## 6 Conclusions  
In this paper, a novel unsupervised deep-learning model-based utterance-level feature extraction for speaker recognition was proposed. In order to capture the variability that has not been fully represented by the linear projection in the traditional i-vector framework, we designed a VAE for GMM adaptation and exploited the latent variable as the non-linear representation of the variability in the given speech. Analogous to the standard VAE, the proposed architecture is composed of an encoder and a decoder network, where the former estimates the distribution of the latent variable given the Baum-Welch statistics of the speech and the latter generates the ideal GMM supervector from the latent variable. Moreover, to take the uncertainty caused by short duration speech utterances into account while extracting the feature, the VAE is trained to generate a GMM supervector in such a way  
Figure 8: DET curves of the speaker verification experiments using various score-level fusions of the conventional i-vector and the mean and log-variance of the latent variable extracted from the proposed VAE.  
\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 \\ _LM_ & 11.89 & 3.61 & 2.09 & 0.07 \\ _LV_ & 17.78 & 4.65 & 2.57 & 0.08 \\ _i-vector+LM_ & 7.03 & 2.63 & 1.63 & **0.06** \\ ine _i-vector+LV_ & 7.39 & 2.76 & 1.69 & **0.06** \\ _LM+LV_ & 10.26 & 3.50 & 2.02 & 0.07 \\ _i-vector+LM+LV_ & **5.75** & **2.49** & **1.57** & **0.06** \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of results between various score-level fusions of the conventional i-vector and the mean and log-variance of the latent variable extracted from the proposed VAE.  
as to maximize the likelihood. The training stage of the proposed VAE uses a likelihood-based error function instead of the conventional reconstruction errors (e.g., cross-entropy).  
To investigate the characteristics of the features extracted from the proposed system in a practical scenario, we conducted a set of random-digit sequence experiments using the TIDIGITS dataset. We observed that the variance of the latent variable generated from the proposed network apparently demonstrated the level of uncertainty which gradually decreased as the duration of the speech increased. Additionally, using the mean and variance of the latent variable as features provided comparable performance to the conventional i-vector and further improved the performance when used in conjunction with the i-vector. The best performance was achieved by feature-level fusion of the i-vector and the mean and variance of the latent variable.  
In our future study, we will further develop training techniques for the VAE not only to maximize the likelihood but also to amplify the speaker discriminability of the generated latent variable.  
Conceptualization, W.H.K. and N.S.K.; Funding acquisition, N.S.K.; Investigation, W.H.K.; Methodology, W.H.K.; Supervision, N.S.K.; Writing--original draft, W.H.K.; Writing--review and editing, N.S.K.  
This work was supported by Samsung Research Funding Center of Samsung Electronics under Project Number SRFC-IT1701-04.  
The authors declare no conflict of interest.