# An Analysis of the Short Utterance Problem for Speaker Characterization +
## 5 Experiments & Results
### Reduction of the Mismatch in a: Phonetic Balance  
In our previous analysis we hypothesized two main sources of degradation in short utterances: The one due the uncertainty in the phoneme estimations \(G_{i}(\mathbf{A})\) and another term caused by mismatches in the phoneme distribution \(\boldsymbol{\alpha}\). In order to test our hypothesis we are going to minimize the errors due to phoneme distribution \(\boldsymbol{\alpha}\). To do so we have prepared an extra dataset, named as **Short Balanced**. This dataset is also obtained from the original data released by the organization. From each original utterance we obtain phoneme labels, one per input feature vector. These phoneme labels in this experiment were obtained by automatic means, that is, a DNN phoneme classifier [35] consisting of a Wide Residual Network [36] with four blocks. Only 39 phoneme labels were considered, that is, each phoneme label includes all its associated coarticulation. Experiments carried out in TIMIT [37] show error rates around 15% in the classification task. The phoneme labels in an utterance determine its phoneme distribution. This distribution, obtained from the long utterance, must be maintained in the new short utterance despite its lower \begin{table}
\begin{tabular}{l c c} \hline \hline
**Scenario** & **EER(\%)** & **MinDCF** \\ \hline Long-Long & 3.25 & 0.16 \\ Long-Short Random & 5.67 & 0.27 \\ Short-Short Random & 8.57 & 0.40 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results, EER (%) and minDCF of SRE10 “coreext-coreext det5 female” experiment with the three scenarios of interest: Long-Long, Long-Short and Short-Short. length. Therefore, given the length of the new short utterance we can determine the newer number of samples per phoneme. Then we randomly choose this number among the all the samples with a certain phoneme, repeating the process for all phonemes. Frames must be considered speech by our VAD to be candidate for the new utterances. For comparison reasons each Short Balanced utterance contains as many samples as in the Short Random counterpart. The comparison between both types of short utterances is shown in Table 2. The comparison includes the results in the Long-Short and Short-Short scenarios. This information is complemented with the Detection Error Tradeoff (DET) curves in Figure 5, where we also include the Long-Long scenario for comparison reasons. According to the shown results, the new Short Balanced dataset is able to behave much better than the Short Random dataset, despite containing both datasets the same amount of speech. This is because the phonetic balance with respect to the original utterance also reduces the distance between enrollment and test phoneme distributions \(\mathbf{\alpha}\). Therefore, we get rid of this source of error, only remaining those errors due to the phoneme estimations \(G_{i}(\mathbf{A})\). We have also realized that the degradation due to the phonetic distribution mismatch is much more relevant than those related with the uncertainty of the estimations \(G_{i}(\mathbf{A})\). In order to obtain a better understanding we analyze the already obtained results in terms of the type of trial: target and non-target. This study compares the KL2 distance between enrollment and test with respect to the probability of error in each population. In this work the KL2 distance measures how the responsibility distributions for enrollment and test utterances match each other. The obtained results are shown in Table 3. This analysis is performed for the experiments Long-Long, Short-Short Random and Short-Short Balanced. Besides, we study the impact of the KL2 to the classification error in target and non-target trials, that is, the Miss and False Alarm error terms. The decision threshold is set up according to the operating point defined by the evaluation.