## 6 Experiment and Result Analysis  
### Evaluation Indicators of the Data-Derived Effect  
The model was evaluated by calculating the similarity between the generated data-set and the original data-set, and the performance effect of the model was evaluated from two perspectives: similarity of data distribution and correlation of different dimensions. (1) KL divergence Kullback-Leib (KL) divergence, also known as relative entropy, is a metric used to measure the similarity of two probability distributions, can used to express the difference or similarity between two distributions, and is calculated as follows:  
\[D_{KL}(P||Q)=\sum_{i}P(x_{i})\log\frac{P(x_{i})}{Q(x_{i})} \tag{4}\]  
The smaller the KL divergence, the higher the similarity between \(P\) and \(Q\). (2) Mean Cosine Similarity  
Cosine similarity (CS) is the cosine value of the angle between two n-dimensional vectors in n-dimensional space, which is equal to the dot product (vector product) of the two vectors divided by the product of the length (size) of the two vectors. The cosine similarity between n-dimensional vectors \(A\) and \(B\) is calculated as follows: \begin{table}
\begin{tabular}{c c} \hline
**Network Layer** & **Network Layer Structure** \\ \hline
1 & One-dimensional convolution (convolution kernel:16, Step:1) \(\rightarrow\) \\  & Relu activation \(\rightarrow\) Normalization \(\rightarrow\) Maximum pooling \\
2 & One-dimensional convolution (convolution kernel:3, Step:1) \(\rightarrow\) \\  & Relu activation \(\rightarrow\) Normalization \(\rightarrow\) Maximum pooling \\
3 & One-dimensional convolution (convolution kernel:3, Step:1) \(\rightarrow\) \\  & Relu activation \(\rightarrow\) Maximum pooling \\
4 & One-dimensional convolution (convolution kernel:3, Step:1) \(\rightarrow\) \\  & Relu activation \(\rightarrow\) Maximum pooling \\
5 & One-dimensional convolution (convolution kernel:3, Step:1) \(\rightarrow\) \\  & Maximum pooling \\
6 & Flatten the layer \(\rightarrow\) Random inactivation (50\%) \(\rightarrow\) Fully Connected (Relu) \\
7 & Fully Connected (Relu) \(\rightarrow\) (Reu) Random inactivation (50\%) \\
8 & SoftMax fully connected layer \\ \hline \end{tabular}
\end{table} 
Table 2: Network structure. Figure 7: AlexNet network model structure. \[\text{Similarity}(A,B)=\frac{A\bullet B}{\|A\|\times\|B\|}=\frac{\sum\limits_{i=1 }^{n}{(A_{i}\times B_{i})}}{\sqrt{\sum\limits_{i=1}^{n}{A_{i}}^{2}\times\sqrt{ \sum\limits_{i=1}^{n}{B_{i}}^{2}}}} \tag{5}\]  
In this paper, the cosine similarity between the original data-set and the generated data-set of the same category is calculated, the average cosine similarity is calculated cumulatively, and the data similarity is evaluated by the mean cosine similarity, which is calculated as follows:  
\[\overline{Similarity}=\frac{\sum\limits_{i=1}^{m}{\sum\limits_{j=1}^{n}{Similarity(RAW_{i},GEN_{j})}}}{m\times n} \tag{6}\]  
where \(RAW_{i}\) is the \(i\)th indicator vector of the original data and \(GEN_{i}\) is the \(i\)th indicator vector of the generated data. The value of \(\overline{Similarity}\) ranges from [-1,1], with \(-1\) being completely different and \(1\) being completely similar. (3) Cumulative deviation of the correlation coefficient  
The correlation coefficient is a statistic proposed by the statistician [PERSON] to measure the degree of linear correlation between two random variables. It is defined as the covariance of two variables divided by the product of their standard deviations as follows:  
\[\rho_{X_{i},X_{i}}=\frac{E[(X_{i}-E(X_{i}))(X_{j}-E(X_{j}))]}{\sqrt{E[(X_{i}-E (X_{i}))(X_{j}-E(X_{j}))]E[(X_{j}-E(X_{j}))(X_{i}-E(X_{i}))]}} \tag{7}\]  
The correlation coefficient matrix of the original dataset and the generated dataset is calculated, and then the cumulative deviation of the correlation coefficient of the generated dataset relative to the original dataset is calculated by Equation (8).