## 3 Experimental Results and Discussion
### Results and Discussion of Deep Learning Models
In the case of 11 classes, Table 8 shows that our proposed model has the best accuracy at 0.9600, and its corresponding standard deviation is 0.0056; the second best is GoogleNet 1, with an accuracy of 0.9324 and the smallest standard deviation of 0.0026. The worst model for our FBIs is Xception 1, with an accuracy of 0.6551 and the largest standard deviation of 0.0180. In the case of 21 classes, Table 9 shows that our proposed model also has the best accuracy at 0.9370 and its corresponding standard deviation is 0.0063; the second best is also GoogleNet 1 with an accuracy of 0.9266 and the smallest standard deviation at 0.0046. The worst model for our FBIs is also Xception 1, with an accuracy of 0.6410 and the largest standard deviation at 0.0498. Similar to machine learning models, it is expected that the case of 21 classes is generally worse than the case of 11 classes. Based on the same FBIs, five deep learning models (except for Xception 1) on 11 classes are better than the best accuracy of 0.814 (SVMs) from four machine learning models, where the only feature of the estimated Hurst exponents was considered. In the other case of 21 classes, six deep learning models are all better than the best accuracy of 0.56 (SVMs) from four machine learning models. When training time is important, our proposed model is also the first choice. Tables 10 and 11 shows that the training times of 11 classes and 21 classes are 1.41 and 2.71 min, respectively. In addition, these two tables also show the time ratios of other models to our model. The second efficient model is GoogleNet 1, with 4.15 and 8.54 min for 11 classes and 21 classes. The worst efficient model is Xception 2 with 664.21 and 1352.69 min for 11 classes and 21 classes. \begin{table}
\begin{tabular}{p{113.8 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline
**Group of Layers** & **Number of Group** & **Number of Groups** & **Number of Layers** & **Sizes or Number of Filters (Sizes of Convolutional Layers)** \\ \hline an image input layer & 1 & 1 & 1 & 32 \(\times\) 32 \(\times\) 1 \\ \hline a convolutional layer + a batch & & & & \\ normalization layer + a ReLU layer + a maximum pooling layer (2 \(\times\) 2) & & & & 128 (3 \(\times\) 3) + 128(5 \(\times\) 5) + 128 (7 \(\times\) 7) + 128 (9 \(\times\) 9) + 128 (11 \(\times\) 11) \\ \hline a convolutional layer + a batch & & & & \\ normalization layer + a ReLU layer & 3 & 1 & 3 & 128 (13 \(\times\) 13) \\ \hline a fully connected layer + a ReLU layer & 2 & 1 & 2 & 10 times 11 or 21 (Output size of a fully connected layer) \\ \hline a fully connected layer + a softmax layer + a classification layer & 3 & 1 & 3 & 11 or 21 (Output size of a fully connected layer) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The number of layers for our proposed model. \begin{table}
\begin{tabular}{p{113.8 pt} p{56.9 pt} p{56.9 pt}} \hline \hline
**Models** & **Mean** & **Std.** \\ \hline Our model & 0.9600 & 0.0056 \\ AlexNet 2 & 0.8943 & 0.0101 \\ GoogleNet 1 & 0.9324 & 0.0026 \\ GoogleNet 2 & 0.9085 & 0.0091 \\ Xception 1 & 0.6551 & 0.0180 \\ Xception 2 & 0.8940 & 0.0092 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The mean and standard deviation of classification rates of four deep learning models for 11 classes. \begin{table}
\begin{tabular}{p{113.8 pt} p{56.9 pt} p{56.9 pt}} \hline \hline
**Models** & **Mean** & **Std.** \\ \hline Our model & 0.9370 & 0.0063 \\ AlexNet 2 & 0.8358 & 0.0109 \\ GoogleNet 1 & 0.9266 & 0.0046 \\ GoogleNet 2 & 0.8515 & 0.0142 \\ Xception 1 & 0.6410 & 0.0498 \\ Xception 2 & 0.8918 & 0.0127 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The mean and standard deviation of classification rates of four deep learning models for 21 classes. To further analyze the distribution of the incorrectly classified classes, we show two promising models--our proposed model and GoogleNet 1--for discussion.