Characteristics of Peak and Cliff in Branch Length Similarity Entropy Profiles for Binary Time-Series and Their Application

Abstract

A binary time series can be transformed into a Branch Length Similarity (BLS) entropy profile by being mapped to a circumference called a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">time-circle</i> . In this study, we explored how peaks and cliffs are formed and how they relate to time series. Peaks and cliffs are defined as spike shapes in their entropy profile and are called peaks (or cliffs) when their shape is symmetric (or asymmetric). We found that when signal bands with different signal densities are in the same time series, peaks or cliffs are formed on the side of the band with lower signal density. In addition, we found that when the signal density is moderately high, the distribution of peaks and cliffs appears as a global increase-decrease tendency of the entropy profile. The tendency appeared as a barrier in the entropy profile of the image. As an application of our findings, we successfully detected specific patterns in binary images using peaks, cliffs and the barriers.