USE OF THE ESTIMATED ERRORS OF THE DATA IN STRUCTURE-CORRELATION STUDIES

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 describe by the principal components.