A New Perspective on Shape and Distribution: Branch Length Similarity Entropy Approach

This study introduces a fresh perspective on conventional notions of "shape" and "distribution" by utilizing the innovative framework of branch-length similarity (BLS) entropy. In our exploration of "shape," we propose BLS entropy-based interpretations of circularity, elongation, and symmetry. We subject these novel concepts to quantitative evaluation against established benchmarks, highlighting their inherent advantages. The evaluation is conducted using a dataset of 1365 images from the MPEG-7 collection. Additionally, within the context of BLS entropy-driven "distributions," we present an inventive approach involving the construction of networks that connect nodes through Delaunay triangles within a two-dimensional space. In this framework, we employ alpha and beta to quantify both local and global connectivity of individual nodes. To effectively demonstrate the utility of alpha and beta, we apply them to the analysis of intricate foraging dynamics exhibited by a school of fish. Through this application, we uncover shifts in both individual fish behavior and collective school dynamics, providing illuminating insights into their behavioral changes.