###### Abstract
Permutation entropy (PermEn), the other improvement of ApEn, combines entropy with symbolic dynamics [17]. In the PermEn algorithm, partitions are constructed by comparing neighboring time series values. PermEn is widely used in literature due to its robustness and computational efficiency [18]. Despite some advantages, PermEn is not stable regarding its input parameters. Therefore, the accuracy of PermEn depends on several input parameters. Its efficiency is affected by inconsistent results due to different initial parameters [19]. In order to overcome this difficulty, bubble entropy (BubbleEn) was introduced [19]. Similar to PermEn, BubbleEn uses a bubble sort algorithm to rank embedded vectors. However, BubbleEn is less sensitive to initial parameters than PermEn [19]. Increment entropy (IncEn) modifies PermEn to transform ranked time series into symbol sequences [20]. Consequently, IncEn is a suitable measure of entropy in the case of short datasets [20]. In addition to SampEn, PermEn, and their improved entropy measures, some entropy measures directly improve ShEn. [PERSON] et al. extended ShEn for \(A_{m\times n}\) matrices based on the singular value decomposition theorem (SVD) [21; 22]. Singular value decomposition entropy (SVDEn) is defined as the ShEn of the normalized eigenvalues of the diagonal matrix (which appears in SVD). A new measure of entropy based on Poincare plots of time series was introduced by [PERSON] et al. [23]. The Poincare plot is divided into \(n\)\(\times\)\(n\) grids. In each grid, the probability of the number of each point is calculated. A measure of ShEn with respect to probability distributions is known as grid entropy (GridEn) [23]. [PERSON] and [PERSON] proposed phase entropy (PhaseEn), based on GridEn's concept [24]. In PhaseEn, the PhaseEn measure is computed using a second-order Poincare plot and ShEn [24]. In a recent study, [PERSON] et al. introduced attention entropy (AttnEn) which considers only peak points. The results show that AttnEn is robust for short time series [25]. All of the mentioned entropy measures are extensions of the ShEn algorithm, which requires probability density functions. A measure of entropy called NNetEn [26] was introduced by [PERSON] and [PERSON] that uses feedforward neural networks with LogNNet models [27; 28] and does not take into account probability distribution functions. In [29], the researchers showed that NNetEn is robust under noise conditions and outperforms traditional entropy measures. Figure 1 shows the general concept of calculating NNetEn. A time series \(X=(x_{1}\dots\ x_{n})\), of length \(N\), is written to the reservoir (stage 1). In the second stage, a dataset is selected to be used as the basis for calculating the classification metric. We feed the \(Y\) vector from the dataset into the reservoir input (stage 3), and then pass it through normalization (stage 4). A time series element transforms the \(Y\) vector in the reservoir (stage 5). Consequently, the output vector \(Sh\) (stage 6) has a different dimension from the input vector \(Y\). The output vector \(Sh\) is normalized (stage 7) and fed into the output classifier (stage 8). In stage 9, the classifier is trained on the dataset, and in stage 10, it is tested. A linear transformation is performed on the classification metric in order to convert it into NNetEn entropy (Stage 11). In Section 2.3 of the methodology, the details of the steps are explained. A higher degree of irregularity in the time series \(X\) leads to a more efficient process for transforming the input vector \(Y\) into a different dimension, which in turn leads to a higher classification metric, and a higher output entropy. This principle differs from the common principles for calculating entropy based on a probability distribution. The determination of data for entropy estimation (stage 2 in Figure 1) is an important aspect of the study. Initially, LogNNet was developed to compute the NNetEn based on MNIST handwritten dataset [30].