DISCRIMINANT PRINCIPAL COMPONENTS ANALYSIS

When the number of variables exceeds the number of samples, one method of multivariate discriminationis to use principal components analysis to reduce the dimensionality and then to perform canonicalvariates analysis (PC-CVA). This paper proposes an alternative approach in which discriminant analysisis carried out by a weighted principal component analysis of the group means (DPCA). This method doesnot require prior data reduction and produces discriminant factors that are orthogonal in the original dataspace. The theory and performance of the two methods are compared. Although the individual factors ofDPCA are found to be less discriminating than PC-CVA, the overall discrimination, calculated bymultivariate analysis of variance, and the predictive value, estimated by the leaving-one-out error rate,are broadly comparable.     

STATISTICAL F-TESTS FOR ABSTRACT FACTOR ANALYSIS AND TARGET TESTING

Fisher variance ratio tests are developed for determining(1)the number of statistically significantabstract factors responsible for a data matrix and(2)the significance of target vectors projected into theabstract factor space.F-tests,developed from the viewpoint of vector distributions,are applied tovarious data sets taken from the chemical literature.     

MULTIVARIATE RESPONSE SURFACE MODELLING BY PRINCIPAL COMPONENTS ANALYSIS

Analysis of multivariate response data by modelling the principal components of the response has beenapplied to two sets of data. In both cases principal components analysis revealed the relationships amongthe response variables and exploited them to simplify the problem of modelling and optimizing themultivariate response. The models and optima obtained from the principal components comparedfavourably with the individual models and simultaneous optima.     

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.     

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.     

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.     

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.     

BODY DIAGONALIZATION OF CORE MATRICES IN THREE-WAY PRINCIPAL COMPONENTS ANALYSIS:THEORETICAL BOUNDS AND SIMULATION

In contrast with conventional PCA,a direct superposition and joint interpretation of loading plots is notpossible in three-way PCA,since there may be data variance which is described by unequal componentsof different modes.The contributions to variance of all possible combinations of components aredescribed in the core matrix.Body diagonalization,which is achieved by appropriate rotation ofcomponent matrices,is an essential tool for simplifying the core matrix structure.The maximum degreeof body diagonality which may be obtained from such transformations is analysed from both themathematical and simulation viewpoints.It is shown that,at least in the average case,high degrees canbe expected,which makes the procedure reasonable for many practical applications.Furthermore,simulation as well as theoretical derivation show that the success of body diagonality depends on the so-called polarity of the core array.The methodology is illustrated by a three-way data example fromenvironmental chemistry.     

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。     

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.     

RAPID ESTIMATION OF THE NUMBER OF COELUTING COMPONENTS IN LIQUID CHROMATOGRAPHY BY FACTOR ANALYSIS

Evaluation of the results of factor analysis of sets of spectroscopically detected chromatograms is carriedout by examining the shapes of the abstract factors.This is done either by visual inspection or by analysisof the power density spectra produced from them.Owing to constraints imposed by the column functionand the spectroscopic instrument function,the information content of the chromatograms necessarilyoccurs at low spatial frequencies.As a consequence,it appears as relatively broad features in the abstractchromatograms and as a peak in the low-frequency region of the corresponding power density plot.Onthe basis of examination of the power density distribution,a well-defined distinction is made betweenprimary and secondary abstract factors.The major uncertainty encountered in determining the numberof chemical components appears to arise from effects of contaminants in reagents.     

WINDOW FACTOR ANALYSIS:THEORETICAL DERIVATION AND APPLICATION TO FLOW INJECTION ANALYSIS DATA

Window factor analysis(WFA)is a self-modeling method for extracting the concentration profiles ofindividual components from evolutionary processes such as flow injection,chromatography,titrationsand reaction kinetics.The method takes advantage of the fact that each component lies in a specificregion along the evolutionary axis,called the‘window’.Theoretical equations are derived.The methodis used to extract the concentration profiles and spectra of seven bismuth species from data obtained byGemperline and Hamilton,who injected bismuth perchlorate into a flowing stream of hydrochloric acid.     

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。     

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。     

ASSESSMENT OF THE EFFECTIVE RANK OF A (CO)VARIANCE MATRIX: A NON-PARAMETRIC GOODNESS-OF-FIT TEST

Each eigenvector of the dispersion matrix[X]~T[X]was shown to be a partial predictor of the originaldata matrix [X],the sum of the predictions from the individual principal components being equal to theexpectance of [X].By comparing the distributions of the members of two neighbouring predictedmatrices,[X]_(1...i)and [X](1...i+1)(i.e.the sums of the first i and i+1 individual predictions respectively),it was shown that they should be indistinguishable provided that i is equal to or greater than the effectiverank of [X],and significantly different otherwise.This was confirmed by analysing the visible absorptionspectra of methyl orange and methyl red solutions as well as the Raman spectra of Na_2SO_4 and MgSO_4solutions.On the grounds of these findings,a non-parametric goodness-of-fit test for assessing theeffective rank of[X]was proposed which proved to be comparatively conservative and more robust thanmost currently used tests.     

FACTOR ANALYSIS OF A SIMULATED DATA MATRIX INVOLVING AQUEOUS COMPLEX EQUILIBRIA

Abstract factor analyses were performed on databases consisting of simulated samples from aqueousequilbria.The program COMPLEX was used to generate equilibrium species in a system of three reactantmetals and five reactant bases.Reactant concentrations and pH were drawn from random-normaldistributions so that sample data vectors comprised a multivariate log-normal distribution of equilibriumconcentrations.In addition,sample groups were created containing different distributions for pH andreactant concentrations.Equilibrium species were shown to contain variance contributed by change in pH among samples aswell as change in reactant concentrations.Factor modelling revealed the qualitative relationships amongthe species and how the relationships change with pH.Factors also revealed those reactants containingvariance in the data matrix.In some cases,reactant variance obscured relationships between pH and theequilibrium species.Since factor modelling of a simulated data matrix revealed the expected chemical equilibriuminteractions,a potentially powerful tool exists for investigating the effects of outliers and error.     

因子分析法在水源保护区水质评价中的应用

通过对松华坝水源保护区2001-2007年的两个监测断面水质进行因子分析,两个断面8项水质指标中TN均超标,其余水质指标均未超标。使用SPSS13．0工具进行分析,结果显示,两个监测断面的主要污染因子各异,牧羊河断面的主要污染物为TN和TP,而冷水河断面的主要污染物为CODMn、BOD5和TP。松华坝水源保护区水质保护形势十分严峻。必须高度重视,采取切实措施,处理好水源区保护和发展的关系,保护好松华坝水源保护区水质,确保昆明市民饮水安全。     

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。     

主成分分析方法在区域经济研究中的应用--以新疆为例

主成分分析方法（PCA）及采用此法做综合评价的原理和步骤，并用两个方面的实例具体阐述了主成分分析方法在区域经济研究中的应用，最后对这种方法的特点及应用中须注意的问题进行了初步总结。