Spherical Principal Component Analysis

Diamond (1966) has applied a filtering procedure in the refinement of protein structures, in which poorly determined linear combinations are not varied. In charge density analysis, the principal component analysis has been tested in a refinement of theoretical structure factors on diborane, B2H6, with a formalism including both one-center and two-center overlap terms (Jones et al. 1972). Not unexpectedly, it was found that the sum of the populations of the 2s and spherically averaged 2p shells on the boron atoms constitutes a well-determined eigenparameter, while the difference is very poorly determined. Correlation between one- and two-center terms was also evident in the analysis. 

Another variant of spherical PCA that accounts for various scales of data parameters is the so-called elliptical principal component analysis (ePCA). In contrast to spherical PCA, in the ePCA algorithm the data samples are projected onto a hyperellipse. The radii of the hyperellipse are the scales of parameters expressed by the robust Qn scale estimator. 

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