Abstract
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 for a consensus sequence of strings demonstrated by one of the authors and co-workers in a previous study. 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 and classifying RNAs by the secondary structure using nucleotide sequences.