1. A pattern-classifying machine for assigning identification labels to unknown input patterns such that each input pattern is classified as a member of only one of several labeled prototype classes, said classifying machine comprising (a) a database consisting of data files of patterns which are known members of each prototype class; (b) a pattern comparator; (c) means for inputting said input patterns and said known members to said comparator; and (d) means for making predetermined transformations of prototype patterns and of input patterns, the improvement comprising: means for generating tangent vector patterns directly from selected transformations of each said prototype pattern, wherein: each selected transformation leaves the prototype label invariant; each selected transformation operates on image vectors in a vector space that represents pixel values; and each of the tangent vector patterns is represented in the vector space as a vector proportional to a difference between transformed and original patterns; means for generating for each said prototype pattern a transformed prototype pattern, by adding to each said prototype pattern selected linear combinations of said first tangent vector patterns; means for computing the Euclidean distance between each of said transformed prototype patterns and a one of said; input patterns and means for determining the smallest of the just-computed Euclidean distances, the smallest said distance determining which labeled prototype pattern is closest to said input pattern.