Novel Features for Binary Time Series Based on Branch Length Similarity Entropy

Branch length similarity (BLS) entropy is defined in a network consisting of a single node and branches. In this study, we mapped the binary time-series signal to the circumference of the time circle so that the BLS entropy can be calculated for the binary time-series. We obtained the BLS entropy values for "1" signals on the time circle. The set of values are the BLS entropy profile. We selected the local maximum (minimum) point, slope, and inflection point of the entropy profile as the characteristic features of the binary time-series and investigated and explored their significance. The local maximum (minimum) point indicates the time at which the rate of change in the signal density becomes zero. The slope and inflection points correspond to the degree of change in the signal density and the time at which the signal density changes occur, respectively. Moreover, we show that the characteristic features can be widely used in binary time-series analysis by characterizing the movement trajectory of Caenorhabditis elegans. We also mention the problems that need to be explored mathematically in relation to the features and propose candidates for additional features based on the BLS entropy profile.