Correlation of features

The loading plot provides the projection of the features onto the PCs. From this plot, information about the correlation of feature variables can be deduced. The correlation of features is described by the cosine of the angle between the loading vectors. The smaller the angle, the higher is the correlation between features. Uncorrelated features are orthogonal... 

Scaling of data is not necessary if the Mahalanobis distance is used. In addition, with this measure distortion occasioned by correlations of features or feature groups is avoided. In contrast, if the Euclidean distance were applied in the case of two highly correlated variables, these variables would be used as two independent features although they provide identical information. 

The drawing software comprises a comprehensive collection of standard tools to sketch 2D chemical structures. To specify all its facilities and tools would go far beyond the scope of this overview, but there are some nice features that are very useful for chemists so they are mentioned here briefly. One of these enables the prediction of H and NMR shifts from structures and the correlation of atoms with NMR peaks (Figure 2-127). lUPAC standard names can be generated... 

Neural networks have been applied to IR spectrum interpreting systems in many variations and applications. Anand [108] introduced a neural network approach to analyze the presence of amino acids in protein molecules with a reliability of nearly 90%. Robb and Munk [109] used a linear neural network model for interpreting IR spectra for routine analysis purposes, with a similar performance. Ehrentreich et al. [110] used a counterpropagation network based on a strategy of Novic and Zupan [111] to model the correlation of structures and IR spectra. Penchev and co-workers [112] compared three types of spectral features derived from IR peak tables for their ability to be used in automatic classification of IR spectra. 

Diffusivity and tortuosity affect resistance to diffusion caused by collision with other molecules (bulk diffusion) or by collision with the walls of the pore (Knudsen diffusion). Actual diffusivity in common porous catalysts is intermediate between the two types. Measurements and correlations of diffusivities of both types are Known. Diffusion is expressed per unit cross section and unit thickness of the pellet. Diffusion rate through the pellet then depends on the porosity d and a tortuosity faclor 1 that accounts for increased resistance of crooked and varied-diameter pores. Effective diffusion coefficient is D ff = Empirical porosities range from 0.3 to 0.7, tortuosities from 2 to 7. In the absence of other information, Satterfield Heterogeneous Catalysis in Practice, McGraw-HiU, 1991) recommends taking d = 0.5 and T = 4. In this area, clearly, precision is not a feature. 

In order to enhance our ligand-based query hypothesis, the structural fragments of the initial query were generalized but linked with the same distance constraints. A search of this final query (see Fig. 4-10) in the same list yielded 690 hits and a statistically significant correlation of the presence of this enantiophore and the enan-tioselectivity of the compounds was found (94 % of those are well resolved on Chi-ralcel OD). Note that out of the 4203 compounds of the Chiralcel OD domain search, a 2D search found 1900 structures that contain the substructural features of the generalized query. 

Figure 6.3 Differentiation of Vibrio parahaemolyticiis strains by region of clinical outbreak, showing the correlation of a mass spectral feature (near dotted line), the region of clinical outbreak, and the presence or absence of the TDH gene in control organisms. (From a linear TOF, reported at the American Society for Mass Spectrometry in...

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