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 in relation to the entropy of the time series recorded in the reservoir of the neural network. NNetEn estimates the chaotic dynamics of time series in an original way and does not take into account probability distribution functions. 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. 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 electroenceph-alography 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。传统的熵度量方法（如香农熵）依赖概率分布函数，但对于时间序列的有效分离，需要新的熵估计方法来表征系统的混沌动力学特性。我们提出的神经网络熵（NNetEn）概念基于对神经网络储备池中记录的时间序列熵值相关的特殊数据集进行分类。NNetEn以原创方式估计时间序列的混沌动力学特性，且不涉及概率分布函数。我们提出了两种新的分类度量指标：R2效率系数和皮尔逊效率系数。通过使用色散分析对正弦映射生成的两个混沌时间序列进行分离验证，证明了NNetEn的有效性。对于两个动力学特性相近的时间序列（r=1.1918与r=1.2243），F比率达到124，反映了所提方法在分类问题中的高效性。针对健康人群与阿尔茨海默病患者的脑电图信号分类，展示了NNetEn特征的实践应用。我们的计算表明，将传统熵度量与NNetEn概念联合使用时，分类准确率呈现协同提升效应。同时提供了算法的Python实现方案。