## 6 Results
### Speaker Tracking  
The application of RBM vectors was further extended to a speaker tracking task. For speaker change detection and segmentation, 20 MFCC features were extracted for all the _small segments_ using a Hamming window of 25 ms with 10 ms shift. We performed segmentation using different sizes of small segments, that is, the \(d\) parameter discussed in Section 4.1 was equal to 2, 2.5 and 3 s. The value of \(\Delta\) was set to 0.25 s. The speech parts smaller than \(d\) were not considered in these experiments and were simply discarded. Figure 5 shows the graph of FAR against MDR for different values of \(d\) and \(\alpha\). The results were computed, accepting a tolerance (collar) of \(\pm\)0.25 s in the position of detected speaker change points. We experimented with different values of d in order to see the behaviour at different working points, that is, \(d=2,2.5\) and 3 s. Then, we experimented with different values of \(\alpha\) and the results are plotted in Figure 5. From the Figure it is clear that the best choice for \(d\) is a 3 s window. The MDR for this window is not very sensitive to alpha as compared to the other window sizes. This is because in our experiments, the segments less than the selected window size were discarded. Thus the segments have longer durations, which have strong boundaries with the neighbouring segments as compared to a window size of 2 and 2.5 s. A strong boundary is not very likely to be missed by the system. That is why, when we vary \(\alpha\), the MDR does not vary a lot and thus the MDR  
Figure 4: Comparison of Impurity Trade-off (IT) curves for the proposed RBM vectors with i-vectors. Different dimensions of RBM vectors are evaluated using different scoring and linkage algorithms for clustering. The dimensions of i-vectors and RBM vectors are given in parenthesis. seems to be insensitive. On the other hand, if the window size is small, the segments have weak boundaries with the neighbour segments and are relatively more likely to be missed by the system. Our actual working point is marked as a black circle which is obtained for \(\alpha=2\) (in Equation (7)). We performed the _final segmentation_ at this point which has less Miss Detection (MDR) as compared to False Alarm (FAR). At this point, a FAR of 10% and MDR of 7.8% are achieved. There is a trade-off between the two metrics (FAR and MDR). One can decrease one of the metrics at the cost of increasing the other. The segments generated in the speaker segmentation were then tested against the target speakers for the tracking task. Table 2 shows the results of speaker tracking for different lengths of RBM vector in terms of Equal Error Rate (EER). In this case EER was the coinciding point between FA and MST. The second column of Table 2 shows the comparison of RBM vector with the baseline i-vectors using cosine scoring. We fixed the length of i-vectors to 800 as a conclusion of the speaker clustering experiments. It is observed that, as the length of the RBM vector is increased, the performance is improved. The best EER of 3.30% was obtained using 2000 dimensional RBM vector, which gained a relative improvement of 11.76% as compared to the baseline 800 dimensional i-vectors. Increasing the dimensions of the RBM vectors does not affect the computational costs of training the models. The dimensions of RBM vectors are only controlled by the number of components while applying PCA to the RBM supervectors, as discussed in Section 2.3  
The third column of Table 2 shows the comparison of the RBM vector with the baseline i-vectors using the PLDA scoring method. For the RBM vector/PLDA framework, the PLDA is trained using the background RBM vectors for 15 iterations. The number of eigenvoices are set to 350, 450 and \begin{table}
\begin{tabular}{c c c} \hline \hline
**Approach** & **EER\% (Cosine)** & **EER\% (PLDA)** \\ \hline i-vector (800) & 3.74 & 2.97 \\ RBM vector (600) & 4.33 & 3.57 \\ RBM vector (800) & 4.03 & 3.47 \\ RBM vector (2000) & 3.30 & 2.74 \\ \hline \hline \end{tabular}
\end{table}