Score space

Because the eigenvectors are ordered according to the maximum variability, a subset of the first k < N scores define the most variability possible in a /c-dimensional subspace. This subspace is referred to as the score space. 

HCA is a common tool that is used to determine the natural grouping of objects, based on their multivariate responses [75]. In PAT, this method can be used to determine natural groupings of samples or variables in a data set. Like the classification methods discussed above, HCA requires the specification of a space and a distance measure. However, unlike those methods, HCA does not involve the development of a classification rule, but rather a linkage rule, as discussed below. For a given problem, the selection of the space (e.g., original x variable space, PC score space) and distance measure (e.g.. Euclidean, Mahalanobis) depends on the specific information that the user wants to extract. For example, for a spectral data set, one can choose PC score space with Mahalanobis distance measure to better reflect separation that originates from both strong and weak spectral effects. 

The complete design is seen in the score space with replicate center points clearly visible. Note that the interpretation of scores plots is not always as straightforward as in this example. The experimental design is not seen if the experiment is not well designed or if the problem is high dimensional. The level of impEcidy modeled components (e.g., component O also has an effect on the relative position of the samples in score space. For this example, the effect of C on the relative placement of the samples in score space is small. 

Scores Plot (Sample Diagnostic) The Factor 2 versus Factor l plot is shown in Figure 5.119 with the points labeled by run order. The samples in this score space form multiple lines with similar slopes. Each line contains the spectra from a single standard (design point) at var ing temperatures. For example, samples 49-54 correspond to spectra collected from a single standard... 

ITTFA starts calculating a PCA model of the original data matrix, D. There is a formal analogy between the PCA decomposition, i.e., D = TPT, and the CR decomposition, i.e., D = CST, of a data matrix. The scores matrix, T, and the loadings matrix, PT, span the same data space as the C and the ST matrices thus, their profiles can be described as abstract concentration profiles and abstract spectra, respectively. This means that any real concentration profile of C belongs to the score space and can be described as a linear combination of the abstract concentration profiles in the T matrix. 

Figure 4 shows the distribution of the ketones in the two dimensional score space (h, t2), resulting from the principal component analysis (PCA) of the table of 78 ketones described by the 11 structure descriptor variables derived from IR, NMR spectra and other properties such as density, molecular weight and so on [31]. The figure also shows 9 compounds selected by a D-optimal design to well span this score space. Figure 5 shows the same score space but with another selection of 12 compounds, claimed to be superior. 

Determine the geometric center of mean for active compounds per target in PCA score space. 

Table 2. Areas of clusters in 2D DFA score space for each addition of a wavelet scale. The Eubacterium data set.

II. The region of extreme samples (bottom right), which show an extreme behaviour because they respect the variable correlation structure captured by the PCA model but get high values in scores space. These samples, whose values are high, are also said to have high leverage because they pull the PC axes towards them ... 

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