Chemometrical principal component analysis

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. 

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). 

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. 

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... 

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

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. 

Determined from principal component analysis and other chemometric techniques. 

One of the keys to multivariate analysis is the ability to reduce the dimensionality of the data so that it can be displayed in two, three or four (time-dependent) dimensional displays. The primary tool for achieving this, principal component analysis (PCA) [158], is the cornerstone of chemometrics as it accomplishes several things ... 

The simplest and most widely used chemometric technique is Principal Component Analysis (PCA). Its objective is to accomplish orthogonal projection and in that process identify the minimum number of sensors yielding the maximum amount of information. It removes redundancies from the data and therefore can be called a true data reduction tool. In the PCA terminology, the eigenvectors have the meaning of Principal Components (PC) and the most influential values of the principal component are called primary components. Another term is the loading of a variable i with respect to a PQ. 

Spectral data are highly redundant (many vibrational modes of the same molecules) and sparse (large spectral segments with no informative features). Hence, before a full-scale chemometric treatment of the data is undertaken, it is very instructive to understand the structure and variance in recorded spectra. Hence, eigenvector-based analyses of spectra are common and a primary technique is principal components analysis (PC A). PC A is a linear transformation of the data into a new coordinate system (axes) such that the largest variance lies on the first axis and decreases thereafter for each successive axis. PCA can also be considered to be a view of the data set with an aim to explain all deviations from an average spectral property. Data are typically mean centered prior to the transformation and the mean spectrum is used a base comparator. The transformation to a new coordinate set is performed via matrix multiplication as... 

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