# Efficient Open-Set Recognition for Interference Signals Based on Convolutional Prototype Learning
## 5 Performance Analysis
### Comparison of Different Methods  
The openness [35] of dataset Jamming-N is defined as:  
\[\textit{Openess}=1-\sqrt{\frac{2\times N}{N+K}} \tag{27}\]  
where the total number of classes is \(K\), and the known number of classes is \(N\). Figure 8: OSR performance of the HCPL using different feature extractors. (**a**) The classification accuracy of HCPL using three feature extractors. (**b**) AURoc of HCPL using three feature extractors. Figure 9: Variance of AURoc using different feature extractors. In this part, we compare the OSR performances of Softmax [26], GCPL [22], CG-Encoder [1], HCPL-CNN and HCPL-HAFRNet. Note that Softmax and GCPL use the CNN shown in Figure 6b as the feature extractor, and the training strategy follows the proposed method. Softmax has no hyperparameters in the loss function, while the weight parameters for the generative loss of GCPL is set as 0.1, which can get the best performance in the simulation through many parameter adjustment experiments. The network structure, parameter setting and training strategy of CG-Encoder are as follows [1]. The OSR experiments results of the above five algorithms on three different openness datasets: Jamming-3, Jamming-5 and Jamming-7 are shown in Figure 10.  
As shown in the three diagrams of accuracy of Figure 10, HCPL-HAFRNet has the best classification accuracy of the known classes, which is 2-7% higher than the other methods under different openness and JNR = \(-\)10 dB, while the accuracy of the other methods is close, and all of them increase with the increase of the JNR. When the JNR is in the range of \(-\)10 dB to 5 dB, the accuracy of all five methods increases with the increase of the openness; this is because, when the total number of classes is fixed, the larger the openness is and the  
Figure 10: OSR performance of different methods under different openness. (**a**) The classification accuracy and AUROC using dataset Jamming-3, (**b**) the classification accuracy and AUROC using dataset Jamming-5 (**c**) the classification accuracy and AUROC using dataset Jamming-7. less the classification error source is. When JNR > 5 dB, the accuracy of all five methods is close to 100%. It can be seen from the three diagrams of AUROC of Figure 10 that HCPL-HAFRNet has the best rejection performance of the unknown classes; this is because it uses the HDAM to enhance the information of critical time points and channels and ignore unimportant information. When JNR > 0 dB, the performance of CG-Encoder on different openness datasets is second only to that of HCPL-HAFRNet, but it is much worse than that of the other methods under low JNR. The HCPL-CNN performs better than GCPL under different openness and various JNR, because the HCPL-CNN constrains the closed space to a hypersphere, while all prototypes are on the hypersphere, i.e., sample features of the known classes are clustered far from the interior of the feature space and leaving space for the unknown classes. The GCPL outperforms Softmax, because it enhances the intraclass compactness and interclass separability of the sample features by prototype loss. Except for Softmax, the performances of the remaining methods increase with the increase of JNR under different openness, and the performances are saturated when JNR > 5 dB. Therefore, when JNR is between 10 dB and 18 dB, the average AUROC is defined as the rejection performance plateau of the unknown classes, and the effect of openness on the performance plateau for the four methods is shown in Table 2.  
From Table 2, it can be seen that the rejection performance plateau of the HCPL-HAFRNet is higher than those of CG-Encoder under different openness, except for Jamming-2. The performance plateau of CG-Encoder is higher than those of the HCPL-CNN and GCPL, but the network of CG-Encoder has 7,259,881 parameters, which is more than 14 times HCPL-CNN and GCPL.