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.

翻译：熵度量是时间序列分类问题的有效特征。传统熵度量方法（如香农熵）依赖于概率分布函数，然而为实现时间序列的有效分离，需要能够表征系统混沌动力学特性的新型熵估计方法。我们提出的神经网络熵（NNetEn）概念，基于LogNNet神经网络储层中记录的时间序列熵值与特殊数据集（MNIST-10和SARS-CoV-2-RBV1）分类结果的关联性。NNetEn以原创方式估计时间序列的混沌动力学特征。基于NNetEn算法，我们提出两个新的分类评估指标：R2效率（R2 Efficiency）和皮尔逊效率（Pearson Efficiency）。通过正弦映射的两类混沌时间序列分离实验，采用离散分析（ANOVA）验证了NNetEn的有效性。对于两个动力学相近的时间序列（r = 1.1918和r = 1.2243），F比值达到124，表明该方法在分类问题中具有高效性。针对健康人群与阿尔茨海默病患者的脑电信号分类实验，展示了NNetEn特征的实际应用价值。计算结果表明，传统熵度量与NNetEn概念联合使用时，可产生提升分类准确率的协同效应。本文还提供了算法的Python实现方案。