# A Simple Unsupervised Knowledge-Free Domain Adaptation for Speaker Recognition
## 6 Conclusions  
This paper explores the issue of domain mismatch in speaker verification tasks based on deep embedding networks. We hypothesize that the primary problem in domain mismatch lies not in the decrease in speaker discriminability, but instead of the presence of systematic distortions in the embedding space such as shifting, rotation, and scaling.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Method** & **EER(\%)** & **minDCF (\(P_{tar}\) = 0.05)** \\ \hline Pretrain & 14.22 & 0.5137 \\ \hline Global Shift & 11.48 & 0.4351 \\ +Rotation (1 st) & 11.48 & 0.4351 \\ ++Scaling & 10.66 & 0.4122 \\ ++Rotation (2 nd) & 10.66 & 0.4122 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Performance after each stage of the C-LDA operations.  
In light of this assumption, we propose a distribution normalization approach using a full-rank LDA and train it in an unsupervised manner by using pseudo labels produced by hierarchical clustering. We term this method as C-LDA. Theoretical analysis shows that C-LDA when combined with cosine scoring, can compensate for global shift and scaling on within-class covariance.  
Our experiments were conducted using VoxCeleb2 as the source-domain dataset and CN-Celeb1 as the target-domain dataset, which contains multiple genres and represents a multi-domain adaptation test scenario. The results highlight that C-LDA achieves an EER of 10.66% on the CN-Celeb1 evaluation set, without any knowledge of the source model and any human labels for the target data. This performance surpasses that of most of the compared front-end and back-end adaptation methods. In more detailed experiments, it was found that C-LDA shows even more performance superiority to single-domain tests where the adaptation data is limited. Importantly, C-LDA is not sensitive to the settings of the clustering algorithm, making it highly suitable for practical usage. All these findings strongly support our distributional distortion assumption and underscore C-LDA as a vital tool to tackle the domain-mismatch problem.  
Future work involves investigating scenarios with serious domain mismatch, such as the singing genre in our test. For these scenarios, the distributional distortion assumption may not hold and linear compensation could fail. We have seen this trend in our experiment, where self-supervised learning for the front-end model achieves better performance than C-LDA and other adaptation methods. Dedicated research is required to study what happens in the embedding space before designing the solution. Another area of research is to investigate frame-level compensation rather than embedding-level compensation. Visualization tools are important to understand the behavior of the features, and layer-by-layer compensation is considered.  
Conceptualization, W.L., L.L. and D.W.; Methodology, W.L., L.L. and D.W.; Validation, W.L.; Formal analysis, W.L.; Resources, L.L. and D.W.; Writing--original draft, W.L.; Writing--review & editing, L.L. and D.W.; Visualization, W.L.; Supervision, L.L. and D.W.; Funding acquisition, L.L. and D.W. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China (NSFC) under Grants No.62171250/62301075 and also the Fundamental Research Funds for the Central Universities of China.  
Not applicable.  
The data presented in this study are openly available in VoxCeleb2 at [[https://doi.org/10.1016/j.csl.2019.101027](https://doi.org/10.1016/j.csl.2019.101027)]([https://doi.org/10.1016/j.csl.2019.101027](https://doi.org/10.1016/j.csl.2019.101027)), reference number [49] and in CN-Celeb1 at [[https://doi.org/10.1109/ICASSP40776.2020.9054017](https://doi.org/10.1109/ICASSP40776.2020.9054017)]([https://doi.org/10.1109/ICASSP40776.2020.9054017](https://doi.org/10.1109/ICASSP40776.2020.9054017)), reference number [50].  
The authors declare no conflicts of interest.