一种训练前馈神经网络的局部线性化最小二乘算法

提出了一种新的训练前馈神经网络的局部线性化最小二乘算法。新算法将整个网络的权值训练看作非线性系统的参数识别,并将非线性系统的全局参数识别转化为一系列局部子系统的参数识别,最终将局部子系统的参数识别转化为线性化的最小二乘问题。     

A Unified Self-Stabilizing Neural Network Algorithm for Principal Takagi Component Extraction

Neural Processing Letters - In this paper, we develop efficient methods for the computation of the Takagi components and the Takagi subspaces of complex symmetric matrices via the complex-valued...     

A Recursive Orthogonal Least Squares Algorithm for Training RBF Networks

A recursive orthogonal least squares (ROLS) algorithm for multi-input, multi-output systems is developed in this paper and is applied to updating the weighting matrix of a radial basis function network. An illustrative example is given, to demonstrate the effectiveness of the algorithm for eliminating the effects of ill-conditioning in the training data, in an application of neural modelling of a multi-variable chemical process. Comparisons with results from using standard least squares algorithms, in batch and recursive form, show that the ROLS algorithm can significantly improve the neural modelling accuracy. The ROLS algorithm can also be applied to a large data set with much lower requirements on computer memory than the batch OLS algorithm.     

一种反演积雪面积的范数最小二乘算法

针对常规光谱混合分析算法在积雪面积反演中存在的端元变化误差及运算效率的问题,提出了一种范数最小二乘算法(norm least squares,NLS).为验证算法的精度和实用性,利用藏南地区的MODIS影像进行反演实验,同时采用全约束最小二乘法(fully constrained least squares,FCLS)...     

基于总体最小二乘法的图像降噪

来自图像传感器的数字图像会受到各种噪声的干扰,其中主要包括加性噪声、乘性噪声和混合噪声。乘性噪声随信号幅度改变而改变,没有理想的去除方法。为此,运用基于总体最小二乘法的图像估计降噪方法,研究图像块尺寸选取对降噪性能的影响,分析成像系统中去马赛克环节影响噪声传播的内在规律,并通过比较实验给出总体最小二乘法降噪的性能优势。     

总体最小二乘波达方向估计方法

在到达时间差定位技术中,当传感器位置坐标存在误差时,最小二乘法(LS)所得估计值不再具有最优无偏性,导致测向精度下降。针对该问题,提出基于总体最小二乘的测向方法。将非线性的观测方程转化为伪线性方程,构成增广矩阵并对其进行奇异值分解,从而得到目标位置。理论分析和仿真结果表明,与经典的LS法和LS-Tylar法相比,该方法的定位精度较高。     

合作SCC系统的总LS信号检测方法

为了克服已有信道估计算法无法及时跟踪信道变化的缺陷,在合作OFDM系统中引入了总LS（Total Least Squares,TLS）信号检测方法来实现信道状态信息估计。TLS方法同时考虑了信道噪声和信道时变特性,能够对信道和信号的变化同时进行跟踪估计。因为充分考虑了信道的时变性,且复杂度较低、收敛速度较快,所以在高速移动通信环境下,TLS方法能够很好地估计信道信息。仿真结果表明,与传统的LS法和ML法相比,该算法在改善误码性能方面优势明显。     

A Framework for Moving Least Squares Method with Total Variation Minimizing Regularization

In this paper, we propose a computational framework to incorporate regularization terms used in regularity based variational methods into least squares based methods. In the regularity based variational approach, the image is a result of the competition between the fidelity term and a regularity term, while in the least squares based approach the image is computed as a minimizer to a constrained least squares problem. The total variation minimizing denoising scheme is an exemplary scheme of the former approach with the total variation term as the regularity term, while the moving least squares method is an exemplary scheme of the latter approach. Both approaches have appeared in the literature of image processing independently. By putting schemes from both approaches into a single framework, the resulting scheme benefits from the advantageous properties of both parties. As an example, in this paper, we propose a new denoising scheme, where the total variation minimizing term is adopted by the moving least squares method. The proposed scheme is based on splitting methods, since they make it possible to express the minimization problem as a linear system. In this paper, we employed the split Bregman scheme for its simplicity. The resulting denoising scheme overcomes the drawbacks of both schemes, i.e., the staircase artifact in the total variation minimizing based denoising and the noisy artifact in the moving least squares based denoising method. The proposed computational framework can be utilized to put various combinations of both approaches with different properties together.     

Recursive Update Algorithm for Least Squares Support Vector Machines

In this Letter an efficient recursive update algorithm for least squares support vector machines (LSSVMs) is developed. Using the previous solution and some matrix equations, the algorithm completely avoids training the LSSVM all over again whenever new training sample is available. The gain in speed using the recursive update algorithm is illustrated on four data sets from UCI repository: the Statlog Australian credit, the Pima Indians diabetes, the Wisconsin breast cancer, and the adult income data sets.     

基于距离平方差的目标定位估计算法研究

无线传感器网络定位技术作为无线传感器网络的重要支撑技术之一,具有很大的实际价值和研究意义。无线传感器网络的目标定位估计技术主要应用于目标跟踪和目标运动分析,在工业领域具有广阔的发展前景。无线传感器网络由许多在空间中分布的传感器组成,这些传感器能够测量出传感器与定位目标之间的距离,但是该观测距离因为受环境影响所以是有噪音的。目前基于距离的最小二乘估计的定位算法已得到广泛关注,但是该问题是一个非凸问题,精确求解十分困难。因此学者们提出了基于距离平方的最小二乘估计的定位算法,该算法的数学模型虽然相对精确,但是计算起来十分复杂。本文基于距离平方差,提出了新的目标定位估计算法,该算法计算简单,稳定性强,且能得到与基于距离平方的最小二乘估计的定位算法相当的结果。仿真实验结果表明,无论在低噪音水平、中噪音水平还是高噪音水平下,本文提出的新算法都更有优势,在工程领域有极高的应用价值。     

最小二乘双支持向量机的在线学习算法

针对具有两个非并行分类超平面的最小二乘双支持向量机,提出了一种在线学习算法。通过利用矩阵求逆分解引理,所提在线学习算法能充分利用历史的训练结果,避免了大型矩阵的求逆计算过程,从而降低了计算的复杂性。仿真结果验证了所提学习算法的有效性。     

时序数据的非线性最小二乘迭代分解算法

从时序数据中精确地分解出趋势、周期及随机噪声等数据成分，能有助于人们掌握事物在演变过程中所蕴藏的内在规律.基于非线性最小二乘法，提出一种性能更为高效的时序数据分解算法。首先，基于关键转折点和趋势导数的方法从待分解序列中概要地析出各种不同的数据成分，然后，分别利用多项式函数、正弦谐波级数及自回归模型对相应的数据成分进行拟合，最后，在加法模型中迭代求解各种数据成分的非线性最小二乘参数。实验表明，新设计的算法在分解精度和计算成本等指标上均优于现有的算法。     

基于GPU的最小二乘蒙特卡罗算法期权定价

期权是以金融产品作为行权品种的交易合约。随着期权交易规模和交易量的迅速增长,期权定价的计算量越来越大,在传统CPU平台上对期权进行定价变得越来越困难。图形处理器（GPU）平台的出现和发展为解决期权定价计算提供了解决方案。在GPU上使用最小二乘蒙特卡罗算法（Least Squares Monte Carlo,LSM）实现了对一维和四维美式期权定价计算：首先利用CURAND库产生大量随机数,然后并行化期权标的价格变化路径,最后对最小二乘法和贴现定价进行并行化。为提高GPU平台上LSM方法的计算效率,对整个过程进行了优化。实际测试结果表明,在CPU+GPU上实现一维和四维美式期权定价相对CPU平台的加速比最高分别达到20.275和47.538,且比其他文献的方法整体性能有较大的提升。     

A Dynamic Self-Stabilizing Algorithm for Constructing a Transport Net

transport net corresponding to an undirected biconnected graph on a distributed or network model of computation. The algorithm is resilient to transient faults and does not require initialization. In addition, it is capable of handling topology changes in a transient manner. The paper includes a correctness proof of the algorithm. Finally, it concludes with some final remarks. Received November 26, 2001 Published online February 18, 2002     

基于加权最小二乘优化的DV-HOP定位算法

确定事件发生的传感器节点位置是大多数无线传感网络应用场景中不可缺失的一部分。目前,在资源受限的无线传感网络中设计高精度定位算法仍是一个极具挑战性问题。为此,深入分析了DV-HOP算法中误差产生的原因,提出一种改进的DV-HOP算法。该算法为了降低计算所带来的固有误差,估算坐标时采用不直接对估算方程进行平方的方法;此外,为了进一步降低误差,采用了加权最小二乘法进行坐标估算;最后,采用理论分析的方法对算法进行了误差分析。仿真结果表明改进的算法与传统DV-HOP算法及文献[16-17]中的算法相比定位精度得到明显改善,分别提高了40%、28%和15%。     

A Least Squares Solution for Camera Distortion Parameters

Most applications in optical metrology need a well calibrated camera. In particular, a calibrated camera includes a distortion mapping, parameters of which are determined in a final non-linear optimization over all camera parameters. In this article we present a closed form solution for the distortion parameters provided that all other camera parameters are known. We show that for radial, tangential, and thin prism distortions the determination of the parameters form a linear least squares problem. Therefore, a part of the camera calibration error function can be minimized by linear methods in closed form: We are able to decouple the calculation of the distortion parameters from the non-linear optimization. The number of parameters in the non-linear minimization are reduced. Several experimental results confirm the benefit of the approach.     

AR估计滤波误差能量最小二乘递推法

利用滤波误差能量给出了一个新的最小二乘快速递推算法。数值试验表明，该算法计算稳定性好，对噪声不敏感，能快速递推到高阶模型，并将该算法同Ｍａｒｐｌｅ算法等作了比较。     

一种基于偏最小二乘法的室外光照估计算法

针对固定视点下的室外场景在线视频光照求解问题,提出一种基于偏最小二乘室外场景实时光照估计算法.在离线阶段提取场景中对光照变化较为敏感的区域,并将这些区域像素值的均值与方差的无偏估计作为场景图像的统计参数,再利用偏最小二乘回归分析建立场景的光照参数与图像统计参数之间的模型;在在线阶段使用所建立的模型实时估计视频每一帧的光照条件.实验结果表明,使用该算法所求解的光照参数对虚拟物体进行绘制并将其融入视频中后,合成场景真实感很强.