GRID principal component analysis

It is clear that for an unsymmetrical data matrix that contains more variables (the field descriptors at each point of the grid for each probe used for calculation) than observables (the biological activity values), classical correlation analysis as multilinear regression analysis would fail. All 3D QSAR methods benefit from the development of PLS analysis, a statistical technique that aims to find the multidimensional direction in the X space that explains the maximum multidimensional variance direction in the F space. PLS is related to principal component analysis (PCA)." ° However, instead of finding the hyperplanes of maximum variance, it finds a linear model describing some predicted variables in terms of other observable variables and therefore can be used directly for prediction. Complexity reduction and data... 

Corresponding to the dimension d = 2, the poset shown in Fig. 19 can alternatively be visualized by a two-dimensional grid as is shown in Fig. 22. Both visualizations have their advantages. Structures within a Hasse diagram, e.g., successor sets, or sets of objects separated from others by incomparabilities, can be more easily disclosed by a representation like that of Fig. 19. In multivariate statistics reduction of data is typically performed by principal components analysis or by multidimensional scaling. These methods minimize the variance or preserve the distance between objects optimally. When order relations are the essential aspect to be preserved in the data analysis, the optimal result is a visualization of the sediment sites within a two-dimensional grid. 

Figure 8 PLS analysis derives vectors u and t from the Y block (or y vector BA, = logarithms of relative affinities or other biological activities) and the X block (S,y = steric field variable of molecule i in the grid point j E,y = electrostatic field variable of molecule i in the grid point j) that are related to principal components. These latent variables are skewed within their confidence hyperboxes to achieve a maximum intercorrelation (diagram). SAMPLS is a PLS modification which first derives the covariance matrix of the X block and then the PLS result from this covariance matrix. Especially in cross-validation (see below), SAMPLS analysis is much faster than ordinary PLS analysis...

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