A New Measure to Characterize the Self-Similarity of Binary Time Series and its Application

In this study, the branch-length similarity entropy profile is estimated by mapping the time-series signal to the circumference of the time circle, and the self-similarity is defined based on the profile. To explore the self-similarity property, the effect of the distance between two signals, “0” and “1”, on the entropy value for signal “1” is investigated. Furthermore, two application problems are addressed: quantification of the mixing state of fragments and clusters, and characterization of the behavioral trajectory of an organism. The results indicate that use of the self-similarity property solves both the problems. Additionally, the problems that must be addressed to broaden the applicability of self-similarity are discussed.