Principal component analysis versus fuzzy principal component analysis A case study: the quality of danube water (1985-1996)

Principal component analysis (PCA) is a favorite tool in environmetrics for data compression and information extraction. PCA finds linear combinations of the original measurement variables that describe the significant variations in the data. However, it is well-known that PCA, as with any other multivariate statistical method, is sensitive to outliers, missing data, and poor linear correlation between variables due to poorly distributed variables. As a result data transformations have a large impact upon PCA. In this regard one of the most powerful approach to improve PCA appears to be the fuzzification of the matrix data, thus diminishing the influence of the outliers. In this paper we discuss and apply a robust fuzzy PCA algorithm (FPCA). The efficiency of the new algorithm is illustrated on a data set concerning the water quality of the Danube River for a period of 11 consecutive years. Considering, for example, a two component model, FPCA accounts for 91.7% of the total variance and PCA accounts only for 39.8%. Much more, PCA showed only a partial separation of the variables and no separation of scores (samples) onto the plane described by the first two principal components, whereas a much sharper differentiation of the variables and scores is observed when FPCA is applied.     

Using principal component analysis for the study of the retention behaviour of phenol derivatives under reversed-phase conditions

Summary The retention time of 11 ring-substituted phenol derivatives was measured on six different reversed-phase HPLC columns and the log k, theoretical plate number (N) and asymmetry factor (F) values were calculated for each solutes on each column. The similarities and dissimilarities among the columns and solutes were elucidated by principal component analysis followed with nonlinear mapping technique and cluster analysis. Calculations indicated that the retention characteristics of porous graphitized carbon stationary phase considerably deviate from those of octadecyl- and hexyl-coated silica, octadecyl-coated polystyrene-divinylbenzene polymer and polybutadiene-coated alumina. The differences among these columns were markedly smaller. The retention behaviour of aminophenols differed from those of other phenol derivatives proving the importance of molecular polarity in the retention. It was established that the mode of calculation slightly modifies the similarity and dissimilarity among the columns and solutes, therefore, the use of more than one calculation method is proposed.     

Application of a quartz crystal nanobalance and principal component analysis for the detection and determination of histidine

The aim of the present investigation was to develop a biosensor based on a quartz crystal nanobalance (QCN) for the detection of histidine (His). A thin layer of nickel was electrochemically deposited over the gold crystal electrode and exposed to H₂O₂ to form nickel oxide. The composite electrode was then used to determine His. The frequency shifts were linear with respect to the concentration of His in solution. His can be measured in the range of 100–2000 mg L⁻¹. A lower limit of detection of 48 mg L⁻¹ and a sensitivity factor of 0.0307 Hz/mg L⁻¹ was obtained. Some possible interferences were checked for, and the performance of the sensor was found to be unaffected by any interference except for those from arginine, cysteine and NaH₂PO₄. Principal component analysis (PCA) was used to process the frequency response data of the single piezoelectric crystal at various times, considering the different adsorption–desorption dynamics of His and the interfering compounds. Over 85% of the variance in the data was explained by two principal components. A score plot of the data for the first two PCs showed that the modified QCN yields favorable identification and quantification performances for His and the interfering compounds.     

Parallel co-ordinate geometry and principal component analysis for the interpretation of large multi-response experimental designs

In the evaluation of large or complex data sets the use of visualization methods can be of great benefit. In this paper, the use of parallel co-ordinate geometry (PCG) plots, principal component analysis (PCA) and N-way PCA as visualization procedures for large multi-response experimental designs was compared with the more traditional approach of calculating factor effects by multiple linear regression. PCG plots are a recent addition to the visualization tools and offer a possibility to visualize multi-dimensional data in two dimensions while no calculations are required. It was found that PCA and PCG each have their own benefits and disadvantages. Both methods can be used to some extent to select optimal conditions. Moreover, it was possible to use the PCA score plot as a Pareto optimality plot that allowed to select the experiments considered to be Pareto optimal. Therefore, the examined visualization methods can be useful and complementary aids in the interpretation of large multi-response experimental design data and they add a multivariate dimension to the more classical univariate analysis of such data.     

Use of principal component analysis for investigation of factors affecting retention behaviour of ceramides on porous graphitized carbon column

Summary The potentiality of a porous graphitized carbon stationary phase was assessed for ceramide analysis in nonaqueous reversed phase chromatography with an evaporative light scattering detection. The influence of the nature of the mobile phase was first performed under isoeluotropic isocratic conditions. Eight mobile phase compositions in the presence or absence of triethylamine/formic acid were tested with a set of structurally relevant ceramides. Values obtained under these conditions for the peak heights, retention factors, plate numbers, asymmetry factors, relative retentions and Time-Corrected Calibrated Normalised Resolution Product were analysed by Principal Component Analysis. Principal Component Analysis was effective in attributing relationships between the chromatographic behaviour and analytical conditions. The relationship between the increase of the detector response and the presence of triethylamine/formic acid has been confirmed, and the main change of selectivity has been attributed to interactions provided by the weak solvent of the mobile phase. These conclusions have allowed the development of gradient conditions for the analysis of complex ceramide mixtures on porous graphitized carbon column.     

A comparison between neural network method and semi empirical equations to predict the solubility of different compounds in supercritical carbon dioxide

Accuracy of seven semi empirical equations for the estimation of solubility of 30 different compounds in supercritical carbon dioxide has been compared with a new neural network method. To base this comparison on a fair basis, a unique set of experimental data was used for both optimization of semi empirical equations’ parameters and training, validation and testing of neural network. Results showed that neural network method with an average relative deviation of about 5.3% was more accurate than the best semi empirical equation with an average relative deviation of about 15.96% for same compounds. It was also found that the average relative deviation of semi empirical equations varies sharply among different compounds, while this quantity is less dependent on material type for neural network method.     

Application of principal component analysis to a full profile correlative analysis of FTIR spectra

We have demonstrated an informatics methodology for finding correlations between the full profile Fourier transform infrared spectra of polycrystalline 3C‐silicon carbide (poly‐SiC) films and their growth conditions, thereby developing high‐throughput structure‐process relationships. Because SiC films are a structural element in photonic sensors, this paper focuses on the interpretation of their optical response, the multivariate tracking of critical processing pathways, and the identification of controlling processing mechanisms. Using principal component analysis, we have developed a data analysis tool to aid in the assessment of the relative contributions of experimental parameters in low‐pressure chemical vapor deposition processes to optical responses on the basis of the size of eigenvalues of the spectral data set. The applied methodology for identifying spectral relationships of stoichiometry, dopant chemistry, and microstructure of poly‐SiC provides more effective guidelines to manipulate optical responses by controlling multiple experimental parameters. Copyright © 2011 John Wiley & Sons, Ltd.     

Structural and mechanical properties of alkali hydrides investigated by the first-principles calculations and principal component analysis

The structural and mechanical properties of alkali hydrides (LiH, NaH, KH, RbH, and CsH) were investigated via first-principles calculations which cover the optimized structural parameters. The density functional theory in combination with the generalized gradient approximation (GGA) were used in this study. From the present study, one could note that alkali hydrides are brittle materials and mechanically stable. It was found that stiffness and shear resistance are greater in LiH than in other hydrides. It is more brittle in nature, and comparatively harder than the other materials under study; it also presents a high degree of anisotropy. The results were then investigated and analyzed with principal component analysis (PCA), which is one of the most common techniques in multivariate analysis, was used to explore the correlations among material properties of alkali hydrides and to study their trends. The alkali hydrides obtained by the first-principles calculations were also compared with the alkaline-earth metal hydrides (BeH₂, MgH₂, CaH₂, SrH₂, and BaH₂) and discussed in this work.     

Benefits of applying combined diffuse reflectance FTIR spectroscopy and principal component analysis for the study of blue tempera historical painting

This paper explores the application of diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) to the examination of historic blue pigments and blue tempera paintings commonly found on works of art. The discussion is mainly focused on the practical benefits of using this technique joined to principal component analysis (PCA), a powerful multivariate analysis tool. Thanks to the study of several replica samples that contain either pure blue pigments (azurite, lapis lazuli and smalt), or pure binder (rabbit glue) and mixtures of each of the pigments with the binder (tempera samples), different aspects of these benefits are highlighted. Comparative results of direct spectra and multivariate analysis using transmittance-Fourier transform infrared spectroscopy (T-FTIR) are discussed throughout this study. Results showed an excellent ability of PCA on DRIFT spectra for discriminating replica samples according to differing composition. Several IR regions were tested with this aim; the fingerprint IR region exhibited the best ability for successfully clustering the samples. The presence of the binder was also discriminated. Only using this approach it was possible to completely separate all the studied replica samples. This demonstrates the potential benefits of this approach in identifying historical pigments and binders for conservation and restoration purposes in the field of Cultural Heritage.     

Multivariate calibration techniques applied to the spectrophotometric analysis of one-to-four component systems

The UV spectrophotometric analysis of a multicomponent mixture containing paracetamol, caffeine, tripelenamine and salicylamide by using multivariate calibration methods, such as principal component regression (PCR) and partial least-squares regression (PLS), was described. The calibration set was based on 47 reference samples, consisting of quaternary, ternary, binary and single-component mixtures, with the aim to develop models able to predict the concentrations of unknown samples containing as many as one-to-four components. The calibration models were optimized by an appropriate selection of the number of factors as well as wavelength ranges to be used for building up the data matrix and excluding any information about the interfering excipients included in pharmaceutics. The PCR and PLS models were compared and their predictive performance was inferred by a successful application to the assays of synthetic mixtures and pharmaceutical formulations.     

Phase equilibria of the ternary system vinyl acetate/(R,S)-1-phenylethanol/carbon dioxide at high pressure conditions

Phase equilibrium measurements, correlations and predictions are presented for the binary systems (R,S)-1-phenylethanol/CO₂ and vinyl acetate/CO₂ and for the ternary system vinyl acetate/(R,S)-1-phenylethanol/CO₂. Experiments for the ternary system were performed in the temperature range of 323–343 K and in the pressure range of 7–12 MPa, using a high pressure phase equilibrium apparatus with a high pressure visual variable volume cell. Phase compositions were determined by taking samples of each phase and analysing them by gas chromatography. Equilibrium data were correlated with the Peng–Robinson equation of state combined with the Mathias–Klotz–Prausnitz mixing rule. A good correlation of both phases behaviour was obtained with an average absolute deviation (AAD) of 6.80%. Predictions for the binary sub-systems and for the ternary system were performed using the Peng–Robinson and the Soave–Redlich–Kwong equation of state, with the predictive mixing rule MHV1.     

A principal component analysis based method to discover chemical differences in comprehensive two-dimensional gas chromatography with time-of-flight mass spectrometry (GCxGC-TOFMS) separations of metabolites in plant samples

Comprehensive two-dimensional gas chromatography combined with time-of-flight mass spectrometry (GC × GC-TOFMS) provides high resolution separations of complex samples with a mass spectrum at every point in the separation space. The large volumes of multidimensional data obtained by GC × GC-TOFMS analysis are analyzed using a principal component analysis (PCA) method described herein to quickly and objectively discover differences between complex samples. In this work, we submitted 54 chromatograms to PCA to automatically compare the metabolite profiles of three different species of plants, namely basil (Ocimum basilicum), peppermint (Mentha piperita), and sweet herb stevia (Stevia rebaudiana), where there were 18 chromatograms for each type of plant. The 54 scores of the m/z 73 data set clustered in three groups according to the three types of plants. Principal component 1 (PC 1) separated the stevia cluster from the basil and peppermint clusters, capturing 61.84% of the total variance. Principal component 2 (PC 2) separated the basil cluster from the peppermint cluster, capturing 16.78% of the total variance. The PCA method revealed that relative abundances of amino acids, carboxylic acids, and carbohydrates were responsible for differentiating the three plants. A brief list of the 16 most significant metabolites is reported. After PCA, the 54 scores of the m/z 217 data set clustered in three groups according to the three types of plants, as well, yielding highly loaded variables corresponding with chemical differences between plants that were complementary to the m/z 73 information. The PCA data mining method is applicable to all of the monitored selective mass channels, utilizing all of the collected data, to discover unknown differences in complex sample profiles.     

Application of principal component analysis to gas sensing characteristics of Cr0.8Fe0.2NbO4 thick film array

The transient changes in resistances of Cr_0.8Fe_0.2NbO₄ thick film sensors towards specified concentrations of H₂, NH₃, acetonitrile, acetone, alcohol, cyclohexane and petroleum gas at different operating temperatures were recorded. The analyte-specific characteristics such as slopes of the response and retrace curves, area under the curve and sensitivity deduced from the transient curve of the respective analyte gas have been used to construct a data matrix. Principal component analysis (PCA) was applied to this data and the score plot was obtained. Distinguishing one reducing gas from the other is demonstrated based on this approach, which otherwise is not possible by measuring relative changes in conductivity. This methodology is extended for three Cr_0.8Fe_0.2NbO₄ thick film sensor array operated at different temperatures.     

Characterization of 1,3-alternate calix[4]arene-silica bonded stationary phases and their comparison to selected commercial columns by using principal component analysis

Twelve calix[4]arene stationary phases in 1,3-alternate conformation, synthesized in the authors’ laboratory, were characterized in terms of their surface coverage, hydrophobic selectivity, aromatic selectivity, shape selectivity, hydrogen bonding capacity and ion-exchange capacity. The set of tests commonly used for evaluation of commercially available stationary phases was applied to assess fundamental chromatographic properties of the calixarene phases. The new calixarene phases were compared to each other, to Caltrex and LiChrosorb C-18 columns. Principal component analysis has been used to provide comparison between 1,3-alternate calix[4]arene phases and commercially available phenyl, fluorophenyl and fluoroalkyl columns.     

Application of unfold principal component analysis and parallel factor analysis to the exploratory analysis of olive oils by means of excitation-emission matrix fluorescence spectroscopy

Discrimination between virgin olive oils and pure olive oils is of primary importance for controlling adulterations. Here, we show the potential usefulness of two multiway methods, unfold principal component analysis (U-PCA) and parallel factor analysis (PARAFAC), for the exploratory analysis of the two types of oils. We applied both methods to the excitation-emission fluorescence matrices (EEM) of olive oils and then compared the results with the ones obtained by multivariate principal component analysis (PCA) based on a fluorescence spectrum recorded at only one excitation wavelength. For U-PCA and PARAFAC, the ranges studied were λ_ex=300-400 nm, λ_em=400-695 nm and λ_ex=300-400 nm, λ_em=400-600 nm. The first range contained chlorophylls, whose peak was much more intense than those of the rest of species. The second range did not contain the chlorophylls peak but only the fluorescence spectra of the remaining compounds (oxidation products and Vitamin E). The three-component PARAFAC model on the second range was found to be the most interpretable. With this model, we could distinguish well between the two groups of oils and we could find the underlying fluorescent spectra of three families of compounds.     

Evaluation of the predictive power of biplot axes to automate the construction and layout of biplots based on the accuracy of direct readings from common outputs of multivariate analyses: 1. application to principal component analysis

Predictive biplots, as developed by J.C. Gower and coworkers, can be a very useful tool to aid the interpretation of the outcomes of multivariate analyses. This paper covers a statistical methodology that enables the automation of the construction of predictive biplots, as well as an R function, AutoBiplots.PCA( ), which applies the methodology to principal components analysis. A case study based on the sensory analysis of coffees is used to illustrate the methodology as well as the outputs of the R function. The method relies on the definition of a variable's mean standard predictive error, mspe, as the degree of accuracy in the process of predicting the original values from the biplots, which is compared with a predefined tolerance value (T_axis) to decide if the correspondent biplot axis is drawn in the biplot. Standard predictive errors, spe, are calculated for each unit in relation to each biplot axis in each two‐dimensional plot and are compared with a predefined tolerance value (T_units) to decide which units shall be faced as outliers. The R function automates the process, enabling the user to decide on the degree of precision of the actual analysis. Besides providing a solution for the automatic production of predictive biplots, the methodology offers new insights for the interpretation of multivariate analyses outputs on the basis of a sound principle, the degree of precision of the analysis. This provides an automatic way for the selection of variables that explain latent dimensions and also helps in deciding on the number of important latent dimensions for model developments. Copyright © 2012 John Wiley & Sons, Ltd.     

Bibliometric analysis and an overview of the application of the non-precious materials for pyrolysis reaction of plastic waste

Huge plastic consumption and depletion of fossil fuels are at the top of the world's environmental and energy challenges. The scientific community has tackled these issues through different approaches. Catalytic pyrolysis of plastic wastes to valuable products has been proved as a sustainable route which fits with the circular economy aspects. The design of catalytic materials is the central factor for performing the catalytic conversion of plastic wastes. This review aims to conduct a Bibliometric analysis of the pyrolysis of plastic wastes and non-precious-based catalysts by mapping research studies over the last fifty years. The analysis was developed via VOSviewer and RStudio tools. It showed the historical progress regarding plastic waste pyrolysis to produce valuable products and chemicals worldwide. The research shows that the top five countries with the highest citations and publications in this field were Spain, China, England, the USA and India. The Journal of Analytical and Applied Pyrolysis had the most comprehensive coverage of plastic waste. The relationship between the catalyst and the mechanism of plastic waste can influence the production yield and selectivity. The research gap and underrepresented research topics were identified, and previous research studies on developing non-precious-based catalysts that were most relevant to the current topic were reviewed and discussed. The challenges and perspectives on catalyst preparation and development for material complexity were critically discussed. Challenges of previous studies and directions for future research were provided. This report might guide the reader to take a general look at plastic waste valorization by pyrolysis and easily understand the main challenges.