# Deep Learning-Based Low-Frequency Passive Acoustic Source Localization
## 4 Results
### Case 2
#### 4.2.3 Discussion  
For the monopole source, the prediction accuracy of the model for both source frequencies was very high when the number of classes was less (20), and decreased gradually as the number of classes increased. Between the two source frequencies, the model performed better at the higher frequency. The small size of the input image (CSM) significantly reduced the network size and the parameters to be optimized, hence the model trained very quickly. At the same time, a small input reduced the scope of learning as we were very limited in the number of convolution and pooling layers that we could apply. A consequence of this is the drop in performance as the problem becomes more complex. Fewer convolution layers means that the network cannot learn deeper and more abstract features of a complex problem, resulting in potentially overfitting and a decrease in the accuracy of prediction. This can be seen in Table 3. While the model can give good results in this case, when the number of classes \(N\) is small, the drop-off in performance is stark as \(N\) increases. This is a clear limitation of the CSM as an input feature with few microphones.  
In the case of the sinusoidal plane wave source (Table 4), the GCC map allowed us to obtain an appropriately sized input feature. At the same time, selectively picking the portion of the GCC feature map containing the essential information helped keep the input size in check to save computational time and resources.  
Comparing the accuracy values for source frequencies 100 Hz and 300 Hz in Table 4 with those obtained for the monopole source (Table 3), it is evident that the model displays a  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Classes (N)** & **Class Size** & **Accuracy (\(\theta\), 10 Hz)** & **Accuracy (\(\theta\), 100 Hz)** & **Accuracy (\(\theta\), 300 Hz)** \\ \hline
20 & 9\({}^{\circ}\) & \(\approx\)84\% & \(\approx\)97\% & \(\approx\)98\% \\ \hline
30 & 6\({}^{\circ}\) & \(\approx\)76\% & \(\approx\)96\% & \(\approx\)97\% \\ \hline
45 & 4\({}^{\circ}\) & \(\approx\)63\% & \(\approx\)95\% & \(\approx\)96\% \\ \hline
60 & 3\({}^{\circ}\) & \(\approx\)52\% & \(\approx\)93\% & \(\approx\)95\% \\ \hline
90 & 2\({}^{\circ}\) & \(\approx\)40\% & \(\approx\)89\% & \(\approx\)93\% \\ \hline
180 & 1\({}^{\circ}\) & \(\approx\)20\% & \(\approx\)79\% & \(\approx\)86\% \\ \hline \end{tabular}
\end{table}
Table 4: Accuracy values for a test set of 10,000 samples for a sinusoidal plane wave source. The accuracy (for 100 Hz and 300 Hz) is higher and the drop-off in model performance as \(N\) increases is gradual as compared with the monopole source, thus highlighting the superiority of GCC as an input feature in this case.  
superior performance with the GCC input feature, which is again down to the difference in the input size. The model can thus learn much better with GCC as the input. This highlights the advantage of using a time-domain input feature (GCC) as opposed to a frequency-domain feature (CSM) for detecting very low source frequencies when the number of microphones is limited. For the infrasound source, the accuracy for smaller class sizes can be improved with more training. An accuracy value greater than 60% for 45 classes for an infrasound source in the presence of noise shows the robustness and reliability of GCC as an input feature.