## 4 Conclusions  
This paper proposed three new speaker recognition methods: LSTM-MFCC-TL, BLSTM-MFCC-TL, and BLSTM-MFCCAE-TL. First, we combined LSTM with MFCC features and used the triplet loss function to propose the LSTM-MFCC-TL method. The cluster training method proposed in this paper was introduced in detail and was used to improve triplet loss training and prediction in environments with poor hardware equipment. We then proposed the BLSTM-MFCC-TL method based on the LSTM-MFCC-TL method combined with the BLSTM model, and the speaker recognition accuracy was improved. It was also confirmed that the accuracy of using the BLSTM model training for speaker recognition is better than that of using the LSTM model. The third method proposed in this study was based on the BLSTM-MFCC-TL method combined with a pretrained AE to extract AE features, yielding the BLSTM-MFCCAE-TL method. Although the BLSTM-MFCCAE-TL method required more computation time than the BLSTM-MFCC-TL method without adding AE features, it achieved better accuracy. After the three proposed methods were trained for 20 epochs, the LSTM-MFCC-TL method achieved an accuracy of 89.07%. The BLSTM-MFCC-TL method achieved 91.18% validation set accuracy. The BLSTM-MFCCAE-TL method achieved a validation accuracy of 93.08%. The AE architecture used in this paper is primarily based on reference [16], so we also adopted this architecture for experimental comparison. Since the research in [16] was conducted for denoising word recognition, we adapted the architecture described in [16] to develop a GMM-HMM-MFCCAE method specifically for speaker recognition to compare the training effectiveness. The GMM-HMM-MFCCAE method achieved a validation accuracy of 64.48%. The average computation times for the LSTM-MFCC-TL, BLSTM-MFCC-TL, BLSTM-MFCCAE-TL, and GMM-HMM-MFCCAE methods were 0.2698 s, 0.3856 s, 0.4052 s, and 1.5286 s, respectively. From the results, it can be observed that the accuracy of the BLSTM model is 2.11% higher than that of the LSTM model. This indicates that the BLSTM is able to better capture the features \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Epoch** & \multicolumn{2}{c}{**LSTM-MFCC-TL**} & **BLSTM-MFCC-TL** & **BLSTM-MFCCAE-TL** \\ \hline
20 th & Train accuracy & 91.49\% & 93.68\% & 96.01\% \\  & Validation accuracy & 89.07\% & 91.18\% & 93.08\% \\ \hline
40 th & Train accuracy & 91.50\% & 94.22\% & 97.39\% \\  & Validation accuracy & 89.36\% & 91.38\% & 94.17\% \\ \hline
60 th & Train accuracy & 94.68\% & 96.64\% & 98.06\% \\  & Validation accuracy & 91.80\% & 93.69\% & 94.78\% \\ \hline
80 th & Train accuracy & 95.30\% & 97.06\% & 98.49\% \\  & Validation accuracy & 92.70\% & 94.10\% & 95.03\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Speaker recognition accuracy comparison table of the three proposed methods at the 20 th, 40 th, 60 th, and 80 th epoch. of the speaker. The BLSTM-MFCCAE-TL method, which combines MFCC features and AE features, achieves a 1.9% improvement in speaker identification accuracy compared to the BLSTM-MFCC-TL method. Moreover, our proposed three methods outperform the reference framework's GMM-HMM-MFCCAE method in terms of speaker identification accuracy. In terms of computation time, the BLSTM-MFCCAE-TL method requires some additional processing time due to the inclusion of AE features, but it yields good learning performance. However, compared to the reference architecture GMM-HMM-MFCCAE method, the proposed three methods all demonstrate better computation efficiency. In the experiments of our BLSTM-MFCCAE-TL method, we have demonstrated that incorporating speaker encodings into AE features can effectively enhance speaker identification accuracy. Finally, the performances of our proposed methods outperform the performances of the traditional GMM-HMM-MFCCAE method in terms of computation time and speaker identification accuracy. Conceptualization, Y.-L.C. ; methodology, Y.-L.C. and N.-C.W. ; software, J.-F.C. and R.-Q.L. ; validation, J.-F.C., N.-C.W. and R.-Q.L. ; formal analysis, Y.-L.C. and N.-C.W.