van Heel M (1984) Multivariate statistical classiWcation of noisy images (randomly oriented biological macromolecules). Ultramicroscopy 13:165–183
Multivariate Statistical Analysis (MSA) methods have recently been introduced for analyzing images of biological macromolecules [Van Heel and Frank, Ultramicroscopy 6 (1981) 187]. With these techniques, the significant characteristics of each molecular image can be expressed in merely 2 to 8 factorial coordinate values rather than in the typical 64 X 64 = 4096 pixel grey values that originally described the image. This very large reduction in total amount of data facilitates the understanding of the general behavior of a set of molecular images in terms of classes or of general trends in the data set. The (artificial) intelligence of the procedure, however, lies in the decision-making or classification phase. The theory and philosophy of multivariate statistical classification are reviewed using generalized metrics. Problem-dependent classification rationales are proposed. A set of computer-generated "randomly oriented molecular images" are used to test the classification schemes. This model experiment is a step towards 3D structure analysis of macromolecules based on large numbers of (noisy) electron microscopical images of randomly oriented biological macromolecules.