Principal Component Analysis case studies

A first introduction to principal components analysis (PCA) has been given in Chapter 17. Here, we present the method from a more general point of view, which encompasses several variants of PCA. Basically, all these variants have in common that they produce linear combinations of the original columns in a measurement table. These linear combinations represent a kind of abstract measurements or factors that are better descriptors for structure or pattern in the data than the original measurements [1]. The former are also referred to as latent variables [2], while the latter are called manifest variables. Often one finds that a few of these abstract measurements account for a large proportion of the variation in the data. In that case one can study structure and pattern in a reduced space which is possibly two- or three-dimensional. 

Thus D is a matrix of NS spectra by NW wavelengths C is a matrix of NS times by NC concentrations S is a matrix of NC pure spectra by NW wavelengths In the worst case, C, S and the number of compounds are not known. Malinowski has extensively studied the applicability of principal components analysis (PCA) to determine the number of components in a data matrix. A basic explanation of PCA can be found in and is briefly repeated below ... 

The main goal of this chapter is to present the theoretical background of some basic chemometric methods as a tool for the assessment of surface water quality described by numerous chemical and physicochemical parameters. As a case study, long-term monitoring results from the watershed of the Struma River, Bulgaria, are used to illustrate the options offered by multivariate statistical methods such as CA, principal components analysis, principal components regression (models of source apportionment), and Kohonen s SOMs. 

The kinds of calculations described above are done for all the molecules under investigation and then all the data (combinations of 3-point pharmacophores) are stored in an X-matrix of descriptors suitable to be submitted for statistical analysis. In theory, every kind of statistical analysis and regression tool could be applied, however in this study we decided to focus on the linear regression model using principal component analysis (PCA) and partial least squares (PLS) (Fig. 4.9). PCA and PLS actually work very well in all those cases in which there are data with strongly collinear, noisy and numerous X-variables (Fig. 4.9). 

By analyzing the background information and by scrutinizing the constituents of the reaction system, it is possible to select pertinent descriptors of the system. This allows all aspects on the reaction to be taken into account prior to any experiment. Principal components analysis of the variation of the descriptors over the whole set of possible constituents of the system will reveal the principal properties. Sometimes a descriptor variable which does not contribute at all to any systematic variation over the set of compounds has been included among the descriptors. In such cases, it can reasonably be assumed that the descriptor has little relevance to the problem under study. Irrelevant descriptors are easily detected by principal components analysis. 

Moreda-Pineiro, A. Marcos, A. Fisher, A. Hill, S.J. Evaluation of the Effect of Data Pretreatment Procedures on Classical Pattern Recognition and Principal Components Analysis A Case Study for the Geographical Classification of Tea, J. Environ. Monit. 3(4), 352-360 (2001). 

Ferrer A.. Multivariate Statistical Process Control based on Principal Component Analysis (MSPC-PCA) Some Reflections and a Case Study in an Autobody Assembly Process Quality Engineering. 2007 19 311-325. 

Two studies have suggested that the IR spectra of synovial fluid specimens provide the basis to diagnose arthritis and to differentiate among its variants.A NIR study demonstrated that osteoarthritis, rheumatoid arthritis, and spondyloarthropathy could be distinguished on the basis of the synovial fluid absorption patterns in the range 2000-2400 nm.< In that case, the pool of synovial fluid spectra was subject to principal component analysis, and eight principal component scores for each spectrum were employed as the basis for linear discriminant analysis (LDA). On that basis, the optimal LDA classifier matched 105 of the 109 spectra to the correct clinical designation (see Table 7). 

Ferrer A. Multivariate statistical process control based on principal component analysis (MSPC-IYJA) some reflections and a case study in an autobody assembly process. Qual Eng 2007 19 311-25. 

In 2009, Liu et al. modelled, once again, the groups of melts previously studied by different groups, in which the influence of the anion is ignored, it being the same (bromide) in all cases. Descriptors were calculated with CODESSA, and the sole novelty of this piece of work is the use of a Projection Pursuit Regression (PPR) to derive the model, along with CODESSA built-in Heuristic Method (HM), preceded by Principal Component Analysis (PCA). The authors concluded that PPR performed better than HM... 

Principal Component Analysis as a Tool for Library Design A Case Study Investigating Natural Products, Brand-Name Drugs, Natural Product-Like Libraries, and Drug-Like Libraries... 

Although the software used was not a full-featured factor analysis program, portions of the printed output are useful in studying the spectral data set. Table VI shows some information obtainable from PCR models (large data set) with 5, 10 and 13 factors. In this case, the "factors" are principal components derived entirely from the sample data set. PLS factors are not interpretable in the same manner. 

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