相关论文: Global Permutation Entropy

Here, we propose a new tool to estimate the complexity of a time series: the entropy of difference (ED). The method is based solely on the sign of the difference between neighboring values in a time series. This makes it possible to…

Permutation entropy has become a standard tool for time series analysis that exploits the temporal properties of these data sets. Many current applications use an approach based on Shannon entropy, which implicitly assumes an underlying…

There is no single universally accepted definition of "Complexity". There are several perspectives on complexity and what constitutes complex behaviour or complex systems, as opposed to regular, predictable behaviour and simple systems. In…

The Shannon entropy is a fundamental measure for quantifying diversity and model complexity in fields such as information theory, ecology, and genetics. However, many existing studies assume that the number of species is known, an…

Estimation of permutation entropy (PE) using Bayesian statistical methods is presented for systems where the ordinal pattern sampling follows an independent, multinomial distribution. It is demonstrated that the PE posterior distribution is…

Patch-based transformers have emerged as efficient and improved long-horizon modeling architectures for time series modeling. Yet, existing approaches rely on temporally-agnostic patch construction, where arbitrary starting positions and…

Entropy is being used in physics, mathematics, informatics and in related areas to describe equilibration, dissipation, maximal probability states and optimal compression of information. The Gini index on the other hand is an established…

The Shannon entropy is used as a basis for applying different lemmas and conjectures concerning the set of gaps between prime numbers G_p , thus estimating several measures of it. The same procedures are applied to artificially created…

Permutation Entropy ($PE$) is a powerful nonlinear analysis technique for univariate time series. Recently, Permutation Entropy for Graph signals ($PEG$) has been proposed to extend PE to data residing on irregular domains. However, $PEG$…

The quantification of the complexity of networks is, today, a fundamental problem in the physics of complex systems. A possible roadmap to solve the problem is via extending key concepts of information theory to networks. In this paper we…

Quantifying the complexity of large graphs requires measures that extend beyond predefined structural features and scale efficiently with graph size. This work adopts a generative perspective, modeling large networks as exchangeable graphs…

The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…

The Random Permutation Set (RPS) is a new type of set proposed recently, which can be regarded as the generalization of evidence theory. To measure the uncertainty of RPS, the entropy of RPS and its corresponding maximum entropy have been…

We propose a new interpretation of measures of information and disorder by connecting these concepts to group theory in a new way. Entropy and group theory are connected here by their common relation to sets of permutations. A combinatorial…

Permutation time irreversibility is an important method to quantify nonequilibrium characteristics of complex systems; however, ordinal pattern is a coarse-graining alternative of temporal structure and cannot accurately represent detailed…

Nonlinear dynamics play an important role in the analysis of signals. A popular, readily interpretable nonlinear measure is Permutation Entropy. It has recently been extended for the analysis of graph signals, thus providing a framework for…

We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…

The recent extension of permutation entropy and its derivatives to graph signals has opened up new horizons for the analysis of complex, high-dimensional systems evolving on networks. However, these measures are all fundamentally rooted in…

In estimating the complexity of objects, in particular of graphs, it is common practice to rely on graph- and information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these…

Generalised degrees provide a natural bridge between local and global topological properties of networks. We define the generalised degree to be the number of neighbours of a node within one and two steps respectively. Tailored random graph…