MATLAB principal components

Note the Scores matrix is referred to as the T matrix in principal components analysis terminology. Let us look at what we have completed so far by showing the SVD calculations in MATLAB as illustrated in Table 22-1. 

MATLAB Example 4.2 program to perform principal component... 

The SVD is generally accepted to be the most numerically accurate and stable technique for calculating the principal components of a data matrix. MATLAB has an implementation of the SVD that gives the singular values and the row and column eigenvectors sorted in order from largest to smallest. Its use is shown in Example 4.3. We will use the SVD from now on whenever we need to compute a principal component model of a data set. 

MATLAB Example 4.3 Principal component analysis using the SVD... 

Perform PCA (principal components analysis) on these data and retain the first three loadings (methods for performing PCA are discussed in Chapter 4, Section 4.3 see also Appendix A.2.1 and relevant sections of Appendices A.4 and A.5 if you are using Excel or Matlab). 

Matlab was used to perform Principal Components Analysis (PCA) according to the NIPALS algorithm [75], so that exploratory data analysis could be conducted. PCA is a... 

PLS (Partial Least Squares) regression was used for quantification and classification of aristeromycin and neplanocin A (Figure 4). Matlab was used for PCA (Principal Components Analysis) (according to the NIPALS algorithm) to identify correlations amongst the variables from the 882 wavenumbers and reduce the number of inputs for Discriminant Function Analysis (DFA) (first 15 PCA scores used) (Figure 5). 

In chemometrics, PCR and PLS seem to be the most widely used method for building a calibration model. Recently, we developed a method, called elastic component regression (ECR), which utilizes a tuning parameter a [0,l] to supervise the decomposition of X-matrix [36], which falls into the category of continuum regression [37-40]. It is demonstrated theoretically that the elastic component resulting from ECR coincides with principal components of PC A when a = 0 and also coincides with PLS components when a = 1. In this context, PCR and PLS occupy the two ends of ECR and a (0,l) will lead to an infinite number of transitional models which collectively uncover the model path from PCR to PLS. The source codes implementing ECR in MATLAB are freely available at [41]. In this section, we would like to compare the predictive performance of PCR, PLS and an ECR model with a = 0.5. 

Data generated with the EOS are elaborated by Exploratory Data Analysis (EDA) software, a written-in-house software package based on MATLAB [22]. The EDA software includes the usual (univariate or multivariate) descriptive statistics functions among which Principal Component Analysis (PCA) [23], with the additional utilities for easy data manipulation (e.g. data sub sampling, data set fusion) and plots customization. 

In the statistical analysis toolbox of MATLAB, functions princomp and pcacov enable the computation of principal components. The same method can be extended to detecting a finite number M of known signals. For further information on M-aiy detection, the reader is referred to Ref. 29. 

The PLS toolbox by Eigenvector Research (2004) is a veiy useful tool to perform a principal component analysis. When the toolbox is installed under Matlab, it can be called by typing pea. The following graphical user interface appears ... 

For the principal components analysis (PCA) and partial least squares regression (PLS) in Chapters 22 and 23, this book makes use of a PLS Toolbox, which is a product of Eigenvector Research, Inc. The PLS Toolbox is a collection of essential and advanced chemometric routines that work within the MATLAB conmutational environment. We are grateful to Eigenvector for permission. For Eigenvector product information please contact ... 

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