Simultaneous Envelopes for Multivariate Linear Regression

We introduce envelopes for simultaneously reducing the predictors and the responses in multivariate linear regression, so the regression then depends only on estimated linear combinations of X and Y. We use a likelihood-based objective function for estimating envelopes and then propose algorithms for estimation of a simultaneous envelope as well as for basic Grassmann manifold optimization. The asymptotic properties of the resulting estimator are studied under normality and extended to general distributions. We also investigate likelihood ratio tests and information criteria for determining the simultaneous envelope dimensions. Simulation studies and real data examples show substantial gain over the classical methods, like partial least squares, canonical correlation analysis, and reduced-rank regression. This article has supplementary material available online.     

Tensor Envelope Partial Least-Squares Regression

Partial least squares (PLS) is a prominent solution for dimension reduction and high-dimensional regressions. Recent prevalence of multidimensional tensor data has led to several tensor versions of the PLS algorithms. However, none offers a population model and interpretation, and statistical properties of the associated parameters remain intractable. In this article, we first propose a new tensor partial least-squares algorithm, then establish the corresponding population interpretation. This population investigation allows us to gain new insight on how the PLS achieves effective dimension reduction, to build connection with the notion of sufficient dimension reduction, and to obtain the asymptotic consistency of the PLS estimator. We compare our method, both analytically and numerically, with some alternative solutions. We also illustrate the efficacy of the new method on simulations and two neuroimaging data analyses. Supplementary materials for this article are available online.     

Two‐sided Grassmann manifold algorithm for optimal model reduction

We consider an optimal model reduction problem for large‐scale dynamical systems. The problem is formulated as a minimization problem over Grassmann manifold with two variables. This formulation allows us to develop a two‐sided Grassmann manifold algorithm, which is numerically efficient and suitable for the reduction of large‐scale systems. The resulting reduced system preserves the stability of the original system. Numerical examples are presented to show that the proposed algorithm is computationally efficient and robust with respect to the selection of initial projection matrices. Copyright © 2015 John Wiley & Sons, Ltd.     

Centering and Scaling in Ridge Regression

A simple generalization of the usual ridge regression estimator for the linear regression model is given which avoids the need to center all variables. The estimator is proved to be location invariant. This estimator is of pedagogical interest and in forecasting also of practical importance.     

Fracture and fragmentation of ice: a fractal analysis of scale invariance

The fracture and fragmentation processes of ice are reviewed using fractal concepts. Numerous evidences for the scale invariance of fracture and fragmentation patterns in ice are given, including fracture networks at small (laboratory) and large (geophysical) scales, the distribution of fragment sizes in crushed ice or the distribution of sea ice floe sizes, or self-affine fracture surfaces. These observations strongly argue for the scale invariance of fracture and fragmentation processes in ice. This implies that the fracture mechanisms and the physical parameters revealed at the laboratory scale are still relevant at large scale. However, apparent scale effects can be observed for some parameters if the fractal geometry is ignored or neglected. Scale invariance also implies that the homogenization procedures used in the damage mechanics of ice have to be taken with caution.     

增强联系鉴别分析及在人脸识别中的应用

针对人脸识别中的小样本问题,本文提出了一种名为增强联系鉴别分析的方法并应用人脸识别中.该方法利用将人脸局部流形的结构信息和样本的类别信息进行有效地结合进行维数约简,首先构建人脸数据的近邻图与类别联系图,然后通过解决在一定约束条件下的优化问题来获取低维鉴别流形特征,实现在低维空间中同一类人脸数据聚集,不同类别间的人脸数据间尽可能发散,从而可以更好的应用于分类.在AT&T和Yale人脸图像数据库上的实验结果表明该方法能有效的提高人脸识别的性能.     

Stochastic uncertainty analysis of damage evolution computed through microstructure–property relations

Uncertainties in material microstructure features can lead to uncertainty in damage predictions based on multiscale microstructure–property models. This paper presents an analytical approach for stochastic uncertainty analysis by using a univariate dimension reduction technique. This approach is used to analyze the effects of uncertainties pertaining to the structure–property relations of an internal state variable plasticity–damage model that predicts failure. The results indicate that the higher the strain the greater the scatter in damage, even when the uncertainties in the material plasticity and microstructure parameters are kept constant. In addition, the mathematical sensitivity analysis results related to damage uncertainty are consistent with the physical nature of damage progression. At the beginning, the initial porosity and void nucleation are shown to drive the damage evolution. Then, void coalescence becomes the dominant mechanism. And finally, when approaching closer to failure, fracture toughness is found to dominate the damage evolution process.     

Dimension reduction model for two-spatial dimensional stochastic wind field: Hybrid approach of spectral decomposition and wavenumber spectral representation

A renewed methodology for simulating two-spatial dimensional stochastic wind field is addressed in the present study. First, the concept of cross wavenumber spectral density (WSD) function is defined on the basis of power spectral density (PSD) function and spatial coherence function to characterize the spatial variability of the stochastic wind field in the two-spatial dimensions. Then, the hybrid approach of spectral representation and wavenumber spectral representation and that of proper orthogonal decomposition and wavenumber spectral representation are respectively derived from the Cholesky decomposition and eigen decomposition of the constructed WSD matrices. Immediately following that, the uniform hybrid expression of spectral decomposition and wavenumber spectral representation is obtained, which integrates the advantages of both the discrete and continuous methods of one-spatial dimensional stochastic field, allowing for reflecting the spatial characteristics of large-scale structures. Moreover, the dimension reduction model for two-spatial dimensional stochastic wind field is established via adopting random functions correlating the high-dimensional orthogonal random variables with merely 3 elementary random variables, such that this explicitly describes the probability information of stochastic wind field in probability density level. Finally, the numerical investigations of the two-spatial dimensional stochastic wind fields respectively acting on a long-span suspension bridge and a super high-rise building are implemented embedded in the FFT algorithm. The validity and engineering applicability of the proposed method are thus fully verified, providing a potentially effective approach for refined wind-resistance dynamic reliability analysis of large-scale complex engineering structures.     

A real time procedure for affinely dependent parametric model order reduction using interpolation on Grassmann manifolds

Model order reduction helps to reduce the computational time in dealing with large dynamical systems, for example, during simulation, control, optimization. In many cases, the considered model depends on parameters; Model order reduction techniques are, therefore, preferred to symbolically preserve this dependence or to be adaptive to the change of the model caused by the variation in the values of the parameters. In this paper, we first present the application of the interpolation technique on Grassmann manifolds to this problem. We then improve the method for the models whose system matrices depend affinely on parameters by considerably reducing the computational complexity on the basis of analyzing the structure of sums of singular value decompositions and decomposing the whole procedure into offline and online stages. A numerical example is shown to illustrate the method as well as to prove its effectiveness. Copyright © 2012 John Wiley & Sons, Ltd.     

Optimal Subset Selection-Multiple Regression,Interdependence and Optimal Network Algorithms

Two types of sampling plans are examined as alternatives to simple random sampling in Monte Carlo studies. These plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function.     

Behavior of the Residuals of a Regression Least-Squares Model Which Is Linear in Its Parameters When the Number of Parameters Is Increased. Part 1. State of the Question. Correlation Coefficient between the Residuals

A brief critical review is given of methods and recommendations utilized when analyzing the residuals of a regression least-squares model which is linear in its parameters. The absence of the necessary rigorous solutions and the explicit contradictions present in the recommendations considerably reduce the introduction and utilization efficiency of the information contained in the residuals. A formula is proposed for calculating the correlation coefficient between the residuals together with a compact program created in the Maple V R5 mathematical software applied program package, and examples of calculations are presented.     

数据特征选择与分类在机械故障诊断中的应用

针对机械故障数据的高维性和不平衡性,提出基于格拉斯曼流形的多聚类特征选择和迭代近邻过采样的故障分类方法。对采集到的振动信号,提取时域和频域相关特征,利用多聚类特征选择将高维数据以局部流形结构映射到低维特征集合。无标签样本借助迭代近邻过采样以恢复最大平衡性为目标进行样本分类,并对剩余无标签样本进行模糊分类。选取滚动轴承正常、外圈、内圈以及滚动体的故障数据,并与支持向量机、基于图的半监督学习算法进行对比。结果表明,提出的方法能有效识别出少数类故障,并在整体上有显著的分类效果。     

Behavior of the Residuals of a Regression Least-Squares Model Which Is Linear in Its Parameters when the Number of Parameters Is Increased. Part 2. Interval for Series of Residuals. Problem of Gross Errors

The distribution of residuals in one series of measurements is obtained. It is shown that the normally used t interval for residuals is always wider than the correct one. The question of the detection of gross errors in the graphs of residuals is discussed. Reliable detection of gross errors is possible only for extremely small ratios of the number of parameters of the model to the number of nodes (0.1).     

Efficient Integration of Sufficient Dimension Reduction and Prediction in Discriminant Analysis

Sufficient dimension reduction (SDR) methods are popular model-free tools for preprocessing and data visualization in regression problems where the number of variables is large. Unfortunately, reduce-and-classify approaches in discriminant analysis usually cannot guarantee improvement in classification accuracy, mainly due to the different nature of the two stages. On the other hand, envelope methods construct targeted dimension reduction subspaces that achieve dimension reduction and improve parameter estimation efficiency at the same time. However, little is known about how to construct envelopes in discriminant analysis models. In this article, we introduce the notion of the envelope discriminant subspace (ENDS) as a natural inferential and estimative object in discriminant analysis that incorporates these considerations. We develop the ENDS estimators that simultaneously achieve sufficient dimension reduction and classification. Consistency and asymptotic normality of the ENDS estimators are established, where we carefully examine the asymptotic efficiency gain under the classical linear and quadratic discriminant analysis models. Simulations and real data examples show superb performance of the proposed method. Supplementary materials for this article are available online.     

Sustainability and branchless banking: The development and validation of a distinct measurement scale

This study aimed to develop and validate a new scale for measuring the sustainability and development of branchless banking. The study followed the scale development procedure based on Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA) using SPSS 22 and Structural Equation Modelling (SEM) analyses through SmartPLS. The data was collected from 150 respondents from different stakeholders of branchless banking. The EFA reported with the seven-factor solution including social sustainability, product responsibility, economic sustainability, labor practices and decent work, environmental sustainability, human rights and ethics, and branchless banking development. The structural model further validated the positive impact of human rights and ethics, labor practice and decent work, product responsibility, and social sustainability on the development of branchless banking. The study has a novelty to develop and validate the first-ever scale for measuring sustainable branchless banking. Besides, the study also provides many theoretical and practical implications for different stakeholders including academia, researchers, top management of the banks, and practitioners.     

短缺量滞后供给与顾客等待时间相关的VMI模型

考虑短缺量滞后供给与顾客等待时间负相关,提出了供应商生产批量用于满足订货商多次订货需求的VMI模型.仿真寻优求得系统唯一最优解,短缺量拖后因子和生产率的灵敏度分析表明,二者对VMI系统库存控制策略的制定有较大影响.当短缺量拖后因子较大时,订货商应提高服务水平,缩短订货周期;当供应商生产率较大时,则应延长订货周期并减少生产周期内的订货次数.     

Logistic 组稀疏回归模型的 Bayes 建模及变分推断

在工程应用中,如数据挖掘、成本预测以及风险预测等,Logistic 回归是一类十分重要的预测方法．当前,大部分 Logistic 回归方法都是基于优化准则而设计,这类回归方法具有参数调试过程繁琐、模型解释性差、估计子没有置信区间等缺点．本文从 Bayes 概率角度研究 Logistic 组稀疏性回归的建模与推断问题．具体来说,首先利用高斯-方差混合公式提出 Logistic 组稀疏回归的 Bayes 概率模型;其次,通过变分 Bayes 方法设计出一个高效的推断算法．在模拟数据上的实验结果表明,本文所提出的方法具有较好的预测性能．     

基于共空间模式和均匀流形投影的运动想象脑电信号识别方法

运动想象脑电信号的识别与分类问题一直是脑机领域研究的热点问题。针对此问题,使用区别传统线性降维方法的流形学习方法,将共空间模式算法与均匀流形投影算法相结合,充分利用了脑电信号中的非线性特征,对运动想象脑电信号进行了特征提取和数据降维,并使用KNN分类器进行了分类,对分类效果做出了评价;将降维前后的数据分类结果进行对比,说明了数据降维的优点和必要性;进一步讨论了降维结果在数据可视化方面的表现。发现经过数据降维的特征数据的可视化效果明显优于未经过降维的数据,进一步提出了一种基于共空间模式和均匀流形投影的新型脑电信号识别方法,对进行脑电信号深度剖析。挖掘脑电信号非线性特征提供了参考价值,同时也在数据流形分布以及数据可视化的角度为运动想象脑电信号识别提供了新思路。     

A multilevel projection‐based model order reduction framework for nonlinear dynamic multiscale problems in structural and solid mechanics

A reduction/hyper reduction framework is presented for dramatically accelerating the solution of nonlinear dynamic multiscale problems in structural and solid mechanics. At each scale, the dimensionality of the governing equations is reduced using the method of snapshots for proper orthogonal decomposition, and computational efficiency is achieved for the evaluation of the nonlinear reduced‐order terms using a carefully designed configuration of the energy conserving sampling and weighting method. Periodic boundary conditions at the microscales are treated as linear multipoint constraints and reduced via projection onto the span of a basis formed from the singular value decomposition of Lagrange multiplier snapshots. Most importantly, information is efficiently transmitted between the scales without incurring high‐dimensional operations. In this proposed proper orthogonal decomposition–energy conserving sampling and weighting nonlinear model reduction framework, training is performed in two steps. First, a microscale hyper reduced‐order model is constructed in situ, or using a mesh coarsening strategy, in order to achieve significant speedups even in non‐parametric settings. Next, a classical offline–online training approach is performed to build a parametric hyper reduced‐order macroscale model, which completes the construction of a fully hyper reduced‐order parametric multiscale model capable of fast and accurate multiscale simulations. A notable feature of this computational framework is the minimization, at the macroscale level, of the cost of the offline training using the in situ or coarsely trained hyper reduced‐order microscale model to accelerate snapshot acquisition. The effectiveness of the proposed hyper reduction framework at accelerating the solution of nonlinear dynamic multiscale problems is demonstrated for two problems in structural and solid mechanics. Speedup factors as high as five orders of magnitude are shown to be achievable. Copyright © 2017 John Wiley & Sons, Ltd.     

Total and selective reuse of Krylov subspaces for the resolution of sequences of nonlinear structural problems

This paper deals with the definition and optimization of augmentation spaces for faster convergence of the conjugate gradient method in the resolution of sequences of linear systems. Using advanced convergence results from the literature, we present a procedure on the basis of a selection of relevant approximations of the eigenspaces for extracting, selecting and reusing information from the Krylov subspaces generated by previous solutions in order to accelerate the current iteration. Assessments of the method are proposed in the cases of both linear and nonlinear structural problems. Copyright © 2012 John Wiley & Sons, Ltd.