Matrix Linear Discriminant Analysis

Abstract

We propose a novel linear discriminant analysis (LDA) approach for the classification of high-dimensional matrix-valued data that commonly arises from imaging studies. Motivated by the equivalence of the conventional LDA and the ordinary least squares, we consider an efficient nuclear norm penalized regression that encourages a low-rank structure. Theoretical properties including a nonasymptotic risk bound and a rank consistency result are established. Simulation studies and an application to electroencephalography data show the superior performance of the proposed method over the existing approaches.     

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.     

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.     

面阵图像传感器交汇测量原理及误差分析

分析了面阵传感器相对于线阵传感器在轻武器报靶方面的优势,阐述了面阵传感器交汇测量的原理,建立了相应的数学模型,数学模型只有代入计算,无复杂的迭代计算过程,简单易算.对模型的焦距测量误差和图像细分误差进行相应的计算和分析.通过叠加焦距误差、图像细分误差和相机初始角度误差的影响,进行了综合误差分析,通过实验和统计发现,其相对误差能够达到0.5％,能够满足系统1％的相对误差指标要求.     

判别分析在应征入伍公民心理检测中的应用

目的对应征入伍公民心理检测的结果进行判别分析,并建立判别方程,用于准确、快速地识别精神病高危人群。方法测试对象为某年入伍的3554名新兵,采用第四军医大学研制的群体多项心理测评仪(DXC-6),进行数字搜索和卡特尔16种个性因素测试(the Sixteen Personality Factor Questionnaire,16PF),并挑选部分人员进行明尼苏达多项人格问卷(Minnesota Multiphasic Per-sonality Inventory,MMPI),挑选出测验结果呈阳性的测试者进行访谈,并依据中国精神障碍分类与诊断标准(第三版)(the Chinese Classification of Mental Disorders Version 3,CCMD-3)的标准进行诊断,将诊断结果分为"正常"、"应激性反应"和"疑似精神障碍"三个组别。结果 "正常"组有3423人,"应激性反应"有98人,"疑似精神障碍"有33人;除世故性之外,数字搜索以及16PF各因子得分在这三组之间有均有显著性差异;数字搜索、忧虑性、实验性、怯弱果敢型和心理健康因素五个指标纳入判别方程,交互验证得判别结果的正确率为88.2%,外部样本的正确率为78.2%。结论本研究所建立的判别方程,准确率较高,可以应用于应征公民的心理检测工作。     

The Use of Discriminant Analysis to Investigate the Influence of Non‐Cognitive Factors on Engineering School Persistence

This study identified post‐enrollment attitudes and perceptions that influence students' decisions to remain in an engineering curriculum. Non‐cognitive factors including expectations and perception of the engineering profession, assessment of personal attributes, and subject‐matter confidence were investigated. Discriminant analysis functions were developed to distinguish among three mutually exclusive groups: those who remained in the engineering school, those who remained at the university in a different school, and those who left the university altogether. Self‐reported confidence in college‐level math/science ability and the belief that an engineering degree enhances career security at a respectable salary were found to be significant predictors of both short‐term and long‐term persistence in engineering.     

The Mahalanobis Distance for Functional Data With Applications to Classification

This article presents a new semidistance for functional observations that generalizes the Mahalanobis distance for multivariate datasets. The main characteristics of the functional Mahalanobis semidistance are shown. To illustrate the applicability of this measure of proximity between functional observations, new versions of several well-known functional classification procedures are developed using the functional Mahalanobis semidistance. A Monte Carlo study and the analysis of two real examples indicate that the classification methods used in conjunction with the functional Mahalanobis semidistance give better results than other well-known functional classification procedures. This article has supplementary material online.     

Analysis of Large Heterogeneous Repairable System Reliability Data With Static System Attributes and Dynamic Sensor Measurement in Big Data Environment

ABSTRACT

In the age of Big Data, one pressing challenge facing engineers is to perform reliability analysis for a large fleet of heterogeneous repairable systems with covariates. In addition to static covariates, which include time-invariant system attributes such as nominal operating conditions, geo-locations, etc., the recent advances of sensing technologies have also made it possible to obtain dynamic sensor measurement of system operating and environmental conditions. As a common practice in the Big Data environment, the massive reliability data are typically stored in some distributed storage systems. Leveraging the power of modern statistical learning, this article investigates a statistical approach which integrates the random forests algorithm and the classical data analysis methodologies for repairable system reliability, such as the nonparametric estimator for the mean cumulative function and the parametric models based on the nonhomogeneous Poisson process. We show that the proposed approach effectively addresses some common challenges arising from practice, including system heterogeneity, covariate selection, model specification and data locality due to the distributed data storage. The large sample properties as well as the uniform consistency of the proposed estimator are established. Two numerical examples and a case study are presented to illustrate the application of the proposed approach. The strengths of the proposed approach are demonstrated by comparison studies. Datasets and computer code have been made available on GitHub.     

数据可视化及数值分析技术在不确定度评定中的应用

分析不确定度的传播是不确定度评定中的关键一环。利用数据可视化及数值分析技术,提出了一种分析不确定度传播的新方法。首先介绍了该方法的主要步骤,然后通过在线性和非线性测量模型中应用的实例,对该方法的应用过程作了详细说明。这些实例表明,恰当地应用数据可视化及数值分析技术可以为评定不确定度的传播提供一种直观的定性图示和准确的定量分析。     

OEE多维数据分析系统的应用研究

针对生产领域中重要效率评价指标OEE,研究如何用多维的思路和方法来分析.结合OEE的定义、多维分析基本思想,以及当前各类OEE分析软件特点的基础,为实现对海量多维生产数据准确、高效、灵活的分析,提出一种OEE多维数据分析系统.讨论了多维数据分析技术在OEE数据分析系统的研究和应用的设计过程,并对基于Excel VBA开发的OEE多维数据分析系统进行实证研究.     

二次价值分析在优选瓦楞纸板生产线中的应用

这是一份价值工程在包装领域的一项研究成果报告,它将“二次价值分析”技法连续分级运用于瓦楞纸板生产线的购置中,取得了较为显著的经济效益和社会效益,在同行业中具有推广价值。     

16S rRNA基因与16S-23S rRNA转录单元内间隔区序列分析及其在节旋藻和螺旋藻分类鉴定中的应用

测定了节旋藻属3个品系和螺旋藻属1个品系的全长16SrRNA基因基因和16S rRNA转录单元内间隔区序列（ITS）,分析了已知的节旋藻、螺旋藻和相关品系的相应序列的同源性,构建了系统发生树,并评价了这两段DNA序列在节旋藻、螺旋藻种属分类和种质鉴定中的意义。结果表明：（1）16SrRNA基因序列和ITS序列均可用于节旋藻属和螺旋藻属的属间分类,以两序列为基础的系统学分析结果一致;（2）ITS序列变异程度高于16SrRNA序列,适用于节旋藻和螺旋藻属内品系或种质鉴定;（3）节旋藻属可明确界定,16SrRNA基因序列相似性大于98％,ITS序列相 似性大于88％;（4）螺旋藻属某些品系间16SrRNA序列和ITS序列相似性较低,与不同属间的序列相似性程度为同一水平。