Principal component analysis biplots

Figure 16.2 Principal component analysis biplot using the total cuticular mixtures of Smeringerus mesaensis, summer adult males (10 HaM) and females (10 HaF) with peaks projection (pi to 83) involved in sex-differrention.

Figure 6,7 Principal component analysis biplot of the mean scores and loadings (numbers represent m/z values) for PTR-MS data extracted from sea urchin roe taken from northern (N) and southern (S) locations in New Zealand. Reproduced from [91] with permission from Elsevier.

K. R. Gabriel, The biplot graphic display of matrices with applications to principal components analysis. Biometrika, 58 (1971) 453-467. 

A compromise was developed by Gabriel in 1971 and called the biplot [Gabriel 1971], This is also described by Jackson [1991] and Brereton [1992], It is useful to start with the simple case of two-way analysis. Principal component analysis of X is given as a singular value decomposition. A model with two principal components is (see Chapter 3) ... 

Figure 4 Principal components analysis (PCA) biplot of Fourier transform infrared (FTIR) data from lactose-lysine (3 1 mixture) heated from 30°C to 140°C. Principal components PCI and PC2 account for 74% and 26% of the variation, respectively.

FIGURE 24 Principal component analysis of data sets. (A) GCbreadProcess biplot of PCI versus PC2, (B) NIRbreadProcess scores plot of PC2 versus PCS and (C) NIRbreadProcess loadings plot of PC2 and PCS. The six process steps monitored are coded as follows empty circles, SO empty squares, S2 empty diamonds, S4 filled circles, D filled squares, T filled diamonds, L. 

Gabriel KR. The biplot graphic display with application to principal component analysis. Biometrika 1971 58 453-67. 

For a detailed description of spectral map analysis (SMA), the reader is referred to Section 31.3.5. The method has been designed specifically for the study of drug-receptor interactions [37,44]. The interpretation of the resulting spectral map is different from that of the usual principal components biplot. The former is symmetric with respect to rows and columns, while the latter is not. In particular, the spectral map displays interactions between compounds and receptors. It shows which compounds are most specific for which receptors (or tests) and vice versa. This property will be illustrated by means of an analysis of data reporting on the binding affinities of various opioid analgesics to various opioid receptors [45,46]. In contrast with the previous approach, this application is not based on extra-thermodynamic properties, but is derived entirely from biological activity spectra. 

Analysis of the original 29 Wari samples revealed three easily distinguishable chemical groupings, labeled Wari I, 2, and 3, with two samples identified as outliers (labeled Mejia A and Wari-Unas). What remained of this material (20 samples) was subsequently returned to Williams at the Field Museum. We show here a principal components biplot of the INAA data with only 18 samples plotted (Mejia A and Wari-Unas have been excluded for purposes of clarity), showing the three main analytical groupings (Figure 4). 

Figure 2. Principal component biplot of rotated components 1 and 2 for mean descriptive analysis ratings (n=14 judges x 2 reps). Vectors for the aroma attributes, and the scores for the fifteen samples are shown. Open symbols indicate juice samples, while closed symbols indicate skin extracts. For sample codes, see Table II.

---