  Numbers and numerical vectors account for a large portion of data. However,
recently the amount of string data generated has increased dramatically.
Consequently, classifying string data is a common problem in many fields. The
most widely used approach to this problem is to convert strings into numerical
vectors using string kernels and subsequently apply a support vector machine
that works in a numerical vector space. However, this non-one-to-one conversion
involves a loss of information and makes it impossible to evaluate, using
probability theory, the generalization error of a learning machine, considering
that the given data to train and test the machine are strings generated
according to probability laws. In this study, we approach this classification
problem by constructing a classifier that works in a set of strings. To
evaluate the generalization error of such a classifier theoretically,
probability theory for strings is required. Therefore, we first extend a limit
theorem on the asymptotic behavior of a consensus sequence of strings, which is
the counterpart of the mean of numerical vectors, as demonstrated in the
probability theory on a metric space of strings developed by one of the authors
and his colleague in a previous study [18]. Using the obtained result, we then
demonstrate that our learning machine classifies strings in an asymptotically
optimal manner. Furthermore, we demonstrate the usefulness of our machine in
practical data analysis by applying it to predicting protein--protein
interactions using amino acid sequences.
