A DYNAMICAL SYSTEM ALGORITHM FOR SOLVING A LEAST SQUARES PROBLEM WITH ORTHOGONALITY CONSTRAINTS

This paper introduced a dynamical system (neural networks) algorithm for solving a least squares problem with orthogonality constraints, which has wide applications in computer vision and signal processing. A rigorous analysis for the convergence and stability of the algorithm was provided. Moreover, a so called zero extension technique was presented to keep the algorithm always convergent to the needed result for any randomly chosen initial data. Numerical experiments illustrate the effectiveness and efficiency of the algorithm.

ON A FAMILY OF MULTIVARIATE LEAST-SQUARES ORTHOGONAL POLYNOMIALS

In this paper the new notion of multivariate least-squares orthogonal poly-nomials from the rectangular form is introduced. Their existence and uniqueness isstudied and some methods for their recursive computation are given. As an applica-is constructed.

On a New Family of Weighted Least-square Orthogonal Polynomials in Multivariables

This paper introduces a new notion of weighted least-square orthogonal polynomials in multivariables from the triangular form. Their existence and uniqueness is studied and some methods for their recursive computation are given. As an application, this paper constructs a new family of Pade-type approximates in multi-variables from the triangular form.

An Orthogonal Least Squares Based Approach to FIR Designs

This paper is concerned with the application of forward Orthogonal Least Squares (OLS) algorithm to the design of Finite Impulse Response (FIR) filters. The focus of this study is a new FIR filter design procedure and to compare this with traditional methods known as the fir2() routine provided by MATLAB.

Orthogonal-Least-Squares Forward Selection for Parsimonious Modelling from Data

The objective of modelling from data is not that the model simply fits the training data well. Rather, the goodness of a model is characterized by its generalization capability, interpretability and ease for knowledge extraction. All these desired properties depend crucially on the ability to construct appropriate parsimonious models by the modelling process, and a basic principle in practical nonlinear data modelling is the parsimonious principle of ensuring the smallest possible model that explains the training data. There exists a vast amount of works in the area of sparse modelling, and a widely adopted approach is based on the linear-in-the-parameters data modelling that include the radial basis function network, the neurofuzzy network and all the sparse kernel modelling techniques. A well tested strategy for parsimonious modelling from data is the orthogonal least squares (OLS) algorithm for forward selection modelling, which is capable of constructing sparse models that generalise well. This contribution continues this theme and provides a unified framework for sparse modelling from data that includes regression and classification, which belong to supervised learning, and probability density function estimation, which is an unsupervised learning problem. The OLS forward selection method based on the leave-one-out test criteria is presented within this unified data-modelling framework. Examples from regression, classification and density estimation applications are used to illustrate the effectiveness of this generic parsimonious modelling approach from data.

Design of Radial Basis Function Network Using Adaptive Particle Swarm Optimization and Orthogonal Least Squares

This paper presents a two-level learning method for designing an optimal Radial Basis Function Network (RBFN) using Adaptive Velocity Update Relaxation Particle Swarm Optimization algorithm (AVURPSO) and Orthogonal Least Squares algorithm (OLS) called as OLS-AVURPSO method. The novelty is to develop an AVURPSO algorithm to form the hybrid OLS-AVURPSO method for designing an optimal RBFN. The proposed method at the upper level finds the global optimum of the spread factor parameter using AVURPSO while at the lower level automatically constructs the RBFN using OLS algorithm. Simulation results confirm that the RBFN is superior to Multilayered Perceptron Network (MLPN) in terms of network size and computing time. To demonstrate the effectiveness of proposed OLS-AVURPSO in the design of RBFN, the Mackey-Glass Chaotic Time-Series as an example is modeled by both MLPN and RBFN.

The Equivalence between Orthogonal Iterations and Alternating Least Squares

This note explores the relations between two different methods. The first one is the Alternating Least Squares (ALS) method for calculating a rank-k approximation of a real m×n matrix, A. This method has important applications in nonnegative matrix factorizations, in matrix completion problems, and in tensor approximations. The second method is called Orthogonal Iterations. Other names of this method are Subspace Iterations, Simultaneous Iterations, and block-Power method. Given a real symmetric matrix, G, this method computes k dominant eigenvectors of G. To see the relation between these methods we assume that G = AT A. It is shown that in this case the two methods generate the same sequence of subspaces, and the same sequence of low-rank approximations. This equivalence provides new insight into the convergence properties of both methods.

On Mutually Orthogonal Graph-Path Squares

A decomposition of a graph H is a partition of the edge set of H into edge-disjoint subgraphs . If for all , then G is a decomposition of H by G. Two decompositions and of the complete bipartite graph are orthogonal if, for all . A set of decompositions of is a set of k mutually orthogonal graph squares (MOGS) if and are orthogonal for all and . For any bipartite graph G with n edges, denotes the maximum number k in a largest possible set of MOGS of by G. Our objective in this paper is to compute where is a path of length d with d + 1 vertices (i.e. Every edge of this path is one-to-one corresponding to an isomorphic to a certain graph F).

APPLICATION OF LEAST MEDIAN OF SQUARED ORTHOGONAL DISTANCE (LMD) AND LMD BASED REWEIGHTED LEAST SQUARES (RLS) METHODS ON THE STOCK RECRUITMENT RELATIONSHIP

Analysis of stock recruitment (SR) data is most often done by fitting various SR relationship curves to the data. Fish population dynamics data often have stochastic variations and measurement errors, which usually result in a biased regression analysis. This paper presents a robust regression method, least median of squared orthogonal distance (LMD), which is insensitive to abnormal values in the dependent and independent variables in a regression analysis. Outliers that have significantly different variance from the rest of the data can be identified in a residual analysis. Then, the least squares (LS) method is applied to the SR data with defined outliers being down weighted. The application of LMD and LMD based Reweighted Least Squares (RLS) method to simulated and real fisheries SR data is explored.

Extended Diagonal Exponent Symmetry Model and Its Orthogonal Decomposition in Square Contingency Tables with Ordered Categories

For square contingency tables with ordered categories, this article proposes new models, which are the extension of Tomizawa’s [1] diagonal exponent symmetry model. Also it gives the decomposition of proposed model, and shows the orthogonality of the test statistics for decomposed models. Examples are given and the simulation studies based on the bivariate normal distribution are also given.

A NEW SUFFICIENT CONDITION FOR SPARSE RECOVERY WITH MULTIPLE ORTHOGONAL LEAST SQUARES

A greedy algorithm used for the recovery of sparse signals,multiple orthogonal least squares(MOLS)have recently attracted quite a big of attention.In this paper,we consider the number of iterations required for the MOLS algorithm for recovery of a K-sparse signal x∈R^(n).We show that MOLS provides stable reconstruction of all K-sparse signals x from y=Ax+w in|6K/ M|iterations when the matrix A satisfies the restricted isometry property(RIP)with isometry constantδ_(7K)≤0.094.Compared with the existing results,our sufficient condition is not related to the sparsity level K.

A Backward Stable Hyperbolic QR Factorization Method for Solving Indefinite Least Squares Problem

We present a numerical method for solving the indefinite least squares problem. We first normalize the coefficient matrix. Then we compute the hyperbolic QR factorization of the normalized matrix. Finally we compute the solution by solving several triangular systems. We give the first order error analysis to show that the method is backward stable. The method is more efficient than the backward stable method proposed by Chandrasekaran, Gu and Sayed.

基于PCA-OLS模型的系统等效惯量中长期预测

为综合考虑多重影响因素与系统等效惯量之间的量化关系,本文提出一种基于主成分分析-普通最小二乘法的系统等效惯量中长期预测模型。根据电网实际调度规则搭建简化的开机方式优化模型,构建系统等效惯量中长期预测历史数据集;利用主成分分析对系统等效惯量主要影响因素的多重共线性进行消除,得到主成分表达式;进行多元普通最小二乘法回归,反标准化后得到系统等效惯量解析模型。根据某电网能源发展规划数据,对未来系统惯量水平进行推演,可快速预估不同运行方式下系统等效惯量的演化趋势及非同步电源承载能力。

一种新型径向基函数神经网络学习算法——递归正交最小二乘法(ROLS)

径向基函数神经网络在很多领域都得到了成功的应用。但迄今为止仍没有一种有效的方法来确定隐层中心数目。笔者将递归正交最小二乘 (ROLS)方法引入RBFNN建模训练 ,利用ROLS算法训练网络后所得的有用信息 ,采用后向选择算法 ,逐步去掉那些使网络残差增加最小的中心 ,在得到网络有效中心的同时 ,还满足了精度要求 ,从而大大简化了RBF网络结构 ,节约了大量的存储空间以及计算量。

基于Kalman-OLS的聚丙烯熔融指数软测量

针对聚丙烯装置熔融指数软测量中的非线性和多工况切换操作问题,提出1种基于卡尔曼滤波-正交最小二乘(Kalman-OLS)的非线性自适应软测量方法。通过对聚丙烯装置反应系统进行机理分析,采用正交最小二乘方法(OLS)来拟和辅助变量和熔融指数之间的非线性关系。OLS方法的优化目标函数中同时考虑基于留一法均方误差(LOO MSE)和模型参数的局部正则化(LR),以提高模型的稀疏性和泛化能力。为适应装置多工况操作的现状,进一步提出使用Kalman滤波器对OLS模型参数进行自适应更新。工业数据应用结果表明,提出的Kal-man-OLS方法能够比偏最小二乘(PLS)、OLS方法更准确的预报聚丙烯熔融指数的变化。

基于OLS的径向基函数神经网络实现多种数字信号调制方式自动识别

基于决策论的信号调制样式自动识别方法具有简单易行、适合在线分析的优点,针对一些参数的计算进行了改进,并提出了基于该方法,利用正交最小二乘法(OLS)的径向基函数(RBF)神经网络,实现数字信号调制样式自动识别的方法.提高了该方法的识别能力,对信噪比(SNR)为6～30dB的测试信号识别得到了较好的结果.识别的数字信号为2ASK、4ASK、2PSK、4PSK(QP-SK)、2FSK、4FSK与16QAM.

基于OLS-RBF神经网络的进场飞行时间预测

航空器预计到达时刻(ETA)是航空器进场排序与调度的基础,因此进场航空器飞行时间的快速与准确预测显得尤为重要。基于历史雷达轨迹分析,通过RBF(Radial Basic Function)神经网络构建进场航空器进港时的高度、速度、进场飞行距离与进场飞行时间的映射关系,利用正交最小二乘算法设计基于RBF神经网络的进场飞行时间预测模型。以上海浦东机场VMB进港点进场航班为例进行仿真验证,在考虑航空器机型的情况下,可将航空器飞行时间预测的均方根误差控制在50 s以内。仿真结果表明,提出的方法能够有效地实现进场飞行时间的快速与准确预测。

基于OLS与EPSO算法的RBF企业订单预测模型研究

提出了一种最小正交二乘算法(OLS)和进化粒子群优化算法(EPSO)相结合构建RBF神经网络的企业订单预测模型。OLS采用前向回归算法,从输入数据中选取适当的中心,动态地避免网络规模过大和随机选择中心带来的数值病态问题;EPSO方法调整网络中的参数,如RBF中心位置,RBF宽度和隐层与输出层之间的权值,以提高网络的泛化能力。

关于 HSOLSSOM(2~nu^1)的谱(英文)

本文讨论型为2nt1的有对称正交侣的带洞自正交拉丁方（HSOLSSOM（2nu1））的谱．证明当n≤9时，HSOLSSOM（2nu1）存在的充分必要条件是u为偶数且;当n≥263时，若u为偶数且n≥2（u-2），则HSOLSSOM（2nu1）存在．

Spectrum-effect relationship between components and antitumor activity of Lonicerae Japonicae Flos based on orthogonal partial least squares regression

Lonicerae Japonicae Flos is a significant food and traditional Chinese medicine,known as plant antibiotics.It has rich chemical constituents and significant pharmacological effects.The antitumor activity of Lonicerae Japonicae Flos has been clarified,but the study on its spectrum-effect relationship has not been reported.The compounds responsible for its antitumor activity are still unknown.In this study,processed products of Lonicerae Japonicae Flos at different temperatures were taken as experimental materials,and SMMC-7721,A549,andMGC80-3 cells were tested.The orthogonal partial least squares regressionmethod was used to analyze the common compounds in different processed products and the antitumor activity.The results show that processed products have a stronger inhibitory effect on A549 cells and MGC80-3 cells than SMMC-7721 cells.Compounds such as secologanic acid,isochlorogenic acid A,serotonin,and chlorogenic acid play an important role in their antitumor effects.