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.

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.

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.

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.

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.

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。

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).

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.

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.

基于MOLS的最优二元局部修复码构造

目前局部修复码(Locally Repairable Codes,LRCs)在分布式存储系统中的应用引起了广泛关注。为了减小LRCs的编码和修复复杂度,论文提出一种二元局部修复码(Binary Locally Repairable Codes,BLRCs)的构造算法。首先通过相互正交的拉丁方(Mutually Orthogonal Latin Squares,MOLS)构造特定参数的均衡不完全区组设计(Balanced Incomplete Block Design,BIBD),然后利用BIBD的关联矩阵构造BLRCs的生成矩阵,最后由生成矩阵构造具有信息符号(r,t)-局部性的BLRCs。理论分析表明,论文提出的基于MOLS构造的BLRCs满足最优最小距离界,是最优的二元局部修复码。特别地,当可用性t=2时,基于MOLS构造的BLRCs的码率达到了Parakash等提出的最优码率界。与基于阵列LDPC码构造的BLRCs,基于迭代矩阵构造的BLRCs和直积码相比,论文提出的基于MOLS构造的BLRCs的码率更高。

正交偏最小二乘法探析大承气汤治疗急性胰腺炎多成分多药效关系

目的/意义分析大承气汤治疗急性胰腺炎实验数据,证实多成分多药效关系。方法/过程运用正交偏最小二乘法,分别探析配伍药味、煎煮液的药物成分、血液的药物成分与药效指标的关系。结果/结论配伍药味与药效指标之间、煎煮液的药物成分与药效指标之间、血液的药物成分与药效指标之间均存在一对多、多对一、多对多的作用关系。实验分析结果表明大承气汤治疗急性胰腺炎呈现多成分多药效的特点。

基于单料烟的加热卷烟与传统卷烟香气成分释放差异分析

将10种单料烟分别制备成加热卷烟和传统卷烟两种类型卷烟样品,采用GC-MS分析和正交偏最小二乘法判别分析(OPLS-DA)模型评价加热卷烟气溶胶和传统卷烟主流烟气中香气成分的释放差异。结果表明:加热卷烟气溶胶和传统卷烟主流烟气中分别鉴定出53种和77种香气成分;两者共有香气成分47种,其中13种香气成分在加热卷烟气溶胶中的释放量较为突出,除乙酸、γ-丁内酯外,其他11种均是醛酮类化合物;筛选出两种卷烟中存在显著释放差异的香气成分53种,包含吡嗪吡啶类7种、酮类12种、呋喃类4种、酸类9种、酯类3种、酚类8种、烃类9种、醇类1种,从差异性香气成分在该类别总鉴定成分的占比来看,酚类香气成分在两种卷烟中的释放差异性最为显著,其余依次为烃类、吡嗪吡啶类、酸类、酯类、酮类、呋喃类、醇类。

不同容量下并网模式交流微电网短路故障早期检测与区域定位

随着分布式电源(distributed generation,DG)的容量变化,微电网原有的供电结构发生改变,使得潮流大小、方向和功率结构发生变化,对快速检测和定位微电网中的短路故障区域提出了挑战。在MATLAB/Simulink中搭建低压交流微电网模型;通过高尺度小波能量谱算法对微电网与大电网公共连接点(point of common coupling,PCC)处检测到的电流进行分解,提取适应不同容量情况的短路故障特征值,实现了不同容量下微电网短路故障的早期检测;利用小波能量谱特征结合基于正交最小二乘法(orthogonal least square,OLS)的径向基函数(radial basis function,RBF)神经网络算法提出一种适用于不同容量微电网的短路故障区域定位方法,并进行仿真验证;在此基础上设计并网模式微电网短路故障保护硬件系统,并进行实验验证。结果表明,所设计的保护系统能够快速、准确地同时实现并网模式下交流微电网短路故障的早期检测与区域定位。

红芪搓条前后主要次级代谢产物变化规律研究

目的 考察红芪搓条前后主要次级代谢产物的变化规律。方法 UPLC-MS/MS法测定芒柄花素、芒柄花苷、毛蕊异黄酮、毛蕊异黄酮苷、美迪紫檀素、染料木素、木犀草素、甘草素、异甘草素、香草酸、阿魏酸、γ-氨基丁酸、腺苷、甜菜碱的含量,聚类分析、主成分分析、正交偏最小二乘判别分析进行化学模式识别以寻找差异性成分。结果 搓条后,芒柄花素、毛蕊异黄酮、甘草素、γ-氨基丁酸含量升高,芒柄花苷、毛蕊异黄酮苷、香草酸含量降低。搓条、未搓条药材聚为2类,毛蕊异黄酮苷、芒柄花素、γ-氨基丁酸、香草酸、毛蕊异黄酮、芒柄花苷为差异性成分。结论 本实验阐明红芪搓条前后化学成分差异,可为其他药材搓条机制研究提供参考。

基于化学计量学和指纹图谱的辽宁道地药材北五味子质量评价研究

目的 采用指纹图谱与化学计量学相结合的方法,评价辽宁岫岩产北五味子的质量。方法 采用HPLC法,柱温30℃,流速1 mL/min,流动相采用水-乙腈梯度洗脱,检测波长220 nm,对10批辽宁岫岩五味子基地生产的北五味子建立指纹图谱,运用聚类分析(hierarchical cluster analysis, HCA)、主成分分析(principal component analysis, PCA)及正交偏最小二乘法-判别分析(orthogonal partial least squares-discriminant analysis, OPLS-DA)进行化学模式识别分析。结果 建立了岫岩产北五味子的指纹图谱,相似度为0.970^0.999,共标定了29个共有峰,指认了14个成分;HCA分析10批北五味子可分为2类;PCA共得到6个主要成分,其累计方差贡献率为95.5%;OPLS-DA表明五味子甲素、戈米辛G、五味子丙素、五味子醇乙等11个成分可能是影响北五味子质量的差异性标志物。结论 研究所建立的指纹图谱结合化学模式识别分析,方法准确、稳定、可靠,可用于北五味子药材的质量控制研究。

早期高血压弦脉脉象特点及其瞬时波强技术参数特征分析

目的:应用瞬时波强(WI)技术探测早期高血压弦脉患者颈总动脉各参数,分析早期高血压弦脉的脉象特点;提取弦脉脉象判别的特征参数,探讨早期高血压弦脉患者颈总动脉WI参数的特点,以期为弦脉的精准分型及信息解读提供客观依据。方法:选择52例早期原发性高血压弦脉、50例生理性弦脉、50例平脉受试者,分析其颈总动脉的WI参数,总结早期高血压弦脉的脉象特点,并运用SIMCA14.1统计软件提取脉象分型的主参数。结果:早期高血压弦脉组与平脉组及生理性弦脉组比较,瞬时加速度波强(W1)、负向波面积(NA)值增高,W1-W2间期降低(均P<0.01);而平脉组与生理性弦脉组W1、NA、W1-W2间期比较,差异均无统计学意义(均P>0.05)。平脉组、生理性弦脉组、早期高血压弦脉组的血管压力应变弹性模量(EP)、脉搏波传导速度(PWV)、血管硬化参数(β)数值均逐渐增高(均P<0.01)。平脉组血管顺应性(AC)高于其他2组(均P<0.01),生理性弦脉组AC高于早期高血压弦脉组(P<0.05)。3组R-W1间期比较差异无统计学意义(P>0.05)。基于主成分分析(PCA)和正交偏最小二乘法判别分析(OPLS-DA),生理性弦脉组与平脉组样本区分明显,表明2组WI各参数比较差异均有统计学意义(均P<0.05),特征性的WI参数[投影重要性(VIP值)>1]为EP、PWV、β、AC,其中贡献率为EP>PWV>β>AC。基于PCA和OPLS-DA,生理性弦脉组与早期高血压弦脉组样本区分明显,表明2组WI各参数差异均有统计学意义(均P<0.05),特征性的WI参数(VIP值>1)为EP、PWV、NA、W1、β,其中贡献率为EP>PWV>NA>W1>β。结论:区分早期高血压弦脉组与生理性弦脉组的WI特征性参数为EP、PWV、β、NA、W1。区分平脉组与生理性弦脉组特征性参数为EP、PWV、β、AC。WI技术可为脉象的精准分型和信息解读提供客观依据,值得进一步推广应用。

基于电子鼻和气质联用分析萌芽大蒜挥发性物质差异

为探究萌芽期大蒜挥发性物质的差异,采用电子鼻、捕集阱顶空-气质联用仪(Trap head space-gas chromatography-mass spectrometry,HS-Trap-GC-MS)结合正交偏最小二乘法判别分析(Orthogonal partial least squares discriminant analysis,OPLS-DA)、香气活度值、差异性热图、相关性分析分析大蒜萌芽在0、24、48、72、96 h挥发性物质的差异。电子鼻结合OPLS-DA建立预测模型其预测能力达96.00%。GC-MS分析表明:含硫化合物是不同萌芽期大蒜的主要共有挥发性物质,含硫化合物的相对含量随萌芽时间的延长而呈递减趋势,而种类呈现出递增趋势;二烯丙基二硫醚是样品在萌芽过程中含量降低最多的物质。二烯丙基四硫醚、烯丙硫醇是样品共有关键化合物。差异性热图分析显示:除共有物质含量差异外,硫化丙烯、己醛、叠氮二羧酸二叔丁酯、丙烯醇、6-甲基-2-庚炔、5-甲基噻二唑、2-亚乙基-1,3-二硫烷、2-丙-2-炔基磺酰基丙烷、2,5-二甲基噻吩、2,5-二甲基呋喃、1-戊烯-3-醇、1,3-二噻烷的缺失进一步加大了未萌芽和萌芽大蒜气味的差异。萌芽大蒜主要共有挥发性物质的种类随萌芽时间的延长呈现递增趋势。大蒜主要挥发性物质与电子鼻大多数传感器存在显著相关性。大蒜的气味强度会随萌芽时间的延长而逐步减弱。