## 2 Materials and Methods
### Performance Metrics  
Entropy is estimated using the classification metrics of neural networks: Classification Accuracy, R2 Efficiency and Pearson Efficiency.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Classes** & **Number of Training Images** & **Number of Testing Images** \\ \hline
0 & 5923 & 980 \\ \hline
1 & 6742 & 1135 \\ \hline
2 & 5958 & 1032 \\ \hline
3 & 6131 & 1010 \\ \hline
4 & 5842 & 982 \\ \hline
5 & 5421 & 892 \\ \hline
6 & 5918 & 958 \\ \hline
7 & 6265 & 1028 \\ \hline
8 & 5851 & 974 \\ \hline
9 & 5949 & 1009 \\ \hline Total & 60,000 & 10,000 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Number of images of different classes in MNIST-10 dataset.  
Classification Accuracy (_Acc_): Based on [26], we proposed to use the classification accuracy, which is as follows for multiclass classification:  
\[\text{Metric}:\text{ Accuracy }Acc=\frac{\sum\limits_{i=1}^{K}TP(C_{i,i})}{\sum \limits_{i=1}^{K}\sum\limits_{j=1}^{K}C_{i,j}} \tag{1}\]  
where \(TP(C_{i,j})\) indicates the number of true positive classified elements in class \(i\).  
Here we use a multiclass confusion matrix with dimension \(K\) *\(K\), where \(K\) is the number of different class labels, a \(C_{i,j}\) coefficients of confusion matrix [44].  
There is only one disadvantage to using this metric, which is that it has a significant discreteness of value, which is especially noticeable when using a small dataset. If there are 100 vectors in the test dataset, then the precision value is limited to two decimal places (e.g., 0.55, 0.62, 0.99). In this paper, we present two more classification metrics that evaluate the efficiency of the classification algorithm by analogy with regression problems. These precision values have many significant digits after the decimal point. Figure 2 is presented for clarification. There is a data vector in the output layer of the classifier \(Sout\), and a label vector in the training dataset \(L\). A Pearson correlation coefficient (\(p\)) (Equation (2)) or a determination coefficient (\(R^{2}\)) (Equation (3)) is calculated for each pair.  
\[\text{Pearson correlation coefficient}:\quad\rho=\frac{\sum\limits_{i=1}^{K} \left(L_{i}-\overline{L}\right)(Sout_{i}-\overline{Sout})}{\sqrt{\sum \limits_{i=1}^{K}\left(L_{i}-\overline{L}\right)^{2}}\sqrt{\sum\limits_{i=1}^ {K}\left(Sout_{i}-\overline{Sout}\right)^{2}}} \tag{2}\]  
\[\text{Determination coefficient }(\text{R2}):\quad R^{2}=1-\frac{\sum\limits_{i=1}^{K} \left(L_{i}-Sout_{i}\right)^{2}}{\sum\limits_{i=1}^{K}\left(L_{i}-\overline{ L}\right)^{2}} \tag{3}\]  
where \(\overline{L}\) mean value of vector \(L\), \(\overline{Sout}\) mean value of vector \(Sout\).  
Figure 2: An example of calculating the determination coefficient \(R^{2}\) and the Pearson correlation coefficient \(\rho\) for a database with 10 classes of the MNIST dataset (**a**) and the SARS-CoV-2-RBV1 dataset with binary classification (**b**).  
R2 Efficiency (\(R2E\)):  
The classification efficiency metric R2 Efficiency is proposed as an additional performance measure on this work. This is equal to the average \(R_{i}^{2}\) over all vectors in the testing dataset with the number of vectors \(M\).  
\[\text{Metric}:\text{ R2 Efficiency }R2E=\frac{\sum\limits_{i=1}^{M}R_{i}^{2}}{M} \tag{4}\]  
The more closely the \(Sout\) vector repeats the label vector \(L\), the closer R2 Efficiency is to 1.  
* Pearson Efficiency (\(PE\)):  
The Pearson Efficiency metric is proposed, which is equal to the average \(\rho_{i}\) for all vectors in the testing dataset.  
\[\text{Metric}:\text{ Pearson Efficiency }PE=\frac{\sum\limits_{i=1}^{M}\rho_{i}}{M} \tag{5}\]  
The more closely the \(Sout\) vector repeats the \(L\) label vector, the closer the Pearson Efficiency is to 1.  
As a result, NNetEn is equivalent to the value of one of the three types of metrics.  
\[\text{NNetEn}=\left\{\begin{array}{l}\text{Accuracy}\\ \text{R2 Efficiency}\\ \text{Pearson Efficiency}\end{array}\right. \tag{6}\]  
The metric type is an input parameter to the entropy function (see Section 2.4).