# Regularized Within-Class Precision Matrix Based PLDA in Text-Dependent Speaker Verification
## 5 Experiments
### Results  
We first evaluated the EERs of the proposed method only with the i-vector, which satisfies the prerequisite (close-to-diagonal within-class covariance matrix) of the GLASSO-PLDA. Figure 5 displays the EERs on the validation trials of the RSR 2015 part 1 (Figure 5a) and part 2 (Figure 5b). The dashed red line depicts the EERs of the original PLDA (corresponding to the baseline), and the solid blue line depicts the EERs of the GLASSO-PLDA (corresponding to the proposed method). We confirmed that the GLASSO converged in all conditions, and the performances were improved with the proposed method. The same trend also can be observed in the evaluation trials. Figure 6 reveals the EERs on the evaluation trials of the RSR 2015 part 1 (Figure 6a,c) and part 2 (Figure 6b,d). Except for the interval of the regularization parameter \(\rho>0.0535\) on the male evaluation trials of RSR 2015 part 2 (Figure 6b), the proposed method also demonstrated performance improvements on the evaluation trials. Therefore, the proposed GLASSO-PLDA can improve the performance by detecting the optimum (sparse within-class precision matrix) when the sparse assumption of the true within-class precision matrix holds, and the prerequisite is satisfied. Figure 5: The equal error rates (EERs) (%) of the probabilistic linear discriminant analysis (PLDA) (dashed red line) and graphical least absolute shrinking and selection operator (GLASSO)-PLDA (solid blue line) according to \(\rho\) on the validation trials of the (**a**) RSR 2015 part 1 and (**b**) RSR 2015 part 2 datasets. Figure 6: The EERs (%) of the PLDA (dashed red line) and GLASSO-PLDA (solid blue line) according to \(\rho\) on the evaluation trials of the RSR 2015 part 1 and part 2 datasets: (**a**) male trials of the part 1, (**b**) male trials of the part 2, (**c**) female trials of the part 1, and (**d**) female trials of the part 2. Next, we performed experiments using deep speaker embeddings, which generally do not satisfy the prerequisite of the GLASSO-PLDA. Figure 7 lists the EERs of the validation trials of RSR 2015 part 1 for the (a) d-vector, (b) r-vector, and (c) x-vector. The dashed red line depicts the EERs of the original PLDA, and the solid blue and green lines depict the EERs of the GLASSO-PLDA and PCA-GLASSO-PLDA, respectively. Unlike for the i-vector, the GLASSO did not converge because the within-class covariance/precision matrices of all deep speaker embedding are far from diagonal. For this reason, the GLASSO-PLDA demonstrated performance degradation for all deep speaker embeddings, as mentioned in Section 4. In contrast, the GLASSO with PCA converged by making the within-class covariance/precision matrix close to diagonal. As a result, the PCA-GLASSO-PLDA displayed performance improvements for all deep speaker embeddings in all the conditions. The same trends can be observed in the evaluation trials of RSR 2015 part 1 (Figure 8), the validation trials of RSR 2015 part 2 (Figure 9), and the evaluation trials of RSR 2015 part 2 (Figure 10). There are no EER graphs of the GLASSO-PLDA for the x-vector on the trials of RSR 2015 part 2 (there is no solid blue line in Figures 9c and 10c,f), due to the failure of the estimation of the GLASSO-PLDA model caused by the failure of GLASSO regularization. These results indicate that the GLASSO-PLDA can improve performance when the within-class covariance/precision matrix is close to diagonal. Tables 1 and 2 summarize the EERs of the baseline and proposed methods for each embedding on RSR 2015 parts 1 and 2, respectively. The proposed method is the GLASSO-PLDA for the i-vector and the PCA-GLASSO-PLDA for deep speaker embeddings. For the proposed method, the regularization parameter \(\rho\) was set to that of the lowest EER of the validation trials.