Normalization procedures and factorial representations for classification of correlation-aligned images: A comparative study

Abstract

We have addressed the problem of optimizing procedures of multivariate statistical analysis (MSA) for identifying homogeneous sets of electron micrographs of biological macromolecules, with a view to averaging over consistent sets of images. Using pre-aligned images of negatively stained protein molecules — known a priori to fall into two subtly different classes — we compared how the capacity to discriminate between them was affected by the normalization procedure used, and by the choice of factorial representation. Specifically, these images were analyzed both after being scaled according to constant minimum and maximum (CMM) values, and after imposing constant values of image mean and variance (CMV). The factorial representations compared were correspondence analysis (CA) and the principal components (PC) formalism. When used with PC, CMM normalization was found to give rise to spurious inter-image fluctuations that were more pronounced than the genuine difference between the two kinds of images; even with CA, CMV proved to be a more satisfactory method of normalization. When CMV was used with CA or PC, both factorial representations yielded qualitatively similar results, although according to a quantitative measure of inter-set discrimination, the performance of PC was slightly superior. Even in the best case, however, the two classes of images — as mapped in factorial space — were not fully resolved. The implications of this observation are discussed with regard to potential ambiguities of image classification in practice.