Maximum margin classifier working in a set of strings

Optimal string clustering based on a Laplace-like mixture and EM algorithm on a set of strings

“…In this study, using the probability theory on A * developed in [19][20][21], we constructed the theory of the mixture model and the EM algorithm on A * and derived the optimal procedure for unsupervised string clustering based on the theory. We encountered the interesting phenomenon that an EM algorithm for the Laplace-like mixture on A * , which we sought, could not be written in an explicit manner because of the complex metric structure of A * , but a sequence of algorithms (i.e., a sequence of sequences of computations) that strongly consistently estimates the parameters of the Laplace-like mixture and converges to the EM algorithm with probability one was obtained explicitly.…”

“…This is different from the phenomena that an algorithm halts and that a sequence of approximate solutions from an iterative algorithm converges. The authors addressed the problem of supervised string classification by constructing a theory of a statistical learning machine that works in A * in [19]. Recently, the amount of string data has increased exponentially.…”

“…Our objects in this study are sequences of random variables that take values in A * (random strings), their distributions, and their realizations, i.e., string data. In the following sections, we use a fundamental framework of a probability theory on A * that was proposed in [20] and extended in [19,21]. A summary of this theory is provided in Subsection A1.…”

“…Similarly, statistical methods for string data should also be constructed based on probability theory on a set of strings. In this study, we address the problem of clustering string data in an unsupervised manner by applying probability theory on a set of strings developed in [19][20][21]. Our approach to unsupervised string clustering in this study is based on a mixture model of distributions on a set of strings.…”

“…Finally, in Section 5, we derive a procedure for clustering strings in an unsupervised manner from the Laplace-like mixture and describe that it is asymptotically optimal in the sense that the posterior probability of making correct classifications is maximized. A summary of probability theory on a set of strings that was developed in [19][20][21] and is used in this paper is provided in Subsection A1. In Subsection A4, we show that a result on the strong consistency of maximum likelihood estimators in the case where the parameter space is the set of real numbers (see, for example, [41,47]) can be extended to the case where the parameter space is the direct product of the sets of strings and real numbers.…”