REGRESSION ON MULTIVARIATE IMAGES:PRINCIPAL COMPONENT REGRESSION FOR MODELING,PREDICTION AND VISUAL DIAGNOSTIC TOOLS

Regression between two blocks(usually called‘dependent’or Y and‘independent’or X)of data is a veryimportant scientific and data-analytical tool.Regression on multivariate images is possible and constitutesa meaningful addition to existing univariate and multivariate techniques of image analysis.The regressioncan be used as a modeling tool or for prediction.The form of the regression equation chosen is dependentupon problem specification and information at hand.This paper describes the use of principal componentregression(PCR).Both model building and prediction are presented for continuous Y-variables.The finalgoal is to supply new image material that can be used for visual inspection on a screen.Also,visual toolsfor diagnosis of model and prediction are provided,often based on derived image material.Examplesof modeling and prediction are given for six channels in a seven-channel satellite image     

PRINCIPAL COMPONENTS REGRESSION FOR ROUTINE MULTICOMPONENT UV DETERMINATIONS: A VALIDATION PROTOCOL

A validation protocol for multicomponent spectroscopic assays based on principal componentsregression is described. Factorial design and hypothesis tests are used to establish the linearity andabsence of interaction between components in the regression model. Testing considers multiple responsevariables simultaneously so that correlation between residuals is properly treated. Assay reproducibilityand sensitivity to related substances are evaluated.     

DETECTING AND ADJUSTING FOR NON-LINEARITIES IN CALIBRATION OF NEAR-INFRARED DATA USING PRINCIPAL COMPONENTS

A new regression method for non-linear near-infrared spectroscopic data is proposed.The technique isbased on a model which is linear in the principal components and simple functions(squares and products)of them.Added variable plots are used to determine which squares and products to incorporate into themodel.The regression coefficients are estimated by a Stein estimate which shrinks towards the estimatedetermined by the first several principal components and the selected non-linear terms.The technique isnot computationally intensive and is appropriate for routine predictions of chemical concentrations.Themethod is tested on three data sets and in all cases gives more accurate predictions than does linearprincipal components regression.     

ROBUST PRINCIPAL COMPONENT ANALYSIS BY PROJECTION PURSUIT

Principal component analysis (PCA) is a widely used technique in chemometrics.The classical PCAmethod is,unfortunately,non-robust,since the variance is adopted as the objective function.In thispaper,projection pursuit (PP) is used to carry out PCA with a criterion which is more robust than thevariance.In addition,the generalized simulated annealing (GSA) algorithm is introduced as anoptimization procedure in the process of PP calculation to guarantee the global optimum.The resultsfor simulated data sets show that PCA via PP is resistant to the deviation of the error distribution fromthe normal one.The method is especially recommended for use in cases with possible outlier(s) existingin the data.     

PRINCIPAL COMPONENT ANALYSIS APPLIED TO THE STUDY OF SUCCESSIVE COMPLEX FORMATION DATA IN CU(II)-ETHANOLAMINE SYSTEMS

Application of principal component analysis to Cu(II)-ethanolamine complex formation data is shown.Determination of the number of complex species is obtained from the rank of the matrix of spectral datausing either Gauss elimination or factorial analysis.Relevant information concerning species distributionversus pH is obtained from the plot of the signficant factors upsurging from the evolution of spectraltitration data.     

EXAMINING LARGE DATABASES:A CHEMOMETRIC APPROACH USING PRINCIPAL COMPONENT ANALYSIS

Principal component analysis is used to examine large multivariate databases.The graphical approachto exploratory data analysis is described and illustrated with a single example of chemical compositiondata obtained on environmental dust particles.While the graphical approach to exploratory data analysishas certain advantages over the numerical procedures,the empirical approach described here should beviewed as complementary to the more robust treatments that statistical methodologies afford.     

广东地级市中心城市主成分聚类分析

本文对广东省２０个地级市中心城市进行了主成分聚类分析，并在此基础上对各中心城市的发展方向提出了初步的意见。     

DRIED GRASS SILAGE ANALYSIS BY NIR REFLECTANCE SPECTROSCOPY-A COMPARISON OF STEPWISE MULTIPLE LINEAR AND PRINCIPAL COMPONENT TECHNIQUES FOR CALIBRATION DEVELOPMENT ON RAW AND TRANSFORMED SPECTRAL DATA

Calibrations to predict crude protein (CP) and in vitro dry matter digestibility (IVDMD) in dried grasssilage from reflectance data collected at 19 wavelengths on an InfraAlyzer 400R have been developedusing stepwise multiple linear (SML) and principal component (PC) regression techniques. A directcomparison of the efficacy of each multivariate technique in this application has been possible by usingidentical calibration development and evaluation sample sets. The effect of two data transformation stepsprior to PC regression was also investigated. PC regression of raw reflectance data yielded no significantimprovement in the standard errors of prediction (SEP) for CP and IVDMD over those obtained bySMLR, viz. 0.61 vs 0.63 and 2.9 vs 3.0 respectively. Computation time for development and evaluation ofthe PC regression equation was less than for selection of the best SMLR equation, and PCR equationsmay be more robust. Data transformation to reduce granularity effects prior to PCR did not produce anyimprovement in predictive accuracy for either IVDMD or CP.     

WEIGHTED ANALYSIS OF PRINCIPAL COMPONENTS: TWO APPROXIMATIONS TO STATISTICAL WEIGHTS

Two approximate methods for weighted principal components analysis (WPCA) were devised and testedin numerical experiments using either empirical variances (obtained from replicated data) or assumedvariances (derived from unreplicated data). In the first ('spherical') approximation each data vector wasassigned a weight proportional to the geometrical mean of its variances in all dimensions. Thearithmetical mean of variances was used instead in the other approximation. Both the numericalexperiments with artificial data containing random errors of various kinds (constant, proportional,constant plus proportional, Poisson) and the analysis of two sets of Raman spectra clearly indicated thenecessity of introducing statistical weights. The spherical approximation was found to be slightly betterthan the arithmetical one. The application of statistical weighting was found to improve the performanceof PCA in estimation problems.     

用主分量方法分析广东春季低温阴雨年景

本文利用主分量方法对广东47站1954～1991年2～3月平均温度和广东2～3月间低温阴雨出现年景进行统计分析，根据主分量原理，计算该时期温度的时空分布特征，直接评价低温阴雨出现年景：①广东2～3月温度时空分布极为集中，第1主分量已占埸的总方差的95．1％；③用前4个主分量及其对应的特征向量配合划分温度分布类型；③广东2～3月温度分布主要由2个类型控制，即全省一致的偏低（或高）分布和南暖北冷或南冷北暧分布．由主分量极大值（正）和极小值（负）表明：1957、1968、1969年为全省性温度偏低年，1973和1987年为全省性温度偏高年。这些年份恰好对应广东2～3月低温阴雨严重和轻微（或无）的年份。     

主成分分析在城市PRED系统可持续发展研究中的应用——以广东省所辖21个城市为例

依据1995-1999年广东省所辖21个城市科技人口数量增长率，城市人口数量增长率，耕地面积递减率，森林覆盖递减率，三废处理能力增长率，三废排放增长率，人平工资增长率，人均GDP增长率等指标统计资料，应用主成分分析法分析了广东城市人口，资源，环境和经济发展（PRED）系统的可持续发展过程，并从众多PRED系统因子中揭示出典型的敏感因子（主成分），同时，也为城市PRED）系统的可持续发展过程。并从众多PRED系统因子中揭示出典型的敏感因子（主成分）。同时，也为城市PRED系统可持续发展进程的分类提供新的依据。     

IDENTIFICATION OF FINITE IMPULSE RESPONSE MODELS WITH CONTINUUM REGRESSION

The use of continuum regression(CR)for the identification of finite impulse response(FIR)dynamicmodels is investigated.CR encompasses the methods of principal component regression(PCR),partialleast squares(PLS)and multiple linear regression(MLR).PCR and MLR are at the two extremes of thecontinuum.In PCR and PLS,cross-validation is used to determine the optimum number of factors or‘latent variables’to retain in the regression model.CR allows one to vary the method in addition.Cross-validation then determines both the optimum method and the number of latent variables.The CR‘prediction error surface’—a function of the method and number of latent variables—is elucidated.Theoptimal model is defined as the minimum of this surface.Among the cases studied,the optimal modelusually comes from the region of the continuum between PCR and PLS.Few derive from the regionbetween PLS and MLR.It is also demonstrated that FIR models identified by CR have frequency domainproperties similar to those identified by PCR.     

REAL-TIME FILTERING OF DATA FROM MOBILE,PASSIVE REMOTE INFRARED SENSORS WITH PRINCIPAL COMPONENT MODELS OF BACKGROUND

Real-time monitoring of pollutant levels from a mobile measuring platform requires fast,flexible dataanalysis methods.This paper reports a method for rapid analysis of passive remotely sensed infrared datawith the aid of a Kalman filter.The background spectra produced by emission from the atmosphere aremodelled at the start of the data collection sequence with a simple principal components model obtainedby eigenanalysis of the initial‘blank’data taken with the spectrometer.The species of interest areincluded in the state space model by a separate measurement of their infrared spectra.It is demonstratedthat for best filter performance in detecting the simulated pollutant species SF_6 in the atmosphere,a filtermodel with two principal components describing the emission background works best.The filter‘maps’of SF_6 closely follow the integrated spectral intensities measured after removal of suitable backgrounds.     

CROSS-VALIDATION, INFLUENTIAL OBSERVATIONS AND SELECTION OF VARIABLES IN CHEMOMETRIC STUDIES OF WINES BY PRINCIPAL COMPONENTS ANALYSIS

Cross-validatory estimation of the bilinear model based on principal components is reviewed andKrzanowski's modification of Wold's procedure is described. Two different types of residuals useful forchecking model adequacy are defined and indices measuring the influence of each observed unit on theestimates of the parameters are discussed. A method for the selection of variables derived from Procrustesanalysis is described. Results arising from the study of two sets of enological data are given.     

典范主分量分析及其在山西植被与气候关系分析中的应用

排序是植被分析重要手段,大多数排序方法仅使用植数据。本文引入一个能够同时使用植被数据和环境数据的新方法－－典范主分量分析,它能够更好地描述植被与环境之间的关系。我们用该方法研究了山西植被与气候之间的关系,结果清楚地反映了山西植被与气候的地带分布规律及其相互关系,证明其是有效地植被环境关系分析方法。     

TESTING FOR REDUNDANCY IN PRODUCT QUALITY CONTROL TEST CRITERIA:AN APPLICATION TO AVIATION TURBINE FUEL

Given a set of test criteria that determine a quality specification,the question often arises whether anyof the tests are redundant because of intercorrelations.Simple selection of tests on the basis of partialcorrelations with the other tests is rejected on the basis that the random error in the data may be causingspurious correlations.One method is to use cross-validation to define the systematic principal components and examine thecorrelation structure in this reduced space.It is shown that the presence of principal componentsdominated by individual tests(‘variable specific’PCs),which are indicated by cross-validation as beingnon-systematic,must be taken into account.Having defined the dimensionality,a variable reductionmethod based on Procrustes rotation selects subsets of tests that preserve the structure of the samples inmultivariate space.This is an attractive proposition in the context of maintaining a quality controlspecification.It is also shown that the variable reduction technique can be used to aid the identificationof the true dimensionality of the data space.This approach is applied to a number of routine tests carriedout on aviation turbine fuel.