensions are irrelevant to each other and clusters are usually hidden under noise. As an important extension of the traditional clustering, subspace clustering can be utilized to simultaneously cluster the high dimensional data into several subspaces and associate the low-dimensional subspaces with the corresponding points. In subspace clustering, it is a crucial step to construct an affinity matrix with block-diagonal form, in which the blocks correspond to different clusters. The distance-based methods and the representation-based methods are two major types of approaches for building an informative affinity matrix. In general, it is the difference between the density inside and outside the blocks that determines the efficiency and accuracy of the clustering. In this work, we introduce a well-known approach in statistic physics method, namely link prediction, to enhance subspace clustering by reinforcing the affinity matrix.More importantly,we introduce the idea to combine complex network theory with machine learning. By revealing the hidden links inside each block, we maximize the density of each block along the diagonal, while restrain the remaining non-blocks in the affinity matrix as sparse as possible. Our method has been shown to have a remarkably improved clustering accuracy comparing with the existing methods on well-known datasets.     

Convergence of the interval and point TOR method

In this paper, we present the interval version of the two parameter overrelaxation iterative (TOR) method and we obtain some convergence conditions when the matrix A of the linear system Ax?=?b belongs to some classes of matrice. Similar conditions were obtained for the point TOR method.

Some results for the accelerated overrelaxation interval and point iterative (AOR) method were also obtained, which coincides with those given by Martins in Ref. [7].     

Self-organizing mappings on the Grassmannian with applications to data analysis in high dimensions

We propose a method for extending Kohonen’s self-organizing mapping to the geometric framework of the Grassmannian. The resulting algorithm serves as a prototype of the extension of the SOM to the setting of abstract manifolds. The ingredients required for this are a means to measure distance between two points, and a method to move one point in the direction of another. In practice, the data are not required to have a representation in Euclidean space. We discuss in detail how a point on a Grassmannian is moved in the direction of another along a geodesic path. We demonstrate the implementation of the algorithm on several illustrative data sets, hyperspectral images and gene expression data sets.

     

Spectral multidomain technique with Local Fourier Basis

A novel domain decomposition method for spectrally accurate solutions of PDEs is presented. A Local Fourier Basis technique is adapted for the construction of the elemental solutions in subdomains.C ¹ continuity is achieved on the interfaces by a matching procedure using the analytical homogeneous solutions of a one dimensional equation. The method can be applied to the solution of elliptic problems of the Poisson or Helmholtz type as well as to time discretized parabolic problems in one or more dimensions. The accuracy is tested for several stiff problems with steep solutions.The present domain decomposition approach is particularly suitable for parallel implementations, in particular, on MIMD type parallel machines.This research is supported partly by a grant from the French-Israeli Binational Foundation for 1991–1992.     

Parallel algorithms for the solution of certain large sparse linear systems

A couple of approximate inversion techniques are presented which provide a parallel enhancement to several iterative methods for solving linear systems arising from the discretization of boundary value problems. In particular, the Jacobi, Gauss‐Seidel, and successive overrelaxation methods can be improved substantially in a parallel environment by the extensions considered. A special case convergence proof is presented. The use of our approximate inverses with the preconditioned conjugate gradient method is examined and comparisons are made with some recently proposed algorithms in this area that also employ approximate inverses. The methods considered are compared under sequential and parallel hardware assumptions.     

On the influence of shape and dimensions of particles on the properties of the modified particle-in-cell method

It is considered Harlow's particle-in-cell method modification which consists in the use of finite-size particles for two dimensional gasdynamics computations. The algorithm for computation of motion of finite size particles is described. It is shown that the use of finite size particles can lead to the local violation of the approximation of original differential equations. However the quantities obtained by averaging the numerical solution over certain spatial subdomains approximate the conservation laws. It is shown that if the characteristic particle dimensions tend to zero, then themodified particle-in-cell method passes to the original Harlow's method. Results of numerical experiments are given to illustrate the properties of the modified particle-in-cell method.     

The eigenvalue problem (A − λB)x = 0 for symmetric matrices of high order

Vibrational problems of complex structures treated by the method of finite elements lead to the general eigenvalue problem $\text{(A ? λB)x = 0}$, where $\text{A}$ and $\text{B}$ are symmetric and sparse matrices of high order. The smallest eigenvalues and corresponding eigenvectors of interest are usually computed by a variant of the inverse vector iteration. Instead of this, the smallest eigenvalue can be computed as the minimum of the corresponding Rayleigh quotient for instance by the method of the coordinate relaxation of Faddejew/Faddejewa. The slow convergence of this simple algorithm can however be sped up considerably in analogy to the successive overrelaxation method by a systematic overrelaxation. Numerical experiments indicate indeed a rate of convergence of this coordinate overrelaxation as a function of the relaxation parameter which is comparable to that of the usual seccessive overrelaxation for linear equations. In comparison with known procedures for the solution of the general eigenvalue problem there result some important computational advantages with regard to the amount of work. Finally, the higher eigenvalues can be computed successively by minimizing the Rayleigh quotient of a modified eigenvalue problem based on a deflation process.     

Parallel SSOR preconditioning for lattice QCD

The locally lexicographic symmetric successive overrelaxation algorithm (ll-SSOR) is the most effective parallel preconditioner known for iterative solvers used in lattice gauge theory. After reviewing the basic properties of ll-SSOR, the focus of this contribution is put on its parallel aspects: the administrative overhead of the parallel implementation of ll-SSOR, which is due to many conditional operations, decreases its efficiency by a factor of up to one third. A simple generalization of the algorithm is proposed that allows the application of the lexicographic ordering along specified axes, while along the other dimensions odd–even preconditioning is used. In this way one can tune the preconditioner towards optimal performance by balancing ll-SSOR effectivity and administrative overhead.     

The convergence factor of the parallel Schwarz overrelaxation method for linear systems

After introducing the parallel Schwarz overrelaxation method for linear systems, we analyse the convergence factor of the method in detail. The optimal overrelaxation parameter ω of the method is discussed in this paper. Some examples are also shown.     

An efficient split-step quasi-compact finite difference method for the nonlinear fractional Ginzburg–Landau equations

In this paper, we propose a split-step quasi-compact finite difference method to solve the nonlinear fractional Ginzburg–Landau equations both in one and two dimensions. The original equations are split into linear and nonlinear subproblems. The Riesz space fractional derivative is approximated by a fourth-order fractional quasi-compact method. Furthermore, an alternating direction implicit scheme is constructed for the two dimensional linear subproblem. The unconditional stability and convergence of the schemes are proved rigorously in the linear case. Numerical experiments are performed to confirm our theoretical findings and the efficiency of the proposed method.