# The Domain Mismatch Problem in the Broadcast Speaker Attribution Task
## 4 Methodology
### Clustering and Assignment: The Indirect Assignment Approximation  
One of the great limitations of the previous alternative is the robustness of embeddings when obtained from a low amount of audio [56]. Thus, decisions based on more audio should be more reliable.  
Thus, the next approach, the indirect assignment, straightforwardly follows the diagram block described in Figure 2, also applying the speaker recognition identity assignment block. The functionality of the system is described in Figure 5. Similarly to the direct assignment block, we obtain the embeddings \(\mathbf{\Phi}\) according to the segments estimated from the given audio. However, compared to the direct assignment alternative, this system performs clustering prior to the assignment stage. Afterwards, the identity assignment subtask is performed similarly to the direct assignment approach but with an important difference: While in its predecessor system, the score \(s_{ij}\) compared the embedding \(j\) with the enrolled identity \(i\), but in this new version, \(s_{ij}\) compares all embeddings assigned to the cluster \(\mathcal{C}_{j}\) with the \(i\)th speaker of interest. Again, we consider the calibration subset \(\mathbf{\Phi}_{\text{calib}}\) role to be played by the development subset. This learned calibration is then used with the test subset. Figure 6 shows the flowchart for this approximation.  
Figure 4: Flowchart of the direct assignment approach. Red and yellow boxes, respectively, represent the embedding extraction pipelines for the evaluation audio \(\Omega\) (online) and enrollment audios \(\Omega_{\text{emph}}\) (offline). The obtained embeddings (\(\mathbf{\Phi}\) and \(\mathbf{\Phi}_{\text{emph}}\)) are taken into account in the identity assignment block.  
Figure 5: Diagram of the indirect assignment approach. Embeddings from the audio are first clustered during diarization (\(\mathbf{\mathcal{C}_{1}}\),...,\(\mathbf{\mathcal{C}_{3}}\)). Then, clusters are assigned to the available identities, either the enrolled speakers or the unknown generic cluster (red arrow).  
Our system starts with the embedding extraction from the audio under analysis \(\Omega\) (red box). This process involves a feature extraction of the audio followed by its segmentation (VAD and SCPD stages) and finally the embedding estimation. The estimated embeddings are fed into the clustering block to obtain the diarization labels. Meanwhile, enrollment audios \(\Omega_{entroll}\) undergo a similar embedding extraction pipeline. Then, the identity assignment block is responsible for estimating the final labels according to all the estimated information, i.e., the two sets of embeddings as well as the diarization labels.  
The choice for clustering addition implies a tradeoff: While clustering may boost the system performance, it increases the computational cost and also adds a potential performance degradation due to cluster impurities. Regarding other decisions, as a design choice, we do not exclude the assignment of multiple diarization clusters to a single enrolled speaker. This decision is made under the assumption that we can fix diarization errors.