## Experiments
### Feature-Level Fusion of I-Vector and Latent Variable  
In this subsection, we tested the features obtained by augmenting the conventional i-vector with the mean and variance of the latent variable extracted from the proposed VAE. For performance comparison, we applied the following six different feature sets:  
* _I-vector(400)_: standard 400-dimensional i-vector;
* _I-vector(600)_: standard 600-dimensional i-vector;
* _LM+LV_: concatenation of the 200-dimensional latent variable mean and the log-variance, resulting in a 400-dimensional vector;
* _I-vector(200)+LM_: concatenation of the 200-dimensional i-vector and the 200-dimensional latent variable mean, resulting in a 400-dimensional vector;
* _I-vector(200)+LV_: concatenation of the 200-dimensional i-vector and the 200-dimensional latent variable log-variance, resulting in a 400-dimensional vector;
* _I-vector(200)+LM+LV_: concatenation of the 200-dimensional i-vector and the 200-dimensional latent variable mean and log-variance, resulting in a 600-dimensional vector. As seen from Table 2 and Figure 6, the augmentation of the latent variable greatly improved the performance in all the tested cases. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Class. Err. (\%)** & **EER (\%)** & **DCF08** & **DCF10** \\ \hline _i-vector_ & 12.62 & **3.36** & **2.00** & **0.07** \\ _Autoencode_ & 24.59 & 6.06 & 2.69 & 0.09 \\ _Classify_ & 40.01 & 8.13 & 4.21 & 0.10 \\ _Proposed_ & **11.89** & 3.61 & 2.09 & 0.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of results between using the i-vector and the mean latent variables extracted from VAEs trained for different tasks. Class. Err. : classification error; DCF08: minimum NIST SRE 2008 DCF; DCF10: minimum NIST SRE 2010 DCF; EER: equal error rate. Figure 5: DET curves of the speaker verification experiments using the i-vector and the mean latent variables extracted from VAEs trained for different tasks. By using only the mean and log-variance of the latent variable together (i.e., _LM+LV_), a relative improvement of 24.25% was achieved in terms of EER, compared to the conventional i-vector with the same dimension (i.e., _i-vector(400)_). The concatenation of the standard i-vector and the latent variable mean (i.e., _i-vector(200)+LM_) also improved the performance. Especially in terms of EER, _i-vector(200)+LM_ achieved a relative improvement of 33.58% compared to _i-vector(400)_. This improvement may be attributed to the non-linear feature extraction process. Since the latent variable mean is trained to encode the various variability within the distributive pattern of the given utterance via a non-linear process, it may contain information that is not obtainable from the linearly extracted i-vector. Thus, by supplementing the information ignored by the i-vector extraction process, a better representation of the speech can be obtained. The best verification and identification performance out of all the 400-dimensional features (i.e., _i-vector(400)_, _LM+LV_, _i-vector(200)+LM_, and _i-vector(200)+LV_) was obtained when concatenating the standard i-vector and the latent variable log-variance (i.e., _i-vector(200)+LV_). _I-vector(200)+LV_ achieved a relative improvement of 38.43% in EER and 34.94% in classification error compared to _i-vector(400)_. This may have been due to the capability of the latent variable variance of capturing the amount of uncertainty, which allows the decision score to take advantage of the duration dependent reliability. Concatenating the standard i-vector with both the mean and log-variance of the latent variable (i.e., _i-vector(200)+LM+LV_) further improved the speaker recognition performance. Using the _i-vector(200)+LM+LV_ achieved a relative improvement of 55.30% in terms of EER, compared to the