bluuebunny/crossref_metadata_2025 huggingface dataset:
Selection of optimal regression models via cross‐validation
Authors: Osten David W.
Published: May 2005

A general problem arising in the development of regression models is the selection of the optimal model. Whenever a feature selection procedure, such as step forward, backward elimination, best subset or all possible combinations, or when a data compression approach, such as principal components or partial least‐squares regression, is used, the question of how many regression terms to include in the final model must be addressed.

This work describes the evaluation of four different criteria for selection of the optimal predictive regression model using cross‐validation. The results obtained in this work illustrate the problems which can arise in the analysis of small or inadequately sampled data sets. The common approach, selecting the model which yields the absolute minimum in the predictive residual error sum of squares (PRESS), was found to have particularly poor statistical properties. A very simple change to a criterion based on the first local minimum in PRESS will provide a significant improvement in the cross‐validation result. A criterion based on testing the significance of incremental changes in PRESS with anF‐test may provide more robust performance than the local minimum in PRESS method.
Principal component variable discriminant plots: A novel approach for interpretation and analysis of multi‐class data
Authors: Vogt Nils B.
Published: May 2005

Principal component analysis is a useful method for analysing data‐matrices. By analysing separate class models, i.e. disjoint principal component modelling as in the SIMCA or FCVPC programs (developed for supervised and unsupervised principal component analysis respectively), the principal component variance/covariance decomposition (class models) may be used to investigate and interpret the data‐structure of separate classes. The potential of comparing the loadings of variables on subsequent eigenvectors in two class models where the same variables have been used will give information for determining how the variance/covariance in the two datasets differ. This information may then be used either to formulate a hypothesis or to select variables which are specific for the different classes.
Monte Carlo studies of non‐parametric linear discriminant functions
Authors: Lavine B. K. , Henry D. R.
Published: May 2005

Classification rules using non‐parametric linear discriminant functions are often developed from training sets that are not linearly separable. In these situations it is a common practice among inexperienced workers to use many different pattern recognition methods and then select the results that look the best. However, this practice will only increase the risk of spurious results. To document this, we recently carried out a series of Monte Carlo simulation studies to assess the level of chance classification for two different classification algorithms. The level of chance classification for a given dichotomy is found to vary with the choice of the non‐parametric linear discriminant function employed. Although previous workers have indicated that the degree of separation in the data due to chance is only a function of the object‐to‐descriptor ratio, the results of this study suggest otherwise.
Evaluation of computing capabilities of a hierarchy of mini‐to‐supercomputers: Applications to ion microscopic analysis
Authors: Ling Yong‐Chien , Bernardo Dan N. , Morrison George H.
Published: May 2005

There has been a steadily increasing demand for more computational power in surface and interface analysis. This paper reports attempts to meet these demands through the use of different computing systems, ranging from minicomputer to supercomputer. Representative laboratory data processing programs for ion microscopic analysis are used to evaluate the performance of each system. The bottlenecks and other problems involved in running analytical programs on faster machines are identified and discussed. Results indicate that in order to attain the optimal cost‐performance ratio, programs must be tailored to specific forms required by the computing system. Algorithms must be formulated to exploit available vector and parallel processing capabilities.
Source contributions to ambient aerosol calculated by discriminat partial least squares regression (PLS)
Authors: Vong Richard , Geladi Paul , Wold Svante , Esbensen Kim
Published: May 2005

Partial least squares regression (PLS) is proposed for solving ir pollution source apportionment problems as an alternative method to the frequently used chemical mass balance technique. A discriminant PLS is used to calculate linear mixing proportions for a synthetic ambient aerosol data set where the truth is known. Without sacrificing orthogonality of the source profiles, PLS can resolve the emission sources and accurately predict the emission source contributions. Further extensions of the PLS approach to environmental receptor modelling are discussed.
A multiblock partial least squares algorithm for investigating complex chemical systems
Authors: Wangen L. E. , Kowalski B. R.
Published: May 2005

The details of a general multiblock partial least squares (PLS) algorithm based on one originally presented by Wold et al. have been developed and are completely presented. The algorithm can handle most types of relationships between the blocks and constitutes a significant advancement in the modeling of complex chemical systems. The algorithm has been programmed in FORTRAN and has been tested on two simulated multiblock problems, a three‐block and a five‐block problem. The algorithm combines the score vectors for all blocks predicting a particular block into a new block. This new block is used to predict the predicted block in a manner analogous to the two‐block PLS. In a similar manner if one block predicts more than one other block, the score vectors of all predicted blocks are combined to form a new block, which is then predicted by the predictor block as in the two‐block PLS. Blocks that both predict and are predicted are treated in such a way that both of these roles can be taken into account when calculating interblock relationships. The results of numerical simulations indicate that the computer program is operating properly and that the multiblock PLS produces meaningful and consistent results.
The performance of least squares and robust regression in the calibration of analytical methods under non‐normal noise distributions
Authors: Wolters R. , Kateman G.
Published: May 2005

By means of Monte Carlo simulations a comparison has been made between ordinary least squares regression and robust regression. The robust regression procedure is based on the Huber estimate and is computed by means of the iteratively reweighted least squares algorithm. The performance of both procedures has been evaluated for estimation of the parameters of a calibration function and for determination of the concentration of unknown samples. The influence of the distributional characteristics skewness and kurtosis has been studied, and the number of measurements used for constructing the calibration curve has also been taken into account. Under certain conditions robust regression offers an advantage over least squares regression.
Use of replication and signal‐to‐noise ratios in the identification and estimation of the composition of lubricant basestock mixtures using13C nuclear magnetic resonance spectroscopy and projection into principal component/canonical variates space
Authors: Deane John M. , MacFie Halliday J. H. , King Alexander G.
Published: May 2005

The theory of experimental error in analysis of mixture experiments by abstract factor analysis or target transformation factor analysis is considered. The theoretical implications of using signal‐to‐noise ratios (as weights) or canonical variates analysis to reduce the level of imbedded error in the factor model are examined. The approach is illustrated by application to13C NMR spectra of lubricant basestock mixtures.
Condition numbers, iterative refinement and error bounds
Authors: Kalivas John H. , Lang Patrick
Published: May 2005

Concentration estimates of components present in a sample mixture can be obtained using matrix mathematics. In the past, the condition number of the calibration matrix has been used to give an amplification factor by which uncertainties in data can work through to errors in the concentration estimates. This paper explores an additional interpretation of condition numbers with regards to significant figures and rounding errors. A procedure is suggested which will always give the most accurate concentration estimates provided the calibration matrix is not too ill‐conditioned. Condition numbers have also been used by analytical chemists to discuss the error bounds for concentration estimates. Unfortunately, only one representative error bound can be approximated for all the components. This paper will show how to compute bounds for individual concentration estimates obtained as solutions to a system of m equations and n unknowns. The procedure is appropriate when calibration data and sample responses are inaccurate.
Testing for redundancy in product quality control test criteria: An application to aviation turbine fuel
Authors: Deane John M. , MacFie Halliday J. H.
Published: May 2005

Given a set of test criteria that determine a quality specification, the question often arises whether any of the tests are redundant because of intercorrelations Simple selection of tests on the basis of partial correlations with the other tests is rejected on the basis that the random error in the data may be causing spurious correlations.

One method is to use cross‐validation to define the systematic principal components and examine the correlation structure in this reduced space. It is shown that the presence of principal components dominated by individual tests (‘variable specific’ PCs), which are indicated by cross‐validation as being non‐systematic, must be taken into account. Having defined the dimensionality, a variable reduction method based on Procrustes rotation selects subsets of tests that preserve the structure of the samples in multivariate space. This is an attractive proposition in the context of maintaining a quality control specification. It is also shown that the variable reduction technique can be used to aid the identification of the true dimensionality of the data space. This approach is applied to a number of routine tests carried out on aviation turbine fuel.
The problem of adequate sample size in pattern recognition studies: The multivariate normal case
Authors: Han J. H. , Ward A. J. I. , Lavine B. K.
Published: May 2005

Because many pattern recognition techniques are predicated on the assumption of mutivariate normal data, Monte Carlo simulation studies were performed to determine the number of samples that are necessary to describe a multivariate normal population adequately. From these studies we have learned that hundreds of samples are required. These results suggest that parametric procedures should only be used to analyze very large data sets.
Recursive parameter estimation
Authors: Rutan Sarah C.
Published: May 2005

The use of recursive filtering techniques for parameter estimation in a variety of areas is reviewed. In particular, the Kalman filter algorithm is described, along with several variations, including square‐root, UDUT and information filters. The solution to parameter estimation problems is discussed for both linear and non‐linear models. Applications described include calibration, curve resolution in spectroscopy, chromatography, electrochemistry, kinetic analysis and process monitoring.
Quantifying similarity for handling information in knowledge bases
Authors: Bandemer Hans
Published: May 2005

When constructing diagnostic systems or using knowledge‐based systems, e.g. in analytical chemistry, features of different type and character, represented by numbers, trajectories or linguistic variables such as intensities or colours, must be considered. To find neighbourhoods or to fill in missing values, the notion of similarity is of essential importance. The paper presents a new fuzzy‐set‐theory‐based approach to quantifying similarity and provides a system of rules to be implemented into the diagnostic part of the knowledge base to be used.
Latent features with maximal correlation between two equal sets of variables
Authors: Henrion René , Henrion Günter
Published: May 2005

If in two data tables X and Y objects are characterized by the same variables (measured at different occasions), then looking for common latent features should be more appropriate than choosing latent features in X and Y separately (e.g. as in canonical correlation or PLS). The procedure to be proposed here is a slight modification of the method of linear characteristics (according to De Groot and Li) by disclaiming the assumption of equal inner‐block covariance matrices. In order to find weights defining a latent feature with maximal correlation between X and Y, a system of non‐linear equations has to be solved. The procedure is applied to the investigation of heavy metal concentrations in different human tissues.
Cross‐validation, influential observations and selection of variables in chemometric studies of wines by principal components analysis
Authors: Scarponi Giuseppe , Moret Ivo , Capodaglio Gabriele , Romanazzi Mario
Published: May 2005

Cross‐validatory estimation of the bilinear model based on principal components is reviewed and Krzanowski's modification of Wold's procedure is described. Two different types of residuals useful for checking model adequacy are defined and indices measuring the influence of each observed unit on the estimates of the parameters are discussed. A method for the selection of variables derived from Procrustes analysis is described. Results arising from the study of two sets of enological data are given.
Comments on the power method
Authors: Seasholtz Mary Beth , Pell Randy J. , Gates Kevin E.
Published: May 2005

In a recent short communication, Miyashita et al. have commented on the weakness of the NIPALS algorithm (equivalently the power method) for calculating the eigenvalues out of order. They offer a diagnostic to ascertain when this may have occurred and suggested a modification to the NIPALS algorithm to avoid this situation. Further comments regarding the use of the power method and Miyashita's presentation of its weakness are warranted. The general inadequacies of methods for decomposing a matrix with degenerate eigenvalues and their relationship to the orthogonal design of experiments are discussed.
The start and early history of chemometrics: Selected interviews. Part 1
Authors: Geladi Paul , Esbensen Kim
Published: May 2005

This is a first foray into the historical start and early years of chemometrics from about 1972 onwards. We have gathered interviews with three originators (Kowalski, Wold and Massart) as well as with a selected group of six other well‐known chemometricians who gradually became active in the 1970s (Christie, Clementi, Hopke, Martens, Brown and Deming). The interviews include amongst a host of subjective recollections a succinct record of the key historical literature as highlighted by the interviewees' own rankings of ‘earliest’ and ‘best’.

A discussion of the most general commonalities in these interviews together with other historical material is presented in the second part of the paper.
Factor analysis of a simulated data matrix involving aqueous complex equilibria
Authors: Conny Joseph M. , Meglen Robert R.
Published: May 2005

Abstract factor analyses were performed on databases consisting of simulated samples from aqueous equilbria. The program COMPLEX was used to generate equilibrium species in a system of three reactant metals and five reactant bases. Reactant concentrations and pH were drawn from random–normal distributions so that sample data vectors comprised a multivariate log–normal distribution of equilibrium concentrations. In addition, sample groups were created containing different distributions for pH and reactant concentrations.

Equilibrium species were shown to contain variance contributed by change in pH among samples as well as change in reactant concentrations. Factor modelling revealed the qualitative relationships among the species and how the relationships change with pH. Factors also revealed those reactants containing variance in the data matrix. In some cases, reactant variance obscured relationships between pH and the equilibrium species.

Since factor modelling of a simulated data matrix revealed the expected chemical equilibrium interactions, a potentially powerful tool exists for investigating the effects of outliers and error.
Variations in essential oils of mandarine related to processing and ripening
Authors: Cotroneo Antonella , Dugo Giovanni , Favretto Luciano , Favretto Luciana Gabrielli
Published: May 2005

Mandarine essential oils are extracted from green unripened fruits as well as from red fruits at ripening, both oils having specific uses as natural additives in the food industry. Two processes of production, pressing and peeling, are currently adopted in their production. Capillary gas chromatography with flame ionization detection has been suggested as a sensitive method for the fractionation of volatile components of the essential oils. Principal component analysis was proposed as an exploratory chemometric method for the differentiation of essential oils from fruits at different degrees of ripening, taking into account the processes of production. Product–moment correlations between variables (concentrations of 17 components) were used as starting matrices and the explained variance was adopted as a criterion for eigenvalue selection. Bi‐plots and three‐dimensional plots of unrotated principal component scores were systematically used as well as those of orthogonally rotated factor scores. The 17 variables were reduced to four principal components, which explained 87% of the total variance. Projection on the first three eigenvectors of all data as unrotated component scores allowed for a tentative differentiation of 59 oils according to their degree of ripening. The two processes of production were also differentiated in a sample of 55 oils.
Dependence between fusion temperatures and chemical components of a certain type of coal using classical, non‐parametric and bootstrap techniques
Authors: González‐Manteiga W. , Prada‐Sánchez J. M. , Fiestras‐Janeiro M. G. , García‐Jurado I.
Published: May 2005

A statistical study of the dependence between various critical fusion temperatures of a certain kind of coal and its chemical components is carried out. As well as using classical dependence techniques (multiple, stepwise and PLS regression, principal components, canonical correlation, etc.) together with the corresponding inference on the parameters of interest, non‐parametric regression and bootstrap inference are also performed.
Tutorial to robust statistics
Authors: Rousseeuw Peter J.
Published: May 2005

In this tutorial we first illustrate the effect of outliers on classical statistics such as the sample average. This motivates the use of robust techniques. For univariate data the sample median is a robust estimator of location, and the dispersion can also be estimated robustly. The resulting ‘z‐scores’ are well suited to detect outliers. The sample median can be generalized to very large data sets, which is useful for robust ‘averaging’ of curves or images. For multivariate data a robust regression procedure is described. Its standardized residuals allow us to identify the outliers. Finally, a survey of related approaches is given. (This review overlaps with earlier work by the same author, which appeared elsewhere.)
Splitting of calibration data by cluster analysis
Authors: Naes Tormod , Isaksson Tomas
Published: May 2005

The topic of the present paper is the splitting of calibration data into subgroups with improved linearity in each group. The method proposed is based on a criterion which is a weighted average of a Mahalanobis distance and a squared regression residual. The algorithm used to find the solution is based on fuzzy clustering. Two examples are given to illustrate the theory.
A new serial method for searching the optimum operating conditions of a technological process
Authors: Tran V. , Morat J.‐L. , Bertrand D.
Published: May 2005

A new program, named ANTICOMPLEX, has been specially written for searching the optimum conditions of a technological process. The algorithm is based on an iterative procedure with, at each step, a random sampling for a better exploration of the hyperspace of the parameters. Since the process is considered as a ‘black box’, the program operates by successive reductions of the variation domains with a strategy derived from some function optimization (COMPLEX). This approach is very flexible and the experimenter can stop the investigation at any series of experiments according to the desired accuracy for the optimum region. This program has been successfully tested on several real processes. This paper gives a complete description of the approach together with two illustrations on simulated processes.
Correspondence analysis and adsorbate selection for chemical sensor arrays
Authors: Avila Fernando , Myers D. E. , Palmer Chris
Published: May 2005

Carey et al. utilized principal components analysis (PCA) to analyze frequency shift data obtained from piezoelectric sensors formed by coating quartz crystals with 27 different GC stationary phases and tested using 14 analytes. The objective of the analysis was to determine an optimal reduced set of coatings for detection of the analytes. The results were correlated with those obtained from cluster analysis. In this paper the data are re‐analyzed using correspondence analysis (CA). The advantage of using CA include a symmetric treatment of sensor coatings and analytes and better identification of the representation of the analytes in terms of the detection components. The results obtained by the conjunctive use of PCA, a varimax rotation and cluster analysis were obtained by CA.
Multivariate calibration when data are split into subsets
Authors: Naes Tormod
Published: May 2005

A calibration situation is considered where the calibration data are split into subsets with good linear relationship between y and x within each group. Different strategies for good prediction in this case are proposed. Modifications for collinear data are considered and a simple simulated data set is used for illustration.
Mathematical model for the optimization of the reaction between 2,3‐bis(m‐tolyl)quinolizinium bromide and piperidine using a factorial design
Authors: Martin M. A. , Frutos G. , Del Castillo B. , Alvarez‐Builla J. , Martin P. J.
Published: May 2005

A number of nucleophiles have been successfully identified and quantified using the Kröhnke reaction with 2,3‐diphenyl derivatives of quinolizinium salts. Optimization of the reaction conditions by means of a mathematical model involving analysis of the response surface has led to a better understanding of the factors exerting an influence on the above reaction.

The parameters chosen were temperature, reaction time, base concentration, water concentration and nucleophile concentration. The reaction was developed in polar aprotic solvents (acetone, acetonitrile). To facilitate the nucleophilic attack, the presence of an organic base (triethylamine) was necessary, although concentrations in excess of 0·15M did not alter the development of the reaction. Since pharmaceutical solutions are often aqueous, the influence of water on the reaction was studied. Low water volumes have no significant influence on the opening of the quinolizinium ring by the nucleophilic reagent. However, when the water proportion exceeded that of the organic solvent, the fluorescence intensity was lower than expected. Development of the fluorescent reaction product was first detected 5 min after the reaction started. The fluorescence intensity reached its optimum value after 138 min.
Ranking principal components to reflect group structure
Authors: Krzanowski W. J.
Published: May 2005

Canonical variate analysis is the appropriate descriptive technique for multivariate data which have an a priori group structure, but problems arise with this technique when there are more variables than within‐group degrees of freedom because of singularity of matrices. In such cases it is shown through illustrative examples that principal component analysis is a viable substitute provided that the principal components are ranked according to the canonical variate criterion (ratio‐ of between‐ to within‐group variances) rather than the usual criterion of total variance. This ranking can also be used to select components for subsequent discriminant analysis.
Classification of mass spectra
Authors: Drabløs Finn
Published: May 2005

In order to investigate correlations between the functionality of compounds and the classification of their mass spectra, low‐resolution spectra of monofunctional compounds have been classified by four supervised classification methods. The new classes are characterized by structural features and the correlation between functionality and classification is explained by fragmentation rules. Systematic misclassifications show that low‐resolution mass spectra alone are not suitable for reliable identification of functionality.
Estimation of prediction error for samples within the calibration range
Authors: Karstang Terje V. , Toft Jostein , Kvalheim Olav M.
Published: May 2005

A modification of a technique proposed by Lorber and Kowalski for the estimation of prediction errors is presented. The method is applied to five data sets. The results show that for some data sets the estimated prediction errors are close to the actual prediction errors for samples within the calibration range, while samples outside the calibration range must be background corrected before quantification of the prediction error.
On the integration of kinetic models using a high‐order taylor series method
Authors: Baeza Juan José Baeza , Plá Francisco Pérez , Ramos Guillermo Ramis
Published: May 2005

A general equation to derive kinetic models up to any order is given. This equation greatly facilitates the application of the Taylor series method to the integration of kinetic models up to very high orders. When dealing with non‐stiff models, computing time is always reduced by increasing the integration order, at least up to the 20th order. When the model is stiff, the integration order should be optimized; however, a twelfth order is recommended to integrate weakly stiff models. The use of an algorithm which permits the immediate calculation of the integration step size required to maintain a given accuracy leads to further reductions in computing time. When implemented as recommended here, a high‐order Taylor series method is more rapid and accurate than Runge–Kutta and predictor‐corrector methods and can be advantageously used in combination with optimization methods to perform mechanism studies and in multicomponent kinetic determinations.
A review of three‐dimensional chemical structure retrieval systems
Authors: Willett Peter
Published: May 2005

This paper presents a review of the rapid developments that have taken place over the last few years for the searching of databases of three‐dimensional (3D) molecules. The geometric arrangement of the atoms in a 3D molecule is described by an interatomic distance matrix. This is a form of labelled graph that can thus be searched using the subgraph‐isomorphism algorithms that are widely used for searching databases of two‐dimensional (2D) molecules. Several in‐house and commercial systems have been developed for 3D database searching that are based on such techniques. These systems are reviewed and their effectiveness demonstrated by examples of their use in the discovery of novel, biologically active molecules. Current systems represent a molecule by one or a small number of low‐energy conformations and there is hence much interest in the development of representational techniques and searching algorithms that account for the full set of geometric arrangements that can be adopted by a flexible molecule.
Predictive ability of regression models. Part II: Selection of the best predictive PLS model
Authors: Baroni Massimo , Clementi Sergio , Cruciani Gabriele , Costantino Gabriele , Riganelli Daniela , Oberrauch Ermanno
Published: May 2005

A procedure called GOLPE is suggested in order to detect those variables which increase the predictivity of PLS models. The procedure is based on evaluating the predictive power of a number of PLS models built by different combinations of variables selected according to a factorial design strategy. Examples are given of the efficiency of this variable selection procedure, which shows how these predictive PLS models are better than those obtained by all variables and better than the corresponding ordinary regression models.
Identification of finite impulse response models with continuum regression
Authors: Wise B. M. , Ricker N. L.
Published: May 2005

The use of continuum regression (CR) for the identification of finite impulse response (FIR) dynamic models is investigated. CR encompasses the methods of principal component regression (PCR), partial least squares (PLS) and multiple linear regression (MLR). PCR and MLR are at the two extremes of the continuum. 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 themethodin 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. The optimal model is defined as the minimum of this surface. Among the cases studied, the optimal model usually comes from the region of the continuum between PCR and PLS. Few derive from the region between PLS and MLR. It is also demonstrated that FIR models identified by CR have frequency domain properties similar to those identified by PCR.
Short communication Classification methods for multivariate quality parameters
Authors: Weihs C. , Baumeister W. , Schmidli H.
Published: May 2005

There are many chemical products where product conformity is decided upon by qualitative human judgements of overall product quality. Nowadays, quantitative instrumentally determined quality parameters become available which are intended to replace such qualitative judgements by means of automatic decision rules using multivariate specification limits. Six classification methods to derive such limits are compared in terms of their power to predict corresponding human judgemets on overall color conformity of 17 dyestuffs based on historical quality data. Standard statistical classification methods turned out to be unacceptable for the routine generation of decision rules because of the frequent distinct suboptimality of their predictive power. Instead, a simple non‐statistical classification method utilizing a priori knowledge about the underlying data structure yielded uniformly satisfactory decision rules.
Non‐linear mapping for structure‐activity and structure‐property modelling
Authors: Domine D. , Devillers J. , Chastrette M. , Karcher W.
Published: May 2005

From a review of the theoretical aspects of non‐linear mapping and the different algorithms available in the literature, the methodological and practical problems linked to the use of this multivariate method in structure‐activity and structure‐property relationship studies are underlined. Useful tools for the graphical display of the outputs and the interpretation of the obtained clusters are presented. Statistical parameters estimating the quality of the graphical representation of each individual are also introduced. An example of application on a data matrix of 37 acaricides described by four physicochemical descriptors (π, F, R, MR) is presented.
Graphics for linearity and selectivity and prediction diagnostics for multicomponent spectra
Authors: Brown Philip J.
Published: May 2005

Modern scanning infrared reflectance/absorption spectroscopes measure absorptions or reflectance at a sequence of around 1000 wavelengths. Training data may consist of 10–100 carefully designed sample mixtures whose true compositions are either known by formulation or accurately determined by wet chemistry. In future, one wishes to predict the true composition of a newly presented sample from its spectrum. Varying compositions of a mixture of three sugars in water are used for illustration of several different graphical techniques; the spectral measurements here are near‐infrared (NIR) absorbances, but there is nothing exclusively infrared about the methodology. Graphs display the adequacy of a linear explanation of absorbance variability at each wavelength by wavelength linearity plots. These highlight regions of the spectrum where non‐linearities and interaction effects are substantial. By selecting out these substantially non‐linear regions, one can concentrate on linear formulae for prediction with resultant robust linear modelling. Such selections are further aided by plots which identify the component sugar for which each wavelength is most selective. Such plots offer rather natural pre‐screening as an alternative or supplement to the wavelength selection method of Brown.

We also display prediction diagnostics (R, Rx) which on a sample‐by‐sample basis may diagnose a particularly unusual presented spectrum. These diagnostics are shown to have predictive import for a validation data set.
Multivariate exploratory data analysis and graphics: A tutorial
Authors: Weihs C.
Published: May 2005

Exploratory data analysis (EDA) is a toolbox of data manipulation methods for looking at data to see what they seem to say, i.e. one tries to let the data speak for themselves. In this way there is hope that the data will lead to indications about ‘models’ of relationships not expecteda priori. In this respect EDA is a pre‐step to confirmatory data analysis which delivers measures of how adequate a model is. In this tutorial the focus is on multivariate exploratory data analysis for quantitative data using linear methods for dimension reduction and prediction. Purely graphical multivariate tools such as 3D rotation and scatterplot matrices are discussed after having introduced the univariate and bivariate tools on which they are based. The main tasks of multivariate exploratory data analysis are identified as ‘search for structure’ by dimension reduction and ‘model selection’ by comparing predictive power. Resampling is used to support validity, and variables selection to improve interpretability.
Optimization in organic synthesis. An approach to obtaining kinetic information by sequential response surface modelling. Outline of the principles
Authors: Carlson Rolf , Axelsson Anna‐Karin , Nordahl Åke , Barth Tanja
Published: May 2005

A method is presented by which it is possible to estimate the initial rate of chemical reactions when the experimental conditions are varied according to a response surface design. The method is intended as a complementary method for analysing data obtained from experiments in synthetic chemistry when the objective is to optimize the yield of the reaction.

Data obtained by simulations have been used to develop the method. From the simulated reactions it is shown that sequential analysis of the chemical yield of the reaction makes it possible to estimate models which describe how the parameters of the response surface of the yield vary over time. The derivatives of these time functions of the response surface parameters can be used to define a rate function which describes how the variations in the experimental conditions influence the rate of the reaction.

It is shown how such rate functions can be used to afford reasonable estimates of the initial rates of the reaction. The initial reaction rates thus estimated can be used to determine the kinetic order of the reactants and also to provide estimates of the activation energy of the reaction.

A thorough discussion of how canonical analysis of the rate function may assist in the elucidation of reaction mechanisms is given.
Multivariate selection of variables in industrial quality control: Optimizing aviation fuel final control
Authors: Andrade J. M. , Prada D. , Muniategui S. , Gomez B. , Pan M.
Published: May 2005

This paper deals with a typical question encountered in all industrial analytical laboratories: are all the tests performed in the laboratory to characterize the final product really necessary? In this work the cross‐validation technique, Procrustes rotation techniques and statistical variable selection have been used to reduce the 26 initial British Petroleum and ASTM kerosene specification test to ten ‘essential’ ones. Statistical as well as chemical considerations were used to select the optimum subset of original variables to be retained from all the possible ones.
Comments on the residual bilinearization method
Authors: Wang Yongdong , Borgen Odd S. , Kowalski Bruce R.
Published: May 2005

Through theoretical analysis and computer simulation, this short communication comments on the residual bilinearization (RBL) method and compares it with non‐bilinear rank annihilation (NBRA) for the treatment of second‐order calibration with non‐bilinear data. It is found that these two methods are mathematically equivalent but have different noise propagation properties. The second‐order advantage, namely quantitation in the presence of unknown interferences, can be carried over to non‐bilinear data only if there exists a net analyte rank (NAR) for the analyte of interest.
Statistical thinking and technique for QSAR and related studies. Part I: General theory
Authors: Stone Mervyn , Jonathan Philip
Published: May 2005

The two parts of this paper form a critique of a variety of statistical techniques of actual or potential use in quantitative structure‐activity relationship (QSAR) studies and related fields. Part I explores the statistical thinking that is needed to underpin those techniques. Emphasis as placed on (a) the role of ‘exchangeability’ as an alternative to unrealistic statistical modelling and (b) the use of cross‐validation to limit self‐deception in the use of any particular technique. The problem of the almost unlimited range of molecular descriptors is seriously addressed. (Part II provides a concise critical review of methods‐some well‐established and some new.)
Robust principal component analysis by projection pursuit
Authors: Xie Yu‐Long , Wang Ji‐Hong , Liang Yi‐Zeng , Sun Li‐Xian , Song Xin‐Hua , Yu Ru‐Qin
Published: May 2005

Principal component analysis (PCA) is a widely used technique in chemometrics. The classical PCA method is, unfortunately, non‐robust, since the variance is adopted as the objective function. In this paper, projection pursuit (PP) is used to carry out PCA with a criterion which is more robust than the variance. In addition, the generalized simulated annealing (GSA) algorithm is introduced as an optimization procedure in the process of PP calculation to guarantee the global optimum. The results for simulated data sets show that PCA via PP is resistant to the deviation of the error distribution from the normal one. The method is especially recommended for use in cases with possible outlier(s) existing in the data.
Generalized rank annihilation method. II: Bias and variance in the estimated eigenvalues
Authors: Faber N. M. , Buydens L. M. C. , Kateman G.
Published: May 2005

Rank annihilation factor analysis (RAFA) is a method for multicomponent calibration using two data matrices simultaneously, one for the unknown and one for the calibration sample. In its most general form, the generalized rank annihilation method (GRAM), an eigenvalue problem has to be solved. In this second paper expressions are derived for predicting the bias and variance in the eigenvalues of GRAM. These expressions are built on the analogies between a reformulation of the eigenvalue problem and the prediction equations of univariate and multivariate calibration. The error analysis will also be performed for Lorber's formulation of RAFA. It will be demonstrated that, depending on the size of the eigenvalue, large differences in performance must be expected. A bias correction technique is proposed that effectively eliminates the bias if the error in the bias estimate is not too large. The derived expressions are evaluated by Monte Carlo simulations. It is shown that the predictions are satisfactory up to the limit of detection. The results are not sensitive to an incorrect choice of the dimension of the factor space.
Quantitative analysis of latex in paper coatings by ATR‐FTIR spectroscopy
Authors: Dupuy N. , Duponchel L. , Amram B. , Huvenne J. P. , Legrand P.
Published: May 2005

Attenuated total reflectance Fourier transform infrared spectrometry (ATR‐FTIR) has been used to determine the amount of styrene–butadiene latex on the surface of coated papers and to predict the composition of the polymer. Spectrum recording was performed on the sample in its usual form without any modification.

For quantitative analysis, partial least squares (PLS) regression, principal component regression (PCR) and multi‐linear regression (MLR) were used to calculate models for prediction. The best result is obtained with PLS.

We analysed two series of paper samples. The first analysis concerns the measurement of the quantity of latex of a constant quality on the coating surface. For 15 samples the concentration varied between 5 and 25 parts (grams per 100g of mineral pigments). We compared the predictive results at various resolutions. We obtained a relative error of 0.15 parts in latex at 4 cm−1resolution. The second analysis concerns the measurement of the styrene/butadiene ratio in various types of latex. We obtained a relative error of 0.156 parts for styrene determination and 0.161 parts for butadiene determination.
Interactive variable selection (IVS) for PLS. Part 1: Theory and algorithms
Authors: Lindgren Fredrick , Geladi Paul , Rännar Stefan , Wold Svante
Published: May 2005

A modified PLS algorithm is introduced with the goal of achieving improved prediction ability. The method, denoted IVS‐PLS, is based on dimension‐wise selective reweighting of single elements in the PLS weight vectorw. Cross‐validation, a criterion for the estimation of predictive quality, is used for guiding the selection procedure in the modelling stage. A threshold that controls the size of the selected values inwis put inside a cross‐validation loop. This loop is repeated for each dimension and the results are interpreted graphically. The manipulation ofwleads to rotation of the classical PLS solution. The results of IVS‐PLS are different from simply selectingX‐variables prior to modelling. The theory is explained and the algorithm is demonstrated for a simulated data set with 200 variables and 40 objects, representing a typical spectral calibration situation with four analytes. Improvements of up to 70% in external PRESS over the classical PLS algorithm are shown to be possible.
On the use of conditional maximization in chemometrics
Authors: Tu Xin Ming , Meng Xiao‐Li , Pagano Marcello
Published: May 2005

The purpose of this short communication is to illustrate the use of conditional maximization (CM) in chemometric applications. The CM algorithm is useful in reducing the computational complexity when a high‐dimensional and complicated maximization problem arises from fitting chemometric models. It can also be efficiently combined with the expectation‐maximization (EM) algorithm for handling incomplete data, a problem that sometimes arises when only a part of the intended data can be collected. Three models from fluorescence spectroscopy are used for illustration.
Kernel‐based PLS regression; Cross‐validation and applications to spectral data
Authors: Lindgren Fredrik , Geladi Paul , Wold Svante
Published: May 2005

Multivariate images are very large data structures and any type of regression for their analysis is very computer‐intensive. Kernel‐based partial least squares (PLS) regression, presented in an earlier paper, makes the calculation phase more rapid and less demanding in computer memory. The present paper is a direct continuation of the first paper. In this study the kernel PLS algorithm is extended to include cross‐validation for determination of the optimal model dimensionality. To show the applicability of the kernel algorithm, two examples from multivariate image analysis are used. The first example is an image from an airborne scanner of size 9 × 512 × 512. It consists of nine images which are regressed against a constructed dependent image to test the accuracy of the kernel algorithm when used on large data structures. The second example is a satellite image of size 7 × 512 × 512. Several different regression models are presented together with a comparison of their predictive capabilities. The regression models are also used as examples for showing the use of cross‐validation.
Adaptive, global, extended Kalman filters for training feedforward neural networks
Authors: Blank Thomas B. , Brown Steven D.
Published: May 2005

Finding methods for the optimization of weights in feedforward neural networks has become an ongoing developmental process in connectionist research. The current focus on finding new methods for the optimization of weights is mostly the result of the slow and unreliable convergence properties of the gradient descent optimization used in the original back‐propagation algorithm. More accurate and computationally expensive second‐order gradient methods have displaced earlier first‐order gradient optimization of the network connection weights. The global, extended Kalman filter is among the most accurate and computationally expensive of these second‐order weight optimization methods. The iterative, second‐order nature of the filter results in a large number of calculations for each sweep of the training set. This can increase the training time dramatically when training is conducted with data sets that contain large numbers of training patterns. In this paper an adaptive variant of the global, extended Kalman filter that exhibits substantially improved convergence properties is presented and discussed. The adaptive mechanism permits more rapid convergence of network training by identifying data that contain redundant information and avoiding calculations based on this redundant information.
A frequency deconvolution procedure using a conjugate gradient minimization method with suitable constraints
Authors: Bramanti Emilia , Bramanti Mauro , Stiavetti Paolo , Benedetti Enzo
Published: May 2005

In a variety of spectroscopic techniques the fundamental problem exists of determination of the individual spectral components, intrinsically overlapped in the measured spectrum. This is a typical deconvolution problem and several methods and techniques have been proposed for its solution in the technical literature, but suggestions of new approaches are still of interest. A new deconvolution procedure is presented here based on the use of the conjugate gradient minimization algorithm with the addition of sutiable constraints directly obtained by the application to the measured spectrum of the second‐derivative operator or more sophisticated resolution enhancement procedures. Since in the examined case deconvolution essentially requires the minimization of a non‐convex function, the use of such constraints is extremely important to supply suitable input parameters to the conjugate gradient algorithm to avoid obtaining minimum points which have no physical meaning. In our case each spectral compoent used for deconvolution has been assumed to have a Gaussian analytical definition fully identified by three parameters (amplitude, central frequency, spectral bandwidth), so that the input values required to start the deconvolution process are the number M of Gaussian components and 3M suitable initial approximations of the parameters above. It is shown that all this information can be obtained from the measured data. The deconvolution procedure was implemented by a FORTRAN Microsoft Version 5.1 program and experimental results relative to spectroscopic data obtained by FT‐IR analysis of human serum albumin are reported. The results are discussed and compared with data obtained by the use of other techniques.