Latent property space

Since U and V express one and the same set of latent vectors, one can superimpose the score plot and the loading plot into a single display as shown in Fig. 31,2e. Such a display was called a biplot (Section 17.4), as it represents two entities (rows and columns of X) into a single plot [10]. The biplot plays an important role in the graphic display of the results of PCA. A fundamental property of PCA is that it obviates the need for two dual data spaces and that instead of these it produces a single space of latent variables. 

Principal component analysis (PCA) can be considered as the mother of all methods in multivariate data analysis. The aim of PCA is dimension reduction and PCA is the most frequently applied method for computing linear latent variables (components). PCA can be seen as a method to compute a new coordinate system formed by the latent variables, which is orthogonal, and where only the most informative dimensions are used. Latent variables from PCA optimally represent the distances between the objects in the high-dimensional variable space—remember, the distance of objects is considered as an inverse similarity of the objects. PCA considers all variables and accommodates the total data structure it is a method for exploratory data analysis (unsupervised learning) and can be applied to practical any A-matrix no y-data (properties) are considered and therefore not necessary. 

The description of a colloid should include particle size, mobility, charge and their distributions, charge/mass ratio, electrical conductivity of the media, concentration and mobility of ionic species, the extent of a double layer, particle-particle and particle-substrate interaction forces and complete interfacial analysis. The application of classical characterization methods to nonaqueous colloids is limited and, for this reason, the techniques best suited to these systems will be reviewed. Characteristic results obtained with nonaqueous dispersions will be summarized. Physical aspects, such as space charge effects and electrohydrodynamics, will receive special attention while the relationships between chemical and physical properties will not be addressed. An application of nonaqueous colloids, the electrophoretic development of latent images, will also be discussed. 

The result of a PLS analysis includes the contribution of each input property to the extracted latent variables. Because in CoMFA the input properties are located in 3D space, one can draw contour plots that enclose the regions in space that enclose these contributions. 

The heat-transfer coefficient is a key property of the dryer. It is controlled by the nozzle geometry and spacing, the distance from the web, and the velocity of the air. The evaporation rate is the rate at which heat is supplied for evaporation (heat also goes into heating the coating and the web) divided by the latent heat of... 

PLS with an X- and a Y-block has two main applications calibration and mapping, as shown schematically in Figure 7. A projection plane is spanned by two orthogonal latent variables in x-space. The position of this projection plane is not only defined by X (as in PCA) but also by Y. A complementary map is spanned by the corresponding two orthogonal latent variables in y-space. A cluster analysis of objects is therefore influenced by features and properties together the loadings of both can be interpreted to find out their relationships. 

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