Interval principal component analysis

The difference between interval and ratio scales can be important for including or not including an intercept term in mathematical models for the correct calculation of the correlation coefficient for deciding to mean center or not in principal component analysis and for a host of other decisions in data treatment and modeling. 

Other spectrophotometric techniques have been reported for the analysis of spironolactone. Near infrared diffuse reflectance first-derivative spectroscopy was used for determination of spironolactone in pharmaceutical dosage forms [30]. Readings were taken at 15 nm intervals, and then 81 absorbance readings were imput into a computer for principal component analysis. 

In one study, the homogeneity of pharmaceutical raw materials during blending was followed by visual matching, spectral matching, or principal component analysis of the spectra after discrete time intervals. 

A single printed sensing layer was exposed to methanol, ethanol, acetone and isopropanol vapor, respectively. During the exposure, the absorbance spectrum was continually measured and split into several wavelength intervals. The spectra have been analyzed by principal component analysis and cluster analysis. Actually, it is possible to use a single sensing film to emulate sensor arrays (29). 

In this study, tablets were stored in a hydrator for up to 168 h with tablets withdrawn at regular intervals. After removal from the hydrator, the tablets were weighed and NIR spectra collected prior to the HPLC analysis. Spectra of the intact tablets were collected on an InfraAlyzer 500 in the 1100 to 2500 nm region, using the double-reflecting sample apparatus described by Lodder and Hieftje [82]. The spectra were processed by principal component analysis, and the scores analyzed by the quantile-BEAST algorithm. 

Frequently the efforts are hampered by the lack of a sufficiently large number of samples. In our experience, it appears to be helpful if the number of samples exceeds the number of parameters (wavenumber intervals, principal components, latent variables, etc.) by at least a factor of five. This finding is supported by calculating this ratio between the number of teaching samples and the number of parameters both in the field of diagnostic pattern recognition (see the column ratio in Table 6.2) as well as in the quantitative analysis of serum. 

For a 3D-QSAR autocorrelation matrix, the distances are calculated from the 3D structures of the molecules. Both points on a CoMFA-like lattice and points on the molecular surface have been used for these distance calcula-tions.2 7 208 Similarly, the 3D autocorrelation properties are based on properties at these points (e.g., electrostatic or hydrophobic potential). Wagener et al. used a point density of 10 points/A on the van der Waals surface for the property calculation for the autocorrelation matrix, they considered distances from 1 to 13 A and a distance interval of 1 A to produce an autocorrelation vector of length 12.2° These 12 properties were then analyzed by principal components analysis, a Kohonen map, and a feed-forward multilayer neural... 

FIGU RE 11.9 Principal component analysis score plots from IM-MS data collected in positive and negative mode for rat lymph samples collected in hourly intervals before and after feeding. (Reprinted from Kaplan, K Dwivedi, P. Davidson, S. Yang, Q. Tso, P. Siems, W. Hill, H. H. Jr. Anal. Chem. 2009, 81, 7944-7953. Copyright 2009, American Chemical... 

As can be seen, there is a peak at = 4, meaning that there is an estimated time lag between process input and process output of 4 sampling intervals. The process output should then be shifted four sampling intervis backward in time to make a static principal component analysis meaningful. 

One study has reported 500 and 600 MHz H NMR data on the post mortem CSF from Alzheimer s disease (AD) patients and controls. The main differences between the spectra of the two groups were found to be in the region <52.4-2.9, and principal components analysis showed that separation of the two groups was possible based mainly on lower citrate levels in the AD patients. Non-matching in patient age and the time interval between death and autopsy caused a reduction in the inter-group differences but they were still significant p < 0.05). 

Figure 7. Near-infrared spectral variation in surface sediments of Stor-Skdrtrdsket. The figure shows the spectral variance in the first principal component from a PCA-analysis based on 165 surface sediment samples. The bottom topography is presented as depth curves with a 2-m interval. Modified from Korsman et al. (1999).

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