1.2 REMARK ON INTERPRETATIONS OF THE SHANNON ENTROPY There are standard ways to interpret the Shannon entropy. For instance, the quantity H(p) can be viewed as a measure of the amount of uncertainty in a random experiment described by the probability mass function p, or as a measure of the amount of information one gains by learning the value of such an experiment. Indeed, it is possible to sta...

In this paper, we generalize the permutation entropy (PE) measure to binary sequences, which is based on Shannon’s entropy, and theoretically analyze this measure for random binary sequences. We deduce the theoretical value of PE for random binary sequences, which can be used to measure the randomness of binary sequences. We also reveal the relationship between this PE measure with other random...

This paper motivates and interprets entropy centrality, the measure understood as the entropy of flow destination in a network. The paper defines a variation of this measure based on a discrete, random

Psychological research has found that human perception of randomness is biased. In particular, people consistently show the overalternating bias: they rate binary sequences of symbols (such as Heads and Tails in coin flipping) with an excess of alternation as more random than prescribed by the normative criteria of Shannon's entropy. Within data mining for medical applications, Marcellin propos...

The thermodynamic maximum principle for the Boltzmann-GibbsShannon (BGS) entropy is reconsidered by combining elements from group and measure theory. Our analysis starts by noting that the BGS entropy is a special case of relative entropy. The latter characterizes probability distributions with respect to a pre-specified reference measure. To identify the canonical BGS entropy with a relative e...

This paper proposed a new entropy measure, Fuzzy Measure Entropy (FuzzyMEn), for the analysis of heart rate variability (HRV) signals. FuzzyMEn was calculated based on the fuzzy set theory and improved the poor statistical stability in the approximate entropy (ApEn) and sample entropy (SampEn). The simulation results also demonstrated that the FuzzyMEn had better algorithm discrimination abilit...

We show how to determine the maximum and minimum possible values of one measure of entropy for a given value of another measure of entropy. These maximum and minimum values are obtained for two standard forms of probability distribution (or quantum state) independent of the entropy measures, provided the entropy measures satisfy a concavity/convexity relation. These results may be applied to en...

In this paper we aim at finding conditions under which risk measures can be consistently updated. Since the class of risk measures that allow dynamically consistent updates appears to be limited, we consider weaker notions of consistency in addition to dynamic consistency, concentrating on notions that are still strong enough to ensure uniqueness of updating. We show that a weak type of consist...

This paper proposes a new similarity measure between basket datasets based on associations. The new measure is calculated from support counts using a formula inspired by information entropy. Experiments on both real and synthetic datasets show the effectiveness of the measure. This paper then investigates the applications of the similarity measure. It first studies the problem of finding a mapp...

In a previous paper the authors developed an operator-algebraic approach to Lewis Bowen’s sofic measure entropy that yields invariants for actions of countable sofic groups by homeomorphisms on a compact metrizable space and by measure-preserving transformations on a standard probability space. We show here that these measure and topological entropy invariants both coincide with their classical...