Experimental data modeling principal component analysis

Data handling, statistical modeling (projection of latent structures, principal components analysis), and plotting for QSAR. SIMCA-IPI for integrated process intelligence. VAX and PCs. MODDE for experimental design with multiple regression analysis and partial least squares. PCs (Windows). 

Quantitative analysis for one or more analytes through the simultaneous measurement of experimental parameters such as molecular UV or infrared absorbance at multiple wavelengths can be achieved even where clearly defined spectral bands are not discernible. Standards of known composition are used to compute and refine quantitative calibration data assuming linear or nonlinear models. Principal component regression (PCR) and partial least squares (PLS) regression are two multivariate regression techniques developed from linear regression (Topic B4) to optimize the data. 

After descriptors have been derived, CODESSA has several advanced methods for determining correlations between descriptors and the input experimental data (draining set ). These include five types of regression analysis, a principal components analysis (PCA) treatment, four different types of multivariate analysis, and a unique heuristic method (CODESSA s default approach). These methods help the user to choose significant descriptors, determine the relationships between sets of descriptors, and evaluate the statistical significance of particular models. An intuitive and powerful graphical user interface (GUI) is used for file and information management, as well as to display the results of the correlation searches. 

Principal component analysis (PCA) is frequently the method of choice to compress and visualize the structure of multivariate data [13]. The original experimental data are compressed by representing the total data variance using only a few new variables, called principal components (PCs). These PCs, which are orthogonal to each other, are ranked in a descending order of the variance they model. This means that with PCA, samples are projected onto an optimal direction in the multivariate data space explaining the largest possible variance. As mentioned earlier, the variance of a projection is not robust and the presence of outliers in the data will affect the construction of PCs. A direct way to obtain robust principal components (RPCs) is to replace the classic variance estimator with its robust counterpart. 

Two fundamentally different statistical approaches to biomarker selection are possible. With the first, experimental data can be used to construct multivariate statistical models of increasing complexity and predictive power - well-known examples are Partial Least Square Discriminant Analysis (PLS-DA) (Barker Rayens, 2003 Kemsley, 1996 Szymanska et al., 2011) or Principal Component Linear Discriminant Analysis (PC-LDA) (Smit et al., 2007 Werf et al., 2006). Inspection of the model coefficients then should point to those variables that are important for class discrimination. As an alternative, univariate statistical tests can be... 

The improvement in computer technology associated with spectroscopy has led to the expansion of quantitative infrared spectroscopy. The application of statistical methods to the analysis of experimental data is known as chemometrics [5-9]. A detailed description of this subject is beyond the scope of this present text, although several multivariate data analytical methods which are used for the analysis of FTIR spectroscopic data will be outlined here, without detailing the mathematics associated with these methods. The most conunonly used analytical methods in infrared spectroscopy are classical least-squares (CLS), inverse least-squares (ILS), partial least-squares (PLS), and principal component regression (PCR). CLS (also known as K-matrix methods) and PLS (also known as P-matrix methods) are least-squares methods involving matrix operations. These methods can be limited when very complex mixtures are investigated and factor analysis methods, such as PLS and PCR, can be more useful. The factor analysis methods use functions to model the variance in a data set. 

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