# Individualized Interaural Feature Learning and Personalized Binaural Localization Model +
## 5 Model Training and Interpretation
### Trained Model Interpretation  
Figure 4 shows the changes in feature selection because of different training conditions, by comparing the feature usage account. Given that the features with higher information gain are more likely to be selected as splitting features at each node, the usage account of a feature in the forest describes its dependency on the position estimation. It can be observed that, in the azimuth model trained with noise-free data, the more frequently used features are clustered at frequencies under 1 kHz, which correspond to the phase delays caused by the head width. However, in the model trained by a noisy dataset, the feature usage is more evenly distributed, which indicates that the model tends to use group delays between the ears for the estimation, which is because more features are necessary to a robust estimation with noisy training data. However, an opposite phenomenon is observed in the elevation model. With the decreasing of training data SNR, the more frequently used features are clustered to the frequency range around 3 to 5 kHz. This can be ascribed to the fact that more elevation information is generally drowned by the increasing noise, which cannot provide valid localization information. Such an adaptive selection process can only benefit the model performance when the noise is relatively low, which will diversify the feature usage and tree structures. However, when the noise is too strong and the most valuable features are degraded, the tree structures are homogenised and the robustness of the model will rapidly decrease.  
Figure 5 demonstrates the feature characteristics captured by the splitting values from the direction \([30^{\circ},45^{\circ}]\) and \([30^{\circ},135^{\circ}]\). In each sub-plot, each column shows the additive noise SNR for a training dataset and each row shows the type of features. Each blue circle represents a 'left' condition in a node from a single tree, which is also defined as the upper limit of \(v_{m,k}\) in (14). Similarly, each red cross represents a 'right' condition in a node or the lower limit value of \(v_{m,k}\). The ground truth features are plotted in black solid curves, which are obtained from pure HRTF data. Each marker, either a circle or cross, is considered a classifier to evaluate whether an extracted feature vector fits the conditions for a specific direction. By observing the distribution of markers, it again justifies that the features in frequency above 2 kHz are more valuable. The ground curves almost overlap with the dividing line between circles and crosses, which indicates that the major features have been captured by those upper and lower limits. In each row, the influence of the training condition can be compared. In the case where SNR = \(\infty\), though the curve fits best, the markers are distributed closer, which means that the independence between trees is comparably low, which may lead to over-fitting on some features. Meanwhile, in SNR = 10 dB, the markers are more dispersed and the dividing lines are blurred because of the high noise level, which will cause loss of some details of the feature characteristics, and lead to decreasing localization accuracy.  
Figure 3: OOB errors  
Figure 4: Feature Usage Accounts for training condition (**a**) \(\text{SNR}=\infty\); (**b**) \(\text{SNR}=20\) dB and (**c**) \(\text{SNR}=10\) dB. The first two columns shows the feature usage for azimuth model and the last two columns shows the average feature usage for elevation model.