###### 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 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 time 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 electroencephalography 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 classification; electroencephalography; entropy features; neural network entropy; Python; NNetEn +
Footnote †: journal:  
0000-0001-5002-4882-2233][PERSON]  
0000-0001-500  
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 analysis [6]. To quantify the self-similarity pattern in the given time series, ApEn considers the embedding dimension \(m\), the time delay \(tau\), and the tolerance value \(r\) as the initial parameters. On the basis of initial parameters, a new trajectory matrix is constructed. Using the tolerance \(r\), ApEn is computed by finding the self-similarity value between the rows of the trajectory matrix [6]. In short-length time series, ApEn is not accurate due to a strong dependence on data length [1]. Sample entropy (SampEn) and permutation entropy (PermEn) are introduced independently to overcome these difficulties [1]. The SampEn algorithm ignores self-matching patterns, which reduces computation time. It has been widely used in practical applications to analyze heart rate [7], recognize emotions [8], and analyze MRI signals [9]. The SampEn measure is inefficient when the time series are erratic or spiked [10]. In order to overcome these limitations, the Heaviside function, which is used in the SampEn algorithm, is substituted by a fuzzy membership function [1]. This new measure of entropy is called fuzzy entropy (FuzzyEn). According to experimental results, FuzzyEn performs better than SampEn [11; 12]. In recent years, FuzzyEn has been used to detect epileptic seizures [13], recognize emotions [14], and investigate the dynamic of lung cancer images [15]. [PERSON] and [PERSON] proposed the CoSiEn as another improvement to SampEn [10]. They used a different (angular) metric to search for similar embedding vectors. Their results showed that CoSiEn outperformed SampEn and FuzzyEn in the present \(1/f\) noise or short length dataset. In a study by [PERSON] et al. [16], the distribution entropy (DistEn) was introduced as an improvement over SampEn. According to [PERSON] et al., DistEn is less sensitive than SampEn under initial parameters and gives additional information about time series [5]. Hence, DisEn can be regarded as an independent feature of SampEn.