# An Analysis of the Short Utterance Problem for Speaker Characterization +
## 5 Experiments & Results
### Entrollment-Test Distance versus Log-Likelihood Ratio (LLR)  
Our previous experiments reveal the relationship between the relative distance in terms of phonetic content between enrollment and test utterances and the performance of these trials. Thus, we explore the impact of this distance in the performance.  
For this analysis we opt for the Short-Short scenario. The test role in each evaluation is always played by an utterance from the Short Random dataset. Regarding the enrollment role, we have created the following pool of data, with multiple candidate utterances for each trial:  
* The Short Random dataset experiment previously analyzed.
* Three alternative Short Random datasets. We chop the released original utterances in segments of the range 3-60 s of speech but now the chops are not totally random. They are restricted to differ from the test utterance in the trial a controlled KL2 value. These goal values for the distances are approximately 2, 3 and 4 nats.
* Short Equalized dataset. We equalize the original enrollment utterance to obtain a null relative distance between enrollment and test. By doing so we choose from the enrollment only those contents present in the test utterance and in the same proportion. The amount of audio is the same in both enrollment and test utterances.  
This large data pool allows the analysis of the relationship between enrollment-test relative distance and score. The results are visible in Figure 6. We present a boxplot of the log-likelihood ratio score in terms of the distance in bins of 2 nats. Three values per bin are shown: the mean of the scores, the mean plus the standard deviation of scores and the mean minus the standard deviation of scores. He have differentiated between non-target trials and target trials for a better understanding.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Experiment**} & \multicolumn{2}{c}{**KL2 Distance (nats)**} & \multicolumn{2}{c}{**Population Error (\%)**} \\ \cline{2-5}  & **Target** & **Non-Target** & **Target** & **Non-Target** \\ \hline Long-Long & 1.06 & 1.74 & **28.43** & 0.06 \\ Short-Short Random & 3.62 & 4.61 & 80.40 & **0.01** \\ Short-Short Balanced & 2.55 & 3.47 & 40.79 & 0.03 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Kullback Leibler (KL) distance and Error (%) for both target and non-target trials in experiments Long-Long, Short Short Random and Short-Short Balanced. Error estimated at National Institute of Standards and Technology (NIST) operating point.  
Figure 6 confirms our previous conclusions. First, the score of target trials is strongly influenced by the relative phoneme distance between enrollment and test. The lower the distance, the higher is the score for the target trials. By contrast, non-target trials are almost insensitive to this distance. Their score remain steady for almost all the analysis. In conclusion, degradation is mainly caused by target trials, which strongly depend on the KL2 metric. However, Figure 6 indicates something more. Non-target trials keep stable for almost all the distance range except for low values (0-2 nats), where the score increases. The very high phonetic similarity between enrollment and test utterances increases their log-likelihood ratio despite these trials do not contain the same speaker.