# A Simple Unsupervised Knowledge-Free Domain Adaptation for Speaker Recognition
## 4 Experiments
### Main Results
#### 4.3.3 Embedding vs. Back-End  
Although complex back-end scoring models such as PLDA have faded in most speaker recognition systems, we still compare some representative back-end adaptation methods with C-LDA, to gain further insight into the merit of the proposal. Table 4 presents the comparative results between C-LDA/S-LDA and several representative PLDA adaptation methods. In all these methods, the pre-trained front-end model is frozen and is used to extract the embedding vectors. The PLDA adaptation methods considered in the comparative study are listed below. 1. **Supervised PLDA (S-PLDA)**: PLDA re-trained with CNC1.dev, the development data for the target domain, using the genuine speaker labels. 2. **Adaptive PLDA (A-PLDA)**: An off-the-shelf unsupervised PLDA adaption approach provided by [PERSON] [56]. It estimates the change in the between-speaker and within-speaker covariance by the change on the _total covariances_ from the source domain to the target domain. Note that no speaker labels are required. 3. **CORAL+**[23]: An unsupervised PLDA adaption method, with the idea of distribution alignment between the source and target domain. This approach has shown better performance than several competitive approaches [23]. Figure 2: Embeddings produced by the pre-trained model and the models with different adaptation methods. The pictures are plotted by t-SNE. Each point represents an utterance and each color represents a speaker. The utterances are randomly selected from CNC1.eval. * **Clustering PLDA (C-PLDA)**: The same as S-PLDA, except that the speaker labels are pseudo labels produced by clustering. It is the probabilistic version of C-LDA. Note that C-PLDA does not require the parameters of the source-domain PLDA, so it is knowledge-free, just like C-LDA. The experimental results are shown in Table 4, which involves several interesting observations as follows. Again, we only refer to the EER results in the discussion. * All the embedding and back-end adaptation methods outperform the baseline result without any adaptation (14.22%), demonstrating the efficiency of these methods. * In all the methods, S-PLDA shows the best performance (9.57%). This result is close to the one obtained with front-end fine-tuning (9.50%). It indicates that the PLDA model, if well-trained in the target domain, can effectively solve the domain mismatch problem. * C-LDA (10.66%) vs. C-PLDA (10.11%) and S-LDA (9.75%) vs. S-PLDA (8.87%): It can be observed that C-PLDA performs better than C-LDA, and S-PLDA outperforms S-LDA. This is expected as PLDA scoring utilizes the between-class information and conducts minimum-risk Bayesian decision [57]. * C-LDA (10.66%) vs. S-LDA (9.75%) and C-PLDA (10.11%) vs. S-PLDA (8.87%): This comparison indicates that using pseudo labels produced by clustering leads to inferior performance compared to using the genuine labels; however, compared to the baseline result, the improvement with the cost-free pseudo labels is highly significant. We also note that the disparity between C-LDA and S-LDA (10.66% vs 9.75%) is smaller compared to that between C-PLDA and S-PLDA (10.11% vs 8.87%). This seems to indicate that _LDA relies less on the accuracy of speaker labels compared to PLDA_; thus, it is more suitable for unsupervised learning. We hypothesize that this is because LDA does not need an accurate between-class covariance while PLDA does need one. * C-PLDA (10.11%) vs. A-PLDA (10.86%) vs. CORAL+ (10.54%): All these three methods are unsupervised and are based on PLDA back-end. It shows that C-PLDA performs significantly better than the other two PLDA-based back-end adaptation methods, although it does not require any knowledge of the source-domain PLDA parameters. This further strengthens the evidence that _the pseudo labels generated by the clustering algorithm convey reasonable speaker-related information and can be used to train a strong PLDA model_.