Measuring Over-Generalization in the Minimal Multiple Generalizations of Biosequences

We consider the problem of finding a set of patterns that best characterizes a set of strings. To this end, Arimura et. al. [3] considered the use of minimal multiple generalizations (mmg) for such characterizations. Given any sample set, the mmgs are, roughly speaking, the most (syntactically) specific set of languages containing the sample within a given class of languages. Takae et. al. [17] found the mmgs of the class of pattern languages [1] which includes so-called sort symbols to be fairly accurate as predictors for signal peptides. We first reproduce their results using updated data. Then, by using a measure for estimating the level of over-generalizations made by the mmgs, we show results that explain the high level of accuracies resulting from the use of sort symbols, and discuss how better results can be obtained. The measure that we suggests here can also be applied to other types of patterns, e.g. the PROSITE patterns [4].