# Weighted Cluster-Range Loss and Criticality-Enhancement Loss for Speaker Recognition
## 4 Experiments and Results
### Results  
The speaker identification results on VoxCeleb1 in this work will be compared with the baselines listed in Table 6. Let the Residual (Res)-SA architecture with CRL in [9] be the major baseline. In the first experiment, the self-attention in [9] is replaced with our proposed dual-path attention, and we achieve a top-1 accuracy of 90.0% and top-5 accuracy of 96.3%. Next, to explore the effect of the weighted cluster-range loss, we keep \(\omega_{2}=1\) whilst experimenting with different \(\omega_{1}\). It turns out that when employing the Res-DA architecture, the best performance is achieved when \(\omega_{1}\) is 1.0004 with the top-1 accuracy being 92.0% and the top-5 accuracy being 97.6%. Besides, all the results of weighted cluster-range loss are better than that of cluster-range loss. The results of different \(\omega_{1}\) are listed in Table 7. To evaluate the criticality-enhancement loss, we replace the loss functions mentioned above with CEL+CRL. It turns out that better result is reached using the Res-SA architecture, with the top-1 accuracy being 90.8% and the top-5 accuracy being 97.0%. \begin{table}
\begin{tabular}{p{113.8 pt} p{284.5 pt}} \hline \hline
**Model** & **Description** \\ \hline i-vector + SVM [16] & This implementation of this method is accompanied by the release of the VoxCeleb1 dataset. \\ \hline i-vector/PLDA + SVM [16] & Most of this approach is the same as that of i-vector + SVM, and the only difference is that the PLDA score function is adopted. \\ \hline VGG-like CNN [16] & This approach employs a VGG-like CNN architecture and takes as input spectrograms of dimension 512 \(\times\) 300. \\ \hline VGG-like CNN + SA [8] & The biggest difference between this approach and the former is the employment of self-attention. \\ \hline ResNet-18-SA [8] & The frameworks in [8] extended two representative CNNs, i.e., VGG and ResNet, by the self-attention mechanism. There is only one self-attention layer in these two frameworks, and it is placed after the convolutional layers. The ResNet-18 + SA in this work achieves state-of-the-art performance. \\ \hline Res-SA + CRL [9] & This system integrates self-attention into the residual network. Besides, cluster-range loss was employed as the loss function in [9], which significantly improved the speaker identification performance. The biggest differences between this framework and our work are the attention block and the loss function. The superiority of our framework compared with Res-SA + CRL will be reported in Section 4.4. \\ \hline VGG-like CNN + CL [17] & [PERSON] et al. [17] proposed two VGG-like CNN architectures and named them Network-A and Network-B. Besides, their models were trained jointly using softmax loss and center loss (CL). For speaker identification, Network-B achieved the best performance in their work. \\ \hline ResNet-34 + LDE [18] & In this system, a Learnable Dictionary Encoding (LDE)-based pooling is combined with a ResNet-34 network. Similar to our work, they also employed 64-dimensional Filter-bank (Fbank) coefficients as the input feature. \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Different baselines for speaker identification. \begin{table}
\begin{tabular}{p{113.8 pt} p{284.5 pt} p{284.5 pt} p{284.5 pt}} \hline \hline
**Accuracy** & \(\omega_{1}\) & **Top-1\%** & **Top-5\%** \\ \hline Res-DA + WCRL & 1.0006 & 90.9 & 96.9 \\ Res-DA + WCRL & 1.0005 & 91.2 & 97.3 \\ Res-DA + WCRL & 1.0004 & 92.0 & 97.6 \\ Res-DA + WCRL & 1.0003 & 91.2 & 97.2 \\ Res-DA + CRL & 1.0000 & 90.0 & 96.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Speaker identification results on the VoxCeleb1 dataset with different \(\omega_{1}\) while keeping \(\omega_{2}=1\). WCRL, Weighted Cluster-Range Loss. When compared with the Res-SA architecture, by employing our dual-path attention module, the top-1 accuracy increases by 0.9% and the top-5 accuracy by 0.5%.