Global Permutation Entropy

• URL: http://arxiv.org/abs/2508.19955v1
• Date: Wed, 27 Aug 2025 15:08:12 GMT
• Title: Global Permutation Entropy
• Authors: Abhijit Avhale, Joscha Diehl, Niraj Velankar, Emanuele Verri,
• Abstract summary: We introduce Global Permutation Entropy (GPE), a novel index that considers all possible patterns of a given length, including non-consecutive ones.<n>Its computation relies on recently developed algorithms that enable the efficient extraction of full permutation profiles.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Permutation Entropy, introduced by Bandt and Pompe, is a widely used complexity measure for real-valued time series that is based on the relative order of values within consecutive segments of fixed length. After standardizing each segment to a permutation and computing the frequency distribution of these permutations, Shannon Entropy is then applied to quantify the series' complexity. We introduce Global Permutation Entropy (GPE), a novel index that considers all possible patterns of a given length, including non-consecutive ones. Its computation relies on recently developed algorithms that enable the efficient extraction of full permutation profiles. We illustrate some properties of GPE and demonstrate its effectiveness through experiments on synthetic datasets, showing that it reveals structural information not accessible through standard permutation entropy. We provide a Julia package for the calculation of GPE at `https://github.com/AThreeH1/Global-Permutation-Entropy'.

Related papers

• Local Entropy Search over Descent Sequences for Bayesian Optimization [48.7994415668802]
  A practical alternative is to iteratively refine the neighborhood of an initial design using local optimization methods such as gradient descent.<n>We propose local entropy search (LES), a Bayesian optimization paradigm that explicitly targets the solutions reachable by the descent sequences.
  arXiv  Detail & Related papers  (2025-11-24T15:52:17Z)
• Composition Law of Conjugate Observables in Random Permutation Sorting Systems [0.0]
  We present the discovery of a fundamental composition law governing conjugate observables in the Random Permutation Sorting System (RPSS)<n>The law links the discrete permutation count Np and the continuous elapsed time T through a functional relation connecting the characteristic function of timing to the probability generating function of permutation counts.<n>This framework enables entropy purification, transforming microarchitectural timing fluctuations into uniform randomness via geometric convergence.
  arXiv  Detail & Related papers  (2025-10-09T09:50:21Z)
• A Unified Analysis of Stochastic Gradient Descent with Arbitrary Data Permutations and Beyond [7.325166704015515]
  We aim to provide a unified convergence analysis for permutation-based Gradient Descent (SGD)<n>We categorize existing permutation-based SGD algorithms into four categories: Arbitrary Permutations, Independent Permutations, One Permutation and Dependent Permutations.<n>We develop a unified framework for permutation-based SGD with arbitrary permutations of examples, incorporating all the aforementioned representative algorithms.
  arXiv  Detail & Related papers  (2025-01-27T15:07:02Z)
• From Exponential to Polynomial Complexity: Efficient Permutation Counting with Subword Constraints [0.0]
  Counting distinct permutations with replacement, especially when involving multiple subwords, is a longstanding challenge in analysis. This paper introduces a novel framework that presents closed-form formulas for calculating distinct permutations with replacement. We then extend our foundational formula to handle multiple subwords through the development of an additional formula.
  arXiv  Detail & Related papers  (2024-11-23T19:52:11Z)
• Random sampling of permutations through quantum circuits [0.0]
  We introduce a classical algorithm for random sampling of permutations, drawing inspiration from the Steinhaus-Johnson-Trotter algorithm.<n>We develop a quantum analogue of the classical algorithm using a quantum circuit model for random sampling of permutations.
  arXiv  Detail & Related papers  (2024-09-04T18:19:30Z)
• Efficient unitary designs and pseudorandom unitaries from permutations [35.66857288673615]
  We show that products exponentiated sums of $S(N)$ permutations with random phases match the first $2Omega(n)$ moments of the Haar measure. The heart of our proof is a conceptual connection between the large dimension (large-$N$) expansion in random matrix theory and the method.
  arXiv  Detail & Related papers  (2024-04-25T17:08:34Z)
• TERM Model: Tensor Ring Mixture Model for Density Estimation [48.622060998018206]
  In this paper, we take tensor ring decomposition for density estimator, which significantly reduces the number of permutation candidates. A mixture model that incorporates multiple permutation candidates with adaptive weights is further designed, resulting in increased expressive flexibility. This approach acknowledges that suboptimal permutations can offer distinctive information besides that of optimal permutations.
  arXiv  Detail & Related papers  (2023-12-13T11:39:56Z)
• Sampled Transformer for Point Sets [80.66097006145999]
  sparse transformer can reduce the computational complexity of the self-attention layers to $O(n)$, whilst still being a universal approximator of continuous sequence-to-sequence functions. We propose an $O(n)$ complexity sampled transformer that can process point set elements directly without any additional inductive bias.
  arXiv  Detail & Related papers  (2023-02-28T06:38:05Z)
• Automatic and effective discovery of quantum kernels [41.61572387137452]
  Quantum computing can empower machine learning models by enabling kernel machines to leverage quantum kernels for representing similarity measures between data.<n>We present an approach to this problem, which employs optimization techniques, similar to those used in neural architecture search and AutoML.<n>The results obtained by testing our approach on a high-energy physics problem demonstrate that, in the best-case scenario, we can either match or improve testing accuracy with respect to the manual design approach.
  arXiv  Detail & Related papers  (2022-09-22T16:42:14Z)
• SPANet: Generalized Permutationless Set Assignment for Particle Physics using Symmetry Preserving Attention [62.43586180025247]
  Collisions at the Large Hadron Collider produce variable-size sets of observed particles. Physical symmetries of decay products complicate assignment of observed particles to decay products. We introduce a novel method for constructing symmetry-preserving attention networks.
  arXiv  Detail & Related papers  (2021-06-07T18:18:20Z)
• GANs with Variational Entropy Regularizers: Applications in Mitigating the Mode-Collapse Issue [95.23775347605923]
  Building on the success of deep learning, Generative Adversarial Networks (GANs) provide a modern approach to learn a probability distribution from observed samples. GANs often suffer from the mode collapse issue where the generator fails to capture all existing modes of the input distribution. We take an information-theoretic approach and maximize a variational lower bound on the entropy of the generated samples to increase their diversity.
  arXiv  Detail & Related papers  (2020-09-24T19:34:37Z)
• Relevant OTOC operators: footprints of the classical dynamics [68.8204255655161]
  The OTOC-RE theorem relates the OTOCs summed over a complete base of operators to the second Renyi entropy. We show that the sum over a small set of relevant operators, is enough in order to obtain a very good approximation for the entropy. In turn, this provides with an alternative natural indicator of complexity, i.e. the scaling of the number of relevant operators with time.
  arXiv  Detail & Related papers  (2020-07-31T19:23:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.