Multivariate statistical analysis of coastal sediment data

Multivariate statistical analysis of sediment data (information matrix 123 × 16) from the Gulf of Mexico, USA shows that the data structure is defined by four latent factors conditionally called “inorganic natural”, “inorganic anthropogenic”, “bioorganic” and “organic anthropogenic” explaining 39.24%, 23.17%, 10.77% and 10.67% of the total variance of the data system, respectively. The receptor model obtained by the application of the PCR approach makes it possible to apportion the contribution of each chemical component for the latent factor formation. A separation of the contribution of each chemical parameter is achieved within the frames of “natural” and “anthropogenic” origin of the respective heavy metal or organic matter to the sediment formation process. This is a new approach as compared to the traditional “one dimensional” search with a limited number of preliminary selected tracer components. The model suggested divides natural from anthropogenic influences and allows in this way each participant in the sediment formation process to be used as marker of either natural or anthropogenic effects. Received: 20 March 1999 / Revised: 1 June 1999 / Accepted: 3 June 1999     

Multivariate statistical interpretation of coastal sediment monitoring data

Multivariate statistical analysis of sediment data (input matrix 122 x 15) collected from 122 sampling sites from the western coastline of the USA and analyzed for 15 analytes indicates that the data structure could be explained by four latent factors. These factors are conditionally named "anthropogenic", "organic", "natural", and "hot spots". They explain over 85% of the total variance of the data system, which is an acceptable value for the PCA model. The receptor models obtained after regression of the mass on the absolute principal components scores ensures reliable estimation of the contribution of each possible natural or anthropogenic source to the mass of each chemical component. It can be concluded that the region of interest reveals a different pattern of pollution compared with the eastern coastline treated statistically in a previous study.     

Multivariate statistical interpretation of coastal sediment monitoring data

Multivariate statistical analysis of sediment data (input matrix 122 × 15) collected from 122 sampling sites from the western coastline of the USA and analyzed for 15 analytes indicates that the data structure could be explained by four latent factors. These factors are conditionally named “anthropogenic”, “organic”, “natural”, and “hot spots”. They explain over 85% of the total variance of the data system, which is an acceptable value for the PCA model. The receptor models obtained after regression of the mass on the absolute principal components scores ensures reliable estimation of the contribution of each possible natural or anthropogenic source to the mass of each chemical component. It can be concluded that the region of interest reveals a different pattern of pollution compared with the eastern coastline treated statistically in a previous study.     

An advanced multivariate statistical approach to study coastal sediment data

The present paper deals with the application of classical and fuzzy principal components analysis to a large data set from coastal sediment analysis. Altogether 126 sampling sites from the Atlantic Coast of the USA are considered and at each site 16 chemical parameters are measured. It is found that four latent factors are responsible for the data structure (“natural”, “anthropogenic”, “bioorganic”, and “organic anthropogenic”). Additionally, estimating the scatter plots for factor scores revealed the similarity between the sampling sites. Geographical and urban factors are found to contribute to the sediment chemical composition. It is shown that the use of fuzzy PCA helps for better data interpretation especially in case of outliers.     

Multivariate statistical analysis of a multi-step industrial processes

Monitoring and quality control of industrial processes often produce information on how the data have been obtained. In batch processes, for instance, the process is carried out in stages; some process or control parameters are set at each stage. However, the obtained data might not be utilized efficiently, even if this information may reveal significant knowledge about process dynamics or ongoing phenomena. When studying the process data, it may be important to analyse the data in the light of the physical or time-wise development of each process step. In this paper, a unified approach to analyse multivariate multi-step processes, where results from each step are used to evaluate future results, is presented. The methods presented are based on Priority PLS Regression. The basic idea is to compute the weights in the regression analysis for given steps, but adjust all data by the resulting score vectors. This approach will show how the process develops from a data point of view. The procedure is illustrated on a relatively simple industrial batch process, but it is also applicable in a general context, where knowledge about the variables is available.     

Multivariate statistical analysis of non‐mass‐selected ToF‐SIMS data

Cluster LMIGs are now regarded as the standard primary ion guns on time‐of‐flight secondary ion mass spectrometers (ToF‐SIMS). The ToF‐SIMS analyst typically selects a bombarding species (cluster size and charge) to be used for material analysis. Using standard data collection protocols where the analyst uses only a single primary bombarding species, only a fraction of the ion‐beam current generated by the LMIG is used. In this work, we demonstrate for the first time that it is possible to perform ToF‐SIMS analysis when all of the primary ion intensity (clusters) are used; we refer to this new data analysis mode as non‐mass‐selected (NMS) analysis. Since each of the bombarding species has a different mass‐to‐charge ratio, they strike the sample at different times, and as a result, each of the bombarding species generates a spectrum. The resulting NMS ToF‐SIMS spectrum contains contributions from each of the bombarding species that are shifted in time. NMS spectra are incredibly complicated and would be difficult, if not impossible, to analyze using univariate methodology. We will demonstrate that automated multivariate statistical analysis (MVSA) tools are capable of rapidly converting the complicated NMS data sets into a handful of chemical components (represented by both spectra and images) that are easier to interpret since each component spectrum represents a unique and simpler chemistry. Copyright © 2008 John Wiley & Sons, Ltd.     

Multivariate analysis of time-resolved mass spectral data

Multvariate analysis of time-resolved pyrolysis/mass spectrometric data is described. The approach is based on the variance diagram (VARDIA), a recently developed technique that quantifies the clustering of variables in two-dimensional factor analysis (sub)-spaces in a rotational scanning procedure. A maximum in the VARDIA plot indicates a correlated behavior of the mass variables, indicating a common origin. This common origin is generally caused by a change in the concentration of a chemical component. With this information the “factor spectrum” and the scores of the component can be retrieved. For time-resolved serial data, consideration of the clustering behavior of the variables as a function of time is more appropriate than a rotational scanning procedure. Adaptation of the VARDIA for serial data, such as time-resolved data, is described. This approach has the advantage that all the factors can be used. It will be shown that the resolution of the obtained curve than the total ion current curve as a function of time. Examples will be given for time-resolved data of coal, rubber and wood samples.     

Multivariate statistical analysis of aerosol immission data — An exemplary investigation on the North Frisian island of Pellworm

Element concentrations of 23 elements in different particle size fractions of aerosol samples from the island of Pellworm in the German Bight were analyzed by the help of total reflection X-ray fluorescence analysis. These immission data were investigated with multivariate statistical methods. Multivariate correlation analysis, as a newer chemometric method, demonstrates the autocorrelation of the immission state for different particle size fractions of dustlike aerosols. The immission of smaller particles is more strongly autocorrelated than that of larger particles. The factor analysis of each particle size fraction allows the extraction of two pollution factors for each fraction. The weights of these factors, anthropogenic and sea spray, change with size. The anthropogenic factor is more highly weighed for smaller particles, the sea spray factor is stronger in larger particles. The dependence of factor scores for smaller particles on wind direction indicates the sources of the extracted factors.     

Multivariate exploratory data analysis in chemical industry

Sizeable data bases are now being routinely generated in a variety of contexts in chemical industry. Statistical investigations of such data bases are aimed both at initially uncovering structure and eventually proposing models, in particular for predicting product quality by the mix or characteristics of the chemical compounds. Online Multivariate Exploratory Graphical Analysis (OMEGA) stands for a structured exploratory study of the relationships in a multivariate data set, where, rather than testing for one specific property, as many clues as possible for interesting structures are searched for by different dimension reductions and succeeding interactive graphical analyses. The stability of the projections obtained by the different dimension reduction methods is assessed by simulation producing graphical displays particularly supporting the identification of influential points. The variation of the predictions obtained by the different dimension reduction methods is assessed by cross-validation delivering misclassification rates or cross-validated R² values. The interpretation of the new coordinates corresponding to dimension reduction is supported by loading simplifications and graphical displays for judging its adequacy. The OMEGA strategy has been found to be an effective tool for routine searching for structure.     

Multivariate data analysis for x-ray fluorescence spectrometry

A multivariate data analysis procedure that uses singular value decomposition and the Ho-Kashyap algorithm is proposed to obtain calibration constants for x-ray fluorescence spectrometry. These calibration constants can be used to obtain results from experimental data by means of a simple dot product calculation. The method was tested on experimental data from the literature. Comparison of results showed that the method performs at least as well or better than the Rasberry-Heinrich method or its modifications. The method can be used to express calibration results obtained with a theoretically based program in such a way that they can be used conveniently in routine applications.     

Multivariate statistical treatment of PIXE analysis of some traditional Chinese medicines

Elements in two kinds of 30 traditional Chinese medicines were analyzed by PIXE method, and the data were treated by multivariate statistical methods. The results show that these two kinds of traditional Chinese medicines are almost separable according to their elemental contents. The results are congruous with the traditional Chinese medicine practice.     

Multivariate data analysis of some Finnish water courses

Summary The following parameters were analyzed 2 to 4 times a year from 37 sampling sites; T, O₂, O₂%, Turbidity, Suspended solids, Conductivity, Alkalinity, pH, Color, COD_Mn, Total nitrogen, Total phosphorus, Cl, Fe, Mn, Total sulphur, K, Na, Ca, Mg, SiO₂, Total organic chlorine and Total organic bromine. Samples were taken from waters loaded by chemical pulp mills, other industries, municipal waste waters and agriculture. Also waters under natural conditions were included. Water samples have been collected and analyzed in co-operation with the National Board of Waters and the Environment. The data set was analyzed by Principal Component Analysis (PCA) to determine correlations between variables, especially between Total organic chlorine and Total organic bromine and others. Typically Total organic chlorine and Total organic bromine correlated with Na, Cl and Total sulphur. It is interesting to note that Total organic chlorine and Total organic bromine did not follow each other in all components. Total organic chlorine was predicted using other variables and Partial Least Squares (PLS) method. Very satisfactory correlation was obtained between analyzed and predicted lgTOCl values. Optimally three different object classes were found from the whole data using fuzzy clustering analysis. One class represents waters in a natural condition, one water loaded mainly by agriculture and one represent the rest of the waters.     

Multivariate statistical assessment of polluted soils

This study deals with the application of several multivariate statistical methods (cluster analysis, principal components analysis, multiple regression on absolute principal components scores) for assessment of soil pollution by heavy metals. The sampling was performed in a heavily polluted region and the chemometric analysis revealed four latent factors, which describe 84.5 % of the total variance of the system, responsible for the data structure. These factors, whose identity was proved also by cluster analysis, were conditionally named “ore specific”, “metal industrial”, “cement industrial”, and “steel production” factors. Further, the contribution of each identified factor to the total pollution of the soil by each metal pollutant in consideration was determined.     

Multivariate data analysis of quality parameters in drinking water

The quality of water destined for human consumption has been treated as a multivariate property. Since most of the quality parameters are obtained by applying analytical methods, the routine analytical laboratory (responsible for the accuracy of analytical data) has been treated as a process system for water quality estimation. Multivariate tools, based on principal component analysis (PCA) and partial least squares (PLS) regression, are used in the present paper to: (i) study the main factors of the latent data structure and (ii) characterize the water samples and the analytical methods in terms of multivariate quality control (MQC). Such tools could warn of both possible health risks related to anomalous sample composition and failures in the analytical methods.     

Multivariate calibration of spectral data using dual-domain regression analysis

To date, few efforts have been made to take simultaneous advantage of the local nature of spectral data in both the time and frequency domains in a single regression model. We describe here the use of a novel chemometrics algorithm using the wavelet transform. We call the algorithm dual-domain regression, as the regression step defines a weighted model in the time-domain based on the contributions of parallel, frequency-domain models made from wavelet coefficients reflecting different scales. In principle, any regression method can be used, and implementation of the algorithm using partial least squares regression and principal component regression are reported here. The performance of the models produced from the algorithm is generally superior to that of regular partial least squares (PLS) or principal component regression (PCR) models applied to data restricted to a single domain. Dual-domain PLS and PCR algorithms are applied to near infrared (NIR) spectral datasets of Cargill corn samples and sets of spectra collected on batch chemical reactions run in different reactors to illustrate the improved robustness of the modeling.     

Multivariate 3-way data analysis of amino acid patterns of lakes

Time dependent patterns of amino acid concentrations have been studied by HPLC for different lakes of the Berlin area. Data analysis has been performed by conventional principal component analysis as well as by its more recent N-way extension. It turns out that lakes mainly differ by their general amino acid production as a function of time and season. Apart from this, in a single case there occurs a specific pattern which might be related to an exterior influence. This pattern, although clearly detected, has been not stable over time. Measurements are reproducible with respect to time (comparison of two succeeding years) and to position (comparison of isolated parts of a lake).Dedicated to Professor Dr. K. Doerffel at his 70th birthday with respect to his fundamental contributions to chemometrics     

Multivariate analysis of chromatographic retention data and lipophilicity of phenylacetamide derivatives

One of the most important physicochemical parameters of a molecule that determines its bioactivity is its lipophilicity. Cluster analysis (CA), principal component analysis (PCA), and sum of ranking differences (SRD) were used to compare the lipophilic parameters of twenty phenylacetamide derivatives, obtained experimentally as chromatographic retention data in the presence of different solvents and calculated by different mathematical methods. All the applied methods of multivariate analysis gave approximately similar grouping of the studied lipophilic parameters. In the attempt to group the investigated compounds in respect of their lipophilicity, the obtained results appeared to be dependent on the applied chemometric method. The CA and PCA, grouped the compounds on the basis of the nature of the substituents R₁ and R₂, indicating that they determine to a great extent the lipophilicity of the investigated molecules. Unlike them, the SRD method could not be used to group the studied compounds on the basis of their lipophilic character.     

Multivariate data analysis for Raman imaging of a model pharmaceutical tablet

Spectroscopic imaging techniques provide spatial and spectral information about a sample simultaneously and are finding ever-increasing application in the pharmaceutical industry. Effective extraction of chemical information from imaging data sets is a crucial step during the application of imaging techniques. Multivariate imaging data analysis methods have been reported but few applications of these methods for pharmaceutical samples have been demonstrated. In this study, a bilayer model tablet consisting of avicel, lactose, sodium benzoate, magnesium stearate and red dye was prepared using custom press tooling, and Raman mapping data were collected from a 400 μm × 400 μm area of the tablet surface. Several representative multivariate methods were selected and used in the analysis of the data. Multivariate data analysis methods investigated include principal component analysis (PCA), cluster analysis, direct classical least squares (DCLS) and multivariate curve resolution (MCR). The relative merits and drawbacks of each technique for this application were evaluated. In addition, some practical issues associated with the use of these methods were addressed including data preprocessing, determination of the optimal number of clusters in cluster analysis and the optimization of window size in second derivative calculation.