# Individualized Interaural Feature Learning and Personalized Binaural Localization Model +
## 2 Individualized Feature Selection Using Mutual Information
### Spatial Feature Learning and Selected Feature Vector  
Algorithm 1 describes the MI-based spatial feature learning mechanism used in the remainder of this work. Given an estimated noise level, such as using the method proposed in [29], the spatial feature vector \(\mathbf{v}\) and its corresponding MI in (9) are computed for a set of training speech signals. Figure 2 illustrates the variation of the MI between spatial cues and elevation angle with and without noise, and indicates the changing nature of the importance of individual spatial cues. The error bar reflects the MI variation on different azimuth planes, and the mean MI obtained for the training speech dataset is used thereafter to create a rearranged spatial feature vector \(\mathbf{v}^{\prime}\).  
Figure 1: Mutual Information between the spatial cues and the elevation for a range of azimuths, frequencies and noise conditions.  
Figure 2: MI variation in spatial cues with respect to SNR.  
```
Step 1: Estimate the noise power \(\mapsto\sigma^{2}\). Step 2: Evaluate \(\mathcal{I}_{\theta}(\mathbf{v};\mathbf{\varphi})\); Mutual Information of spatial cues. foreach\(\varphi\) in the HRTF datasetdo foreach\(s(t)\) in the training speech datasetdo  Compute \(X_{i,k}(f_{h})\) for a simulated noise power \(\sigma^{2}\).  Calculate the corresponding \(v_{\mu}\) and \(\mathbf{v}\).  Estimate \(\mathcal{I}_{\theta}(\mathbf{v};\mathbf{\varphi})\).  end foreach Result: Obtain the set of \(\mathcal{I}_{\theta}(\mathbf{v};\mathbf{\varphi})\) for a noise power \(\sigma^{2}\). Step 3: Learn the optimal combination of the spatial cues in \(\mathbf{v}\).  Calculate a mean MI \(\forall\)\(\varphi\) from \(\mathcal{I}_{\theta}(\mathbf{v};\mathbf{\varphi})\). for\(l^{\prime}\gets 1\)to \(2L\)do  Rearrange \(\mathbf{v}\) in descending order of \(\mathcal{I}_{\theta}(v_{\mu};\mathbf{\varphi})\). foreach\(\mathbf{v}\) derived from the training speech datasetdo  Estimate the source location \(\varphi\) from a feature vector \(\mathbf{v}\) of length \(l^{\prime}\).  Calculate the angular localization error of \(\varphi\).  end foreach Result: Obtain \(\mathbf{v}^{\prime}\); the rearranged and selected spatial feature vector from \(\mathbf{v}\), that corresponds to the minimum mean angular localization error.
```  
**Algorithm 1**Spatial feature learning for robust localization  
To arrive at \(\mathbf{v}^{\prime}\), an optimal number of spatial cues to be used in the localization process \(l^{\prime}\) is computed. The average angular localization error, obtained from the estimated source location \((\theta,\varphi)\) and its estimate \((\hat{\theta},\hat{\varphi})\), is used as a metric to determine the optimal \(l^{\prime}\). This results in a set of spatial feature vectors, \(\mathbf{v}^{\prime}(\theta,\varphi)\), applicable to the specified noise level (in the case of some practical applications, it is also possible to pre-train the system for a set of known, approximate noise conditions). The spatial cues extracted from the received signals are rearranged similarly, and the resultant feature vector \(\hat{\mathbf{v}}^{\prime}\) and the \(\mathbf{v}^{\prime}(\theta,\varphi)\) reference features are used to calculate vector distance for localization [25]. The localization performance will be presented in Section 6.