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资源说明：In many pattern recognition problems such as handwritten character recognition, it would be a challenge to design a good classification function, which can eliminate irrelevant variabilities among objects of the same class, while at the same time, being able to identify meaningful differences between objects of different classes. For example, in order for an automatic technique to “recognize” a handwritten digit, the incoming digit pattern needs to be accurately classified into one out of ten possible categories (from “0” to “9”). One straightforward yet inefficient way of implementation would be to match the pattern with a set of prototypes, where almost all possible instances (e.g., different sizes, angles, skews, etc.) of the digit in each category must be stored, according to a certain distance measure. Consequently, the pattern will be classified into the category where the closest match with one of its prototype instances was found. This approach would lead to impractically large prototype sets in order to achieve high recognition accuracy. An alternative method is to use only one prototype for each category, where different “deformed” instances of the same prototype can be generated by geometric transformations (e.g., thickened or rotated) during the matching process so as to best fit the incoming digit pattern. To this end, the concept of Lie operators for the transformations would be applicable.
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