Principal component analysis methodology

They can be used directly in protein families in order to perform selectivity analysis based on consensus principal component analysis methodology. This technique helps to identify regions in the protein space that are selective for one enzyme. The selective region may describe the selective pattern of the target proteins. Moreover, this information can be used to compare different models of the same enzyme. 

Since SOMs are capable of projecting compound distributions in high-dimensional descriptor spaces on two-dimensional arrays of nodes, this methodology is also useful as a dimension reduction technique, similar to others discussed above. SOM projections and the relationships they establish are usually non-linear, in contrast to, for example, principal component analysis (that, as discussed, generates a smaller number of new composite descriptors as linear combinations of the original ones). 

The advent of personal computers greatly facilitated the application of spectroscopic methods for both quantitative and qualitative analysis. It is no longer necessary to be a spectroscopic expert to use the methods for chemical analyses. Presently, the methodologies are easy and fast and take advantage of all or most of the spectral data. In order to understand the basis for most of the current processing methods, we will address two important techniques principal component analysis (PCA) and partial least squares (PLS). When used for quantitative analysis, PCA is referred to as principal component regression (PCR). We will discuss the two general techniques of PCR and PLS separately, but we also will show the relationship between the two. 

The power of principal components analysis is in providing a mathematical transformation of our analytical data to a form with reduced dimensionality. From the results, the similarity and difference between objects and samples can often be better assessed and this makes the technique of prime importance in chemometrics. Having introduced the methodology and basics here, future chapters will consider the use of the technique as a data preprocessing tool. 

R Srinivasan, C. Wang, WK Ho, and KW Lim. Dynamic principal component analysis based methodology for clustering process states in agile chemical plants. Ind. Engg. Chem. Research, 43 2123-2139, 2004. 

Katritzky, A.R., Fara, D.C., Kuanar, M., Hur, E. and Karelson, M. (2005) The classification of solvents by combining classical QSPR methodology with principal component analysis. J. Phys. Chem. A, 109, 10323-10341. 

Then the next step consists on application of multivariate statistical methods to find key features involving molecules, descriptors and anticancer activity. The methods include principal component analysis (PCA), hiererchical cluster analysis (HCA), K-nearest neighbor method (KNN), soft independent modeling of class analogy method (SIMCA) and stepwise discriminant analysis (SDA). The analyses were performed on a data matrix with dimension 25 lines (molecules) x 1700 columns (descriptors), not shown for convenience. For a further study of the methodology apphed there are standard books available such as (Varmuza FUzmoser, 2009) and (Manly, 2004). 

Chapter 4 retrieves the basic ideas of classical univariate calibration as the standpoint from which the natural and intuitive extension of multiple linear regression (MLR), arises. Unfortunately, this generalization is not suited to many laboratory tasks and, therefore, the problems associated with its use are explained in some detail. Such problems justify the use of other more advanced techniques. The explanation of what the multivariate space looks like and how principal components analysis can tackle it is the next step forward. This constitutes the root of the regression methodology presented in the following chapter. 

Experimental designs and principal components analysis were combined to study systematic errors in each stage of the methodologies. 

In order to assess the chromatographic properties of various stationary phases, a number of parameters must be measured. In our favored approach, which uses a modified Tanaka methodology [1], six chromatographic parameters are evaluated (see Table 1). In our latest publication, in which we report the characteri2ation of 135 different RP materials, this equates to 810 values, which have to be compared [2]. In order to simplify the evaluation of this, and other, large chromatographic databases, the chemometrical tool of Principal Component Analysis (PCA) has been successfiJly employed [3—10]. 

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