A new method based on branch length similarity (BLS) entropy to characterize time series

In previous studies, branch length similarity (BLS) entropy was suggested to characterize spatial data, such as an object’s shape and poses. The entropy was defined on a simple network consisting of a single node and branches. The simple network was referred to as the “unit branching network” (UBN). In the present study, I applied the BLS entropy concept to temporal data (e.g., time series) by forming UBNs on the data. The temporal data were obtained from the logistic equation and the movement behavior of Chironomid riparius. Using the UBNs, I calculated a variable, γ, defined as the ratio of the mean entropy value to the standard deviation for the difference values of the sets of two UBNs connected with each other along a given direction. Consequently, I found that ? could be effectively used to characterize temporal data.