Use of the estimated errors of the data in structure-correlation studies
Oliviero Carugo · Acta Crystallographica Section B Structural Science · 1995
Novel statistical and numerical methods of data analysis, which make extensive use of the estimated errors (e.s.d.'s) of the data are presented and applied to structure-correlation problems. The novel procedures concern both univariate (histogram representation, HR) and multivariate (cluster analysis, CA, and principal-component analysis, PCA) statistical techniques. In the case of HR, the problem of optimally selecting the dimensions of the spaces is bypassed by convoluting a series of normal functions. In the case of CA, a probability significance is given to the similarity between two (or more than two) objects. In the case of PCA, a cross-validation technique, which takes into account the e.s.d.'s of the row data, allows the determination of the dimensionality of the principal-component space, easy detection of outliers with respect to any principal component, and evaluation of a more comprehensive percentage of the variance described by the principal components.