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.

本文提出了基于 NNetEn 算法的两种新分类指标：R2 Efficiency 和 Pearson Efficiency，以及将传统熵测量和 NNetEn 特征应用于时间序列分类中的成功实现，通过实验验证了该方法在分类问题中的高效性。

神经网络熵（NNetEn）：通过熵特征分离脑电信号和混沌时间序列，用于计算 NNetEn 的 Python 包

Neural Network Entropy (NNetEn): EEG Signals and Chaotic Time Series  Separation by Entropy Features, Python Package for NNetEn Calculation

Entropy is a fundamental concept in the field of information theory. During
measurement, conventional entropy measures are susceptible to length and
amplitude changes in time series. A new entropy metric, neural network entropy
(NNetEn), has been developed to overcome these limitations. NNetEn entropy is
computed using a modified LogNNet neural network classification model. The
algorithm contains a reservoir matrix of N=19625 elements that must be filled
with the given data. The contribution of this paper is threefold. Firstly, this
work investigates different methods of filling the reservoir with time series
(signal) elements. The reservoir filling method determines the accuracy of the
entropy estimation by convolution of the study time series and LogNNet test
data. The present study proposes 6 methods for filling the reservoir for time
series. Two of them (Method 3 and Method 6) employ the novel approach of
stretching the time series to create intermediate elements that complement it,
but do not change its dynamics. The most reliable methods for short time series
are Method 3 and Method 5. The second part of the study examines the influence
of noise and constant bias on entropy values. Our study examines three
different time series data types (chaotic, periodic, and binary) with different
dynamic properties, Signal to Noise Ratio (SNR), and offsets. The NNetEn
entropy calculation errors are less than 10% when SNR is greater than 30 dB,
and entropy decreases with an increase in the bias component. The third part of
the article analyzes real-time biosignal EEG data collected from emotion
recognition experiments. The NNetEn measures show robustness under
low-amplitude noise using various filters. Thus, NNetEn measures entropy
effectively when applied to real-world environments with ambient noise, white
noise, and 1/f noise.

本文提出了一种新的熵度量学方法 —— 神经网络熵（NNetEn），它能够有效应用于实际环境下带有噪音信号的测量，本文的研究主要围绕着 NNetEn 的计算方法及其在时间序列、噪声和常数偏差方面的表现进行了分析。