Exploration on Bubble Entropy

Abstract

Bubble entropy is a recently proposed entropy metric. Having certain advantages over popular definitions, bubble entropy finds its place in the research community map. It belongs to the family of entropy estimators which embed the signal into an m-dimensional space. Two are the main drawbacks for which those methods are criticized: the high computational cost and the dependence on parameters. Bubble entropy can be an answer to both, since computation can be performed in linear time and the dependence on parameters can be considered minimal in many practical situations. Popular entropy definitions, which are built over an embedding of the signal, mainly rely on two parameters: the size of the embedding space m and a tolerance r, which set a threshold over the distance between two points in the m-dimensional space to be considered similar. Bubble entropy totally eliminates the necessity to define a threshold distance, while it largely decouples the entropy estimation from the selection of the actual size of the embedding space in stationary conditions. Bubble entropy is compared to popular entropy definitions on theoretical and experimental basis. Theoretical analyses reveal significant advantages. Experimental analyses, comparing congestive heart failure patients and controls subjects, show that bubble entropy outperforms other popular, well established, entropy estimators in discriminating those two groups. Furthermore, machine learning-based feature ranking and experiments show that bubble entropy serves as a valuable source of features for AI decision-support algorithms.