正则化稀疏模型

正则化稀疏模型在机器学习和图像处理等领域发挥着越来越重要的作用,它具有变量选择功能,可以解决建模中的过拟合等问题．Tibshirani 提出的 Lasso 使得正则化稀疏模型真正开始流行．文中总结了各种正则化稀疏模型,指出了各个稀疏模型被提出的原因、所具有的优点、适宜解决的问题及其模型的具体形式．最后,文中还指出了正则化稀疏模型未来的研究方向．     

Real-time nonlinear MPC and MHE for a large-scale mechatronic application

Progress in optimization algorithms and in computational hardware made deployment of Nonlinear Model Predictive Control (NMPC) and Moving Horizon Estimation (MHE) possible to mechatronic applications. This paper aims to assess the computational performance of NMPC and MHE for rotational start-up of Airborne Wind Energy systems. The capabilities offered by an automatic code generation tool are experimentally verified on a real physical system, using a model comprising 27 states and 4 inputs at a sampling frequency of 25 Hz. The results show the feedback times less than 5 ms for the NMPC with more than 1500 variables.     

基于多目标分层遗传模糊建模的磨矿过程溢流粒度软测量

提出一种基于多目标分层遗传算法的模糊系统对溢流粒度进行软测量, 该方法将模糊系统分为4 层, 即输入层、隶属度层、规则库层和系统集成层. 为了达到各层共同进化的目的, 设计遗传算法各层编码策略, 构建基于平均绝对百分误差和均方根误差的优化目标函数, 并采用该函数计算各层个体的适应度. 鉴于模糊模型训练过程中可能出现异常解, 将L-M 贝叶斯正则化方法融入训练过程. 对磨矿生产数据的仿真实验验证了所提出方法的有效性.

     

联合模板先验概率和稀疏表示的目标跟踪

目的 虽然基于稀疏表示的目标跟踪方法表现出了良好的跟踪效果,但仍然无法彻底解决噪声、旋转、遮挡、运动模糊、光照和姿态变化等复杂背景下的目标跟踪问题。针对遮挡、旋转、姿态变化和运动模糊问题,提出一种在粒子滤波框架内,基于稀疏表示和先验概率相结合的目标跟踪方法。方法 通过先验概率衡量目标模板的重要性,并将其引入到正则化模型中,作为模板更新的主要依据,从而获得一种新的候选目标稀疏表示模型。结果 在多个测试视频序列上,与多种流行算法相比,该算法可以达到更好的跟踪性能。在5个经典测试视频下的平均中心误差为6.77像素,平均跟踪成功率为97%,均优于其他算法。结论 实验结果表明,在各种含有遮挡、旋转、姿态变化和运动模糊的视频中,该算法可以稳定可靠地跟踪目标,适用于视频监控复杂场景下的目标跟踪。     

A cubic regularization algorithm for unconstrained optimization using line search and nonmonotone techniques

In recent years, cubic regularization algorithms for unconstrained optimization have been defined as alternatives to trust-region and line search schemes. These regularization techniques are based on the strategy of computing an (approximate) global minimizer of a cubic overestimator of the objective function. In this work we focus on the adaptive regularization algorithm using cubics (ARC) proposed in Cartis et al. [Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results, Mathematical Programming A 127 (2011), pp. 245–295]. Our purpose is to design a modified version of ARC in order to improve the computational efficiency preserving global convergence properties. The basic idea is to suitably combine a Goldstein-type line search and a nonmonotone accepting criterion with the aim of advantageously exploiting the possible good descent properties of the trial step computed as (approximate) minimizer of the cubic model. Global convergence properties of the proposed nonmonotone ARC algorithm are proved. Numerical experiments are performed and the obtained results clearly show satisfactory performance of the new algorithm when compared to the basic ARC algorithm.     

Sparse kernel logistic regression based on L 1/2 regularization

The sparsity driven classification technologies have attracted much attention in recent years, due to their capability of providing more compressive representations and clear interpretation. Two most popular classification approaches are support vector machines (SVMs) and kernel logistic regression (KLR), each having its own advantages. The sparsification of SVM has been well studied, and many sparse versions of 2-norm SVM, such as 1-norm SVM (1-SVM), have been developed. But, the sparsification of KLR has been less studied. The existing sparsification of KLR is mainly based on L ₁ norm and L ₂ norm penalties, which leads to the sparse versions that yield solutions not so sparse as it should be. A very recent study on L _1/2 regularization theory in compressive sensing shows that L _1/2 sparse modeling can yield solutions more sparse than those of 1 norm and 2 norm, and, furthermore, the model can be efficiently solved by a simple iterative thresholding procedure. The objective function dealt with in L _1/2 regularization theory is, however, of square form, the gradient of which is linear in its variables (such an objective function is the so-called linear gradient function). In this paper, through extending the linear gradient function of L _1/2 regularization framework to the logistic function, we propose a novel sparse version of KLR, the 1/2 quasi-norm kernel logistic regression (1/2-KLR). The version integrates advantages of KLR and L _1/2 regularization, and defines an efficient implementation scheme of sparse KLR. We suggest a fast iterative thresholding algorithm for 1/2-KLR and prove its convergence. We provide a series of simulations to demonstrate that 1/2-KLR can often obtain more sparse solutions than the existing sparsity driven versions of KLR, at the same or better accuracy level. The conclusion is also true even in comparison with sparse SVMs (1-SVM and 2-SVM). We show an exclusive advantage of 1/2-KLR that the regularization parameter in the algorithm can be adaptively set whenever the sparsity (correspondingly, the number of support vectors) is given, which suggests a methodology of comparing sparsity promotion capability of different sparsity driven classifiers. As an illustration of benefits of 1/2-KLR, we give two applications of 1/2-KLR in semi-supervised learning, showing that 1/2-KLR can be successfully applied to the classification tasks in which only a few data are labeled.     

Turbo码的按位迭代译码仿真与优化

Turbo码的迭代译码次数越多,译码延时和功耗也越大,通过图像传输的Turbo译码仿真分析,提出按不同比特位迭代次数不同的译码方法,并对各比特位的迭代次数进行优化,结果能使总迭代译码次数减少50%,且能保证译码后的图像效果。     

Computations with quasiseparable polynomials and matrices

In this paper, we survey several recent results that highlight an interplay between a relatively new class of quasiseparable matrices and univariate polynomials. Quasiseparable matrices generalize two classical matrix classes, Jacobi (tridiagonal) matrices and unitary Hessenberg matrices that are known to correspond to real orthogonal polynomials and Szegö polynomials, respectively. The latter two polynomial families arise in a wide variety of applications, and their short recurrence relations are the basis for a number of efficient algorithms. For historical reasons, algorithm development is more advanced for real orthogonal polynomials. Recent variations of these algorithms tend to be valid only for the Szegö polynomials; they are analogues and not generalizations of the original algorithms.     

Numerical approximation of solution of nonhomogeneous backward heat conduction problem in bounded region

In this paper we consider a numerical approximation of solution of nonhomogeneous backward heat conduction problem (BHCP) in bounded region based on Tikhonov regularization method. Error estimate at t=0$t=0$ for this method is provided. According to the error estimate, a selection of regularization parameter is given. Meanwhile, a numerical implementation is described and the numerical results show that our algorithm is effective.