Detection of Changes in Binary Sequences

Abstract

In applications, such as biological ones, the segmentation of very long binary sequences is necessary. For example, such problems arise in DNA analysis. Some properties of a DNA sequence can be coded as a binary sequence and it should be separated into the homogeneous increments. In this paper, we propose a new approach for the segmentation of long binary sequences. Our approach is based on a transformation of an initial sequence into a sequence of real numbers. We will call such sequence a diagnostic sequence. After that, in the case of sequences generated by the stochastic mechanisms, we propose to apply the nonparametric change-point detection algorithm of Brodsky-Darkhovsky to the diagnostic sequence. If we don’t know the type of generating mechanism of the sequence, we propose to utilize our theory of ε -complexity to create new diagnostic sequences of ε -complexity coefficients. Subsequently, the change-point detection algorithm of Brodsky-Darkhovsky is applied to these diagnostic sequences. We verify the performance of the proposed methods on simulations.