Chemometrical principal component

Key Words 2D-QSAR traditional QSAR 3D-QSAR nD-QSAR 4D-QSAR receptor-independent QSAR receptor-dependent QSAR high throughput screening alignment conformation chemometrics principal components analysis partial least squares artificial neural networks support vector machines Binary-QSAR selecting QSAR descriptors. 

As used in chemometrics, principal components arc orthogonal (perpendicular) to each other. 

To gain insight into chemometric methods such as correlation analysis, Multiple Linear Regression Analysis, Principal Component Analysis, Principal Component Regression, and Partial Least Squares regression/Projection to Latent Structures... 

Other chemometrics methods to improve caUbration have been advanced. The method of partial least squares has been usehil in multicomponent cahbration (48—51). In this approach the concentrations are related to latent variables in the block of observed instmment responses. Thus PLS regression can solve the colinearity problem and provide all of the advantages discussed earlier. Principal components analysis coupled with multiple regression, often called Principal Component Regression (PCR), is another cahbration approach that has been compared and contrasted to PLS (52—54). Cahbration problems can also be approached using the Kalman filter as discussed (43). 

Because of peak overlappings in the first- and second-derivative spectra, conventional spectrophotometry cannot be applied satisfactorily for quantitative analysis, and the interpretation cannot be resolved by the zero-crossing technique. A chemometric approach improves precision and predictability, e.g., by the application of classical least sqnares (CLS), principal component regression (PCR), partial least squares (PLS), and iterative target transformation factor analysis (ITTFA), appropriate interpretations were found from the direct and first- and second-derivative absorption spectra. When five colorant combinations of sixteen mixtures of colorants from commercial food products were evaluated, the results were compared by the application of different chemometric approaches. The ITTFA analysis offered better precision than CLS, PCR, and PLS, and calibrations based on first-derivative data provided some advantages for all four methods. ... 

Principal Component Analysis (PCA). Principal component analysis is an extremely important method within the area of chemometrics. By this type of mathematical treatment one finds the main variation in a multidimensional data set by creating new linear combinations of the raw data (e.g. spectral variables) [4]. The method is superior when dealing with highly collinear variables as is the case in most spectroscopic techniques two neighbor wavelengths show almost the same variation. 

J.M. Deane, Data reduction using principal components analysis. In Multivariate Pattern Recognition in Chemometrics, R. Brereton (Ed.). Chapter 5, Elsevier, Amsterdam, 1992, pp. 125-165. 

PLS has been introduced in the chemometrics literature as an algorithm with the claim that it finds simultaneously important and related components of X and of Y. Hence the alternative explanation of the acronym PLS Projection to Latent Structure. The PLS factors can loosely be seen as modified principal components. The deviation from the PCA factors is needed to improve the correlation at the cost of some decrease in the variance of the factors. The PLS algorithm effectively mixes two PCA computations, one for X and one for Y, using the NIPALS algorithm. It is assumed that X and Y have been column-centred as usual. The basic NIPALS algorithm can best be demonstrated as an easy way to calculate the singular vectors of a matrix, viz. via the simple iterative sequence (see Section 31.4.1) ... 

J.M. Sutter, J.H. Kalivas and P.M. Lang, Which principal components to utilize for principal component regression. J. Chemometr., 6 (1992) 217-225. 

E. Vigneau, D. Bertrand and E.M. Qannari, Application of latent root regression for calibration in near-infrared spectroscopy. Comparison with principal component regression and partial least squares. Chemometr. Intell. Lab. Syst., 35 (1996) 231-238. 

Multivariate chemometric techniques have subsequently broadened the arsenal of tools that can be applied in QSAR. These include, among others. Multivariate ANOVA [9], Simplex optimization (Section 26.2.2), cluster analysis (Chapter 30) and various factor analytic methods such as principal components analysis (Chapter 31), discriminant analysis (Section 33.2.2) and canonical correlation analysis (Section 35.3). An advantage of multivariate methods is that they can be applied in... 

While principal components models are used mostly in an unsupervised or exploratory mode, models based on canonical variates are often applied in a supervisory way for the prediction of biological activities from chemical, physicochemical or other biological parameters. In this section we discuss briefly the methods of linear discriminant analysis (LDA) and canonical correlation analysis (CCA). Although there has been an early awareness of these methods in QSAR [7,50], they have not been widely accepted. More recently they have been superseded by the successful introduction of partial least squares analysis (PLS) in QSAR. Nevertheless, the early pattern recognition techniques have prepared the minds for the introduction of modem chemometric approaches. 

Wold, S., Esbensen, K., and Geladi, P., Principal component analysis, Chemometrics and Intelligent Laboratory Systems 2, 37-52 (1987a). 

Wold, S., Geladi, P., and Ohman, J., Multi-way principal components and PLS analysis, J. Chemometrics 1, 41-56 (1987b). 

A simple protocol was used to build the compounds compounds were modeled with the corresponding net charges, after which 2D-3D structure conversion was carried out using the program Concord [21]. The 3D dataset obtained was submitted to the VolSurf program, and principal component analysis (PCA) was applied for chemometric interpretation. No metabolic stability information was applied to the model. 

To highlight and explain the quantitative chemical differences between the pitches found in the two archaeological sites, a chemometric evaluation of the GC/MS data (normalized peak areas) by means of principal component analysis (PCA) was performed. The PCA scatter plot of the first two principal components (Figure 8.6) highlights that the samples from Pisa and Fayum are almost completely separated into two clusters and that samples from Fayum form a relatively compact cluster, while the Pisa samples are... 

Chapters 3 6 deal with direct mass spectrometric analysis highlighting the suitability of the various techniques in identifying organic materials using only a few micrograms of samples. Due to the intrinsic variability of artefacts produced in different places with more or less specific raw materials and technologies, complex spectra are acquired. Examples of chemometric methods such as principal components analysis (PCA) are thus discussed to extract spectral information for identifying materials. 

Keywords Chemometrics, Contamination sources, Ebro River, Multivariate curve resolution, Principal component analysis... 

Nowadays, generating huge amounts of data is relatively simple. That means Data Reduction and Interpretation using multivariate statistical tools (chemometrics), such as pattern recognition, factor analysis, and principal components analysis, can be critically important to extracting useful information from the data. These subjects have been introduced in Chapters 5 and 6. 

Principal Component Regression, PCR, and Partial Least Squares, PLS, are the most widely known and applied chemometrics methods. This is particularly the case for PLS, for which there is a tremendous number of applications and a never-ending stream of proposed improvements. The details of these latest modifications are not within the scope of this book and we concentrate on the essential, classical aspects. 

While the results of the work performed by Vaidyanathan et al.44 are scientifically useful, the thorough treatment the authors give to chemometrics is excellent. There is a detailed description of principal components (PCA) with a number of pictures of loadings to help explain the process. Using PC scores, three-dimensional representations of the samples are shown. This is a good paper for someone just beginning to use chemometrics. 

Determined from principal component analysis and other chemometric techniques. 

It was mentioned earlier that PCA is a useful method for compressing the information contained in a large number of x variables into a smaller number of orthogonal principal components that explain most of the variance in the x data. This particular compression method was considered to be one of the foundations of chemometrics, because many commonly used chemometric tools are also focused on explaining variance and dealing with colinearity. However, there are other compression methods that operate quite differently than PCA, and these can be useful as both compression methods and preprocessing methods. 

One chemometric method used to monitor mixing involves comparing the spectrum for the unknown sample with that for one assumed to be homogeneous via the so-called conformity index , which is calculated by projecting the spectrum for the unknown sample onto the wavelength space of the spectrum or mean of spectra for the homogeneous sample. This procedure is similar to that involving the calculation of distances in a principal component space. 

Chemometrics, as defined by Kowalski (1), includes the application of multivariate statistical methods to the study of chemical problems. SIMCA (Soft Independent Method of Class Analogy) and other multivariate statistical methods have been used as tools in chemometric investigations. SIMCA, based on principal components, is a multivariate chemometric method that has been applied to a variety of chemical problems of varying complexity. The SIMCA-3B program is suitable for use with 8- and 16-bit microcomputers. 

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