A majorization algorithm for simultaneous parameter estimation in robust exploratory factor analysis

A new approach for fitting the exploratory factor analysis (EFA) model is considered. The EFA model is fitted directly to the data matrix by minimizing a weighted least squares (WLS) goodness-of-fit measure. The WLS fitting problem is solved by iteratively performing unweighted least squares fitting of the same model. A convergent reweighted least squares algorithm based on iterative majorization is developed. The influence of large residuals in the loss function is curbed using Huber’s criterion. This procedure leads to robust EFA that can resist the effect of outliers in the data. Applications to real and simulated data illustrate the performance of the proposed approach.     

Robust factor analysis for compositional data

Factor analysis as a dimension reduction technique is widely used with compositional data. Using the method for raw data or for improperly transformed data will, however, lead to biased results and consequently to misleading interpretations. Although some procedures, suitable for factor analysis with compositional data, were already developed, they require pre-knowledge of variable groups, or are complicated to handle. We present an approach based on the centred logratio (clr) transformation that does not build on this pre-knowledge, but still recognizes the specific character of compositional data. In addition, by using the isometric logratio transformation it is possible to robustify factor analysis using a robust estimation of the covariance matrix. A back-transformation of the results to the clr space allows an interpretation of the results with compositional biplots. The method is demonstrated with data from the Kola project, a large ecogeochemical mapping project in northern Europe.     

M-regression,false discovery rates and outlier detection with application to genetic association studies

Robust multiple linear regression methods are valuable tools when underlying classical assumptions are not completely fulfilled. In this setting, robust methods ensure that the analysis is not significantly disturbed by any outlying observation. However, knowledge of these observations may be important to assess the underlying mechanisms of the data. Therefore, a robust outlier test is discussed, together with an adequate false discovery rate correction measure, to be used in the context of multiple linear regression with categorical explanatory variables. The methodology focuses on genetic association studies of quantitative traits, though it has much broader applications. The method is also compared to a benchmark rule from the literature and its good performance is validated by a simulation study and a real data example from a candidate gene study.     

Laplacian regularized robust principal component analysis for process monitoring

Principal component analysis (PCA) is one of the most widely used techniques for process monitoring. However, it is highly sensitive to sparse errors because of the assumption that data only contains an underlying low-rank structure. To improve classical PCA in this regard, a novel Laplacian regularized robust principal component analysis (LRPCA) framework is proposed, where the “robust” comes from the introduction of a sparse term. By taking advantage of the hypergraph Laplacian, LRPCA not only can represent the global low-dimensional structures, but also capture the intrinsic non-linear geometric information. An efficient alternating direction method of multipliers is designed with convergence guarantee. The resulting subproblems either have closed-form solutions or can be solved by fast solvers. Numerical experiments, including a simulation example and the Tennessee Eastman process, are conducted to illustrate the improved process monitoring performance of the proposed LRPCA.     

Multi-Level Clustering and its Visualization for Exploratory Spatial Analysis

Exploratory spatial analysis is increasingly necessary as larger spatial data is managed in electro-magnetic media. We propose an exploratory method that reveals a robust clustering hierarchy from 2-D point data. Our approach uses the Delaunay diagram to incorporate spatial proximity. It does not require prior knowledge about the data set, nor does it require preconditions. Multi-level clusters are successfully discovered by this new method in only O(nlogn) time, where n is the size of the data set. The efficiency of our method allows us to construct and display a new type of tree graph that facilitates understanding of the complex hierarchy of clusters. We show that clustering methods adopting a raster-like or vector-like representation of proximity are not appropriate for spatial clustering. We conduct an experimental evaluation with synthetic data sets as well as real data sets to illustrate the robustness of our method.     

Robust method for identifying material parameters based on virtual fields in elastodynamics

We develop an inverse method with the purpose of extracting elastic properties of materials in the framework of transient dynamics. To this end, we create a small linear system based on a set of well-chosen time-dependent virtual fields (VF) and measurement data. The parameters are the solutions of this system and can be quickly extracted. We compare this new method with the classical finite element model updating (FEMU) method for different case studies. In our study, the measurements are synthetic, i.e, they are calculated using a fine finite element (FE) model. Uniform white noise is added to model measurement uncertainties. Results, based on Monte Carlo simulations, show that our method is more robust and accurate than the FEMU method for an acceptable noise level. Our new method appears well-adapted to linear elasticity in transient dynamics.     

一类参数未知混沌系统的鲁棒自适应控制

研究一类含有动态不确定性及未知参数的混沌系统控制问题。基于递推控制方法，通过自适应机制来在线辩识系统未知参数，同时在设计控制器的过程中逐步引入镇定因子，以消除系统不确定性的影响，最终得到一个鲁棒控制器，使得闭环系统渐近稳定。仿真结果表明了该控制策略的有效性。     

Assessment of water quality variation of a monitoring network using exploratory factor analysis and empirical orthogonal function

This study suggests a systematic assessment method that jointly uses the exploratory factor analysis (EFA) and empirical orthogonal function (EOF-patterns) of Principal Component Analysis (PCA) to assess the water quality variation of the monitoring network of Nakdong River, Korea, in which 28 stations measuring 15 water quality parameters are located. The EFA results showed the monitoring stations to be distinguished by two main factors. The representative stations of which the variance was almost explained by the specific factor were selected. We applied PCA to the monitoring data of representative stations, and then analyzed the EOF-patterns that indicate the characteristics of water-quality variation for each factor. With the interpretation of main factors and EOF-patterns causing dominant water quality variations, the monitoring network of Nakdong River could be spatially and seasonally evaluated according to the contribution of each factor.     

Spectral correspondence for point pattern matching

This paper investigates the correspondence matching of point-sets using spectral graph analysis. In particular, we are interested in the problem of how the modal analysis of point-sets can be rendered robust to contamination and drop-out. We make three contributions. First, we show how the modal structure of point-sets can be embedded within the framework of the EM algorithm. Second, we present several methods for computing the probabilities of point correspondences from the modes of the point proximity matrix. Third, we consider alternatives to the Gaussian proximity matrix. We evaluate the new method on both synthetic and real-world data. Here we show that the method can be used to compute useful correspondences even when the level of point contamination is as large as 50%. We also provide some examples on deformed point-set tracking.     

基于鲁棒规范变量分析的故障诊断方法

针对工业过程的建模数据中含有离群点的情况,提出一种基于鲁棒规范变量分析(CVA)的故障诊断方法.该方法使用相关系数的鲁棒估计代替传统的相关系数,通过基于粒子群算法的投影寻踪技术计算最大化鲁棒相关系数的规范变量,从而建立统计模型并监控统计量检测过程的变化.连续搅拌反应器(CSTR)系统的仿真结果说明,鲁棒规范变量分析方法能在含离群点数据的基础上建立准确的统计模型,比规范变量分析更有效地监控过程变化.     

Weighted and robust learning of subspace representations

A reliable system for visual learning and recognition should enable a selective treatment of individual parts of input data and should successfully deal with noise and occlusions. These requirements are not satisfactorily met when visual learning is approached by appearance-based modeling of objects and scenes using the traditional PCA approach. In this paper we extend standard PCA approach to overcome these shortcomings. We first present a weighted version of PCA, which, unlike the standard approach, considers individual pixels and images selectively, depending on the corresponding weights. Then we propose a robust PCA method for obtaining a consistent subspace representation in the presence of outlying pixels in the training images. The method is based on the EM algorithm for estimation of principal subspaces in the presence of missing data. We demonstrate the efficiency of the proposed methods in a number of experiments.     

一种用于图象帧间主运动估计的快速线搜索方法

本文中作者提出了一种新的基于鲁棒统计的快速搜索方法,可以用于图象帧间主运动估计,能够提高提高算法速度,近年来,一种新的参数估计技术－鲁棒统计－被越来越广泛地用于主运动估计,与传统的基于最小二乘的估计方法相比较,鲁棒统计对于外点具有更好的鲁棒性,但运算复杂度较高,而主运动估计中耗时最大的部分是线搜索。因此我们针对鲁棒统计中常用的Ｍ估计函数形式,采用近似函数拟合的方法,设计了一种快速的线搜索方法,与牛     

Robust design considering highly nonlinear structural behavior

The optimization of structures subject to highly nonlinear behavior, particularly crash structures, requires observance of all design-significant scatterings. This paper presents a time-saving method to generate structures satisfying robust design demands. A vital aspect of robust design from the aircraft industries’ point of view is the consideration of fail-safe approaches accounting for possible structural failure from previous loading or manufacturing inaccuracies. Additional structural elements are utilized to prevent (after failure occurred) the structure from deforming out of bounds. This paper presents an approach on how to include this in the robust design process.     

Computing the update of the repeated median regression line in linear time

The repeated median line estimator is a highly robust method for fitting a regression line to a set of n data points in the plane. In this paper, we consider the problem of updating the estimate after a point is removed from or added to the data set. This problem occurs, e.g., in statistical online monitoring, where the computational effort is often critical. We present a deterministic algorithm for the update working in O(n) time and O(n²) space.     

An Approximate Median Polish Algorithm for Large Multidimensional Data Sets

Exploratory data analysis is a widely used technique to determine which factors have the most influence on data values in a multi-way table, or which cells in the table can be considered anomalous with respect to the other cells. In particular, median polish is a simple yet robust method to perform exploratory data analysis. Median polish is resistant to holes in the table (cells that have no values), but it may require many iterations through the data. This factor makes it difficult to apply median polish to large multidimensional tables, since the I/O requirements may be prohibitive. This paper describes a technique that uses median polish over an approximation of a datacube, easing the burden of I/O. The cube approximation is achieved by fitting log-linear models to the data. The results obtained are tested for quality, using a variety of measures. The technique scales to large datacubes and proves to give a good approximation of the results that would have been obtained by median polish in the original data.     

Common weights data envelopment analysis with uncertain data: A robust optimization approach

One of the primary issues on data envelopment analysis (DEA) models is the reduction of weights flexibility. There are literally several studies to determine common weights in DEA but none of them considers uncertainty in data. This paper introduces a robust optimization approach to find common weights in DEA with uncertain data. The uncertainty is considered in both inputs and outputs and a suitable robust counterpart of DEA model is developed. The proposed robust DEA model is solved and the ideal solution is found for each decision making units (DMUs). Then, the common weights are found for all DMUs by utilizing the goal programming technique. To illustrate the performance of the proposed model, a numerical example is solved. Also, the proposed model of this paper is implemented by using some actual data from provincial gas companies in Iran.     

Fast cross-validation of high-breakdown resampling methods for PCA

Cross-validation (CV) is a very popular technique for model selection and model validation. The general procedure of leave-one-out CV (LOO-CV) is to exclude one observation from the data set, to construct the fit of the remaining observations and to evaluate that fit on the item that was left out. In classical procedures such as least-squares regression or kernel density estimation, easy formulas can be derived to compute this CV fit or the residuals of the removed observations. However, when high-breakdown resampling algorithms are used, it is no longer possible to derive such closed-form expressions. High-breakdown methods are developed to obtain estimates that can withstand the effects of outlying observations. Fast algorithms are presented for LOO-CV when using a high-breakdown method based on resampling, in the context of robust covariance estimation by means of the MCD estimator and robust principal component analysis. A robust PRESS curve is introduced as an exploratory tool to select the number of principal components. Simulation results and applications on real data show the accuracy and the gain in computation time of these fast CV algorithms.     

回归模型中变点识别的一种稳健方法

变点识别是数据分析中一个非常重要的研究内容.文中针对目前变点识别研究中忽略了方法的稳健性,未能充分考虑异常值的影响的不足,提出利用一种高度稳健的回归类混合分解算法来识别变点.该方法从混合回归模型的角度,将含有变点的回归模型看作回归类的混合,通过逐步挖掘数据集中的回归类,并对排序后的回归类进行分析,进而确定变点的位置及个数.数值模拟表明,在识别变点的过程中无须预先指定变点的数目,并且具有高度的稳健性和有效性.     

On ?∞, robust stability and performance with ?2 and ?∞ perturbations

In this paper we will consider systems with linear time-invariant perturbations. We will analyze robust performance in the ?₂ and ?_∞ settings. The ?₂ setting gives rise to the familiar case of structured singular values, and a stability criterion is given by the “small μ” theorem. We show that although the necessary and sufficient criterion of robust stability for the ?_∞ case (?_∞ stability with structured ?_∞-gain bounded perturbations) is the same “small μ” criterion, a system with ?₂-gain bounded perturbations is never ?_∞ stable.     

The technology acceptance scale: Its Bayesian psychometrics assessed in a factor analysis via Markov chain Monte Carlo models

The technology acceptance scale (TAS) by van der Laan, Heino, and De Waard (1997) measures the psychological construct of the same term as a sum of attitudes of an operator toward a specific complex sociotechnical system. The TAS has been claimed to comprise two subscales, usefulness and satisfaction. However, recent empirical work has found evidence for only one underlying factor. To provide further insight into the factor structure of the TAS, this study adopts a Bayesian exploratory factor analysis (BEFA) to analyse the data of a flight simulation study regarding single pilot operations. A series of Markov chain Monte Carlo (MCMC) models is used to assess the latent factor structure of the TAS for the two different crewing conditions and their corresponding workstation and cockpit setups of the copilot. A reliable step-by-step data analysis of the MCMC models provides evidence for a one-factor solution of the scale. The divergence to the previous studies which claim two factors can be due to the different applications as well as due to different statistical paradigms and methodological issues in exploratory factor analysis.