Neural Network Entropy (NNetEn) - EEG信号与混沌时间序列的基于熵特征分离及Python计算

Aug 4, 2026

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Entropy measures serve as powerful features for time series classification, but classical choices like Shannon entropy rely on probability distributions and may not adequately capture chaotic dynamics needed for effective separation. Neural Network Entropy (NNetEn) estimates chaotic dynamics from time series recorded in the LogNNet reservoir, using dataset classification as the guiding concept. Two new metrics, R2 Efficiency and Pearson Efficiency, are introduced and validated on sine-map chaotic series via ANOVA, while EEG experiments distinguish healthy subjects and Alzheimer patients. Python implementations are provided.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages24

Reading Time1 h 0 min

AccessFree to download

Abstract

Introduction

Background of entropy in time series analysis

Extended entropy measures: thermodynamic vs Shannon entropy

ApEn, SampEn, and PermEn

FuzzyEn and related improvements

Article Neural Network Entropy (NNetEn): EEG Signals and Chaotic Time Series Separation by Entropy Features, Python Package for NNetEn Calculation Andrei Velichko 1*, Maksim Belyaev 1, Yuriy Izotov 1, Murugappan Murugappan 2,3,4 and Hanif Heidari 5 1 Institute of Physics and Technology, Petrozavodsk State University, 185910 Petrozavodsk, Russia 2 Intelligent Signal Processing (ISP) Research Lab, Department of Electronics and Communication Engineering, Kuwait College of Science and Technology, Block 4, Doha, Kuwait. 3 Department of Electronics and Communication Engineering, Faculty of Engineering, Vels Institute of Sciences, Technology, and Advanced Studies, Chennai, India 6 Centre of Excellence for Unmanned Aerial Systems (CoEUAS), Universiti Malaysia Perlis, 02600, Arau, Perlis, Malaysia. 5 Department of Applied Mathematics, Damghan University, Damghan, Iran * [Correspondence: velichko@petrsu.ru](Correspondence: velichko@petrsu.ru); Abstract: Entropy measures are effective features for time series classification problems. Traditional entropy measures, such as Shannon entropy, use probability distribution function. However, for the effective separation of time series, new entropy estimation methods are required to characterize the chaotic dynamic of the system. Our concept of Neural Network Entropy (NNetEn) is based on the classification of special datasets (MNIST-10 and SARS-CoV-2-RBV1) in relation to the entropy of the time series recorded in the reservoir of the LogNNet neural network. NNetEn estimates the chaotic dynamics of time series in an original way. Based on the NNetEn algorithm, we propose two new classification metrics: R2 Efficiency and Pearson Efficiency. The efficiency of NNetEn is verified on separation of two chaotic time series of sine mapping using dispersion analysis (ANOVA) . For two close dynamic time series (r = 1.1918 and r = 1.2243), the F-ratio has reached the value of 124 and reflects high efficiency of the introduced method in classification problems. The EEG signal classification for healthy persons and patients with Alzheimer disease illustrates the practical application of the NNetEn features. Our computations demonstrate the synergistic effect of increasing classification accuracy when applying traditional entropy measures and the NNetEn concept conjointly. An implementation of the algorithms in Python is presented. Keywords: time series separation; EEG; classification, entropy features, LogNNet, Python, NNetEn 1. Introduction During the past 160 years, the concept of entropy has been applied to thermodynamical systems [1]. Over the years, the concept of entropy has been extended in various ways to solve scientific problems related to biomedical, healthcare, thermodynamics, physics, and others. Using horizon entropy, Jacobson and Parentani assessed the energy of black hole horizons [2]; Bejan studied entropy from the thermodynamic standpoint [3] . Bagnoli described the concept of entropy using the relationship between a thermal engine and a waterwheel [4]. His results showed that the concept of entropy is not restricted to thermal engines but can be applied to a wider variety of machines as well. A distribution entropy measure was used by Karmakar et al. for detecting short-term arrhythmias in heart rate [5] . There are two types of extended entropy measures: thermodynamic entropy and Shannon entropy. In thermodynamics, the entropy measure is related to the energy of a physical system. A Shannon entropy measure is an entropy measure that is used in information theory. Information/Shannon entropy measures are used to quantify the degree of freedom (DoF) or complexity of time series in practical applications. The technological advances in digitalization and their wide applications in practical problems in recent decades have made information entropy measures very popular. The approximate entropy (ApEn) measure is a well-known entropy measure employed in biosignal ana

FAQs

什么是 Neural Network Entropy（NNetEn）？

NNetEn是一种用于时间序列分类与分离的熵特征估计概念，基于在LogNNet神经网络储库中记录的时间序列熵来表征其混沌动态。它通过特定数据集的分类关系来估计熵特征。

NNetEn提出了哪些新的分类评价指标？

文中提出了两项新的分类度量：R2 Efficiency 和 Pearson Efficiency，用于衡量基于NNetEn的分类有效性。

NNetEn在EEG信号和混沌时间序列上如何验证？

NNetEn通过对两个混沌时间序列的分离使用ANOVA/离散分析验证效率；并进一步在健康人群与阿尔茨海默病患者的EEG信号分类中展示其实际应用效果，同时结合传统熵度量可提升分类准确率。

Aug 4, 2026

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