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In this paper, the multiclass supervised training problem is considered when a discrete set of classes is assumed. Upon generating affine models for finite data sets, we have observed the invariance of certain measures of performance after a trained classifier has been presented with test data of unknown classification. Specifically, after constructing mappings between training vectors and their desired targets, the class membership and ranking of test data has been found to remain either invariant or close to invariant under a transformation of the set of target vectors. Therefore, we derive conditions explaining how this type of invariance can arise when the multiclass problem is phrased in the context of linear networks. A bioinformatics example is then presented in order to demonstrate various principles outlined in this work.