Supervised classification employing multiple templates, and a decision based on the highest similarity, is also called multireference classification (van Heel and Stoffler-Meilicke, 1985). It is used in the alignment of a heterogeneous image set, as follows: after a preliminary reference-free alignment of the entire set followed by classification, for instance by HAC, class averages are created, which are then in turn used as multiple references. Each image of the original data set is then presented with the choice among these references, and is then classified according to its greatest similarity, as (normally) measured by the cross-correlation coefficient. Early applications in single-particle averaging are found in the works of Alasdair Steven and coworkers (Fraser et al., 1990; Trus et al., 1992). The most important application of multireference classification is 3D projection matching: the comparison of an experimental projection with projections of a 3D reference, computed for a regular angular grid. This method will be discussed at some length in chapter 5, section 7.2.
An obvious disadvantage of supervised classification, as with all reference-based schemes, is that its outcome depends strongly on the choice of the template, thus allowing, to some extent, subjective decisions to influence the course of the structural analysis.
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