## 4 Experimental Results and Analysis
### Verification for Automatic R-Vector Extraction  
First, we verified the efficiency of automatically extracted R-vector comprising seven rhythm metrics (%V, \(\Delta\)V, \(\Delta\)C, Varco-V, Varco-C, nPVI-V, and rPVI-C). To investigate the efficiency of each element of R-vector, we employed the Linear Mixed Effects (LME) model approach that is useful for analyzing data that are non-independent, multilevel, or correlated. As the speech files of each language corpus are recorded repeatedly by speakers, extracted R-vectors may contain variations of individual speakers. The LME considers this as a random effect and concentrates on checking the discriminability of each metric without the random effect by estimating a random effect via a maximum likelihood technique. Each metric is fit to the LME using the 'nlme' provided as an R package [33]. In this process, each metric is set as a predictor variable, and a language code is set to a response variable. Then, the speaker information is established to a random effect. The following equation is an example code for fitting %V in the LME model. \[Model=lme(\%V\text{-}LANG,\,random=\text{-}1|SPK,\,data=DB,\,method=\"ML\")\]  
The results of verification based on the LME for each corpus are presented as a table and a boxplot. Tables provide the level of significance according to the number of asterisk marks along with a code of a language giving the higher value than its counterpart. The overall tendency of distribution of each metric value can be observed in the boxplot figures, in which the x-axis and y-axis denote the languages and the values of each metric. Each boxplot gives five components: the 1 st, 2 nd, 3 rd, 4 th quantile, and a median value as a middle line. In addition, dots outside the box are outliers. First, we examined the efficiency of R-vector for English and Korean using the SiTEC corpus. As indicated in Table 3, all metrics are capable of discriminating Korean from English significantly, mostly giving three asterisk marks. In most metrics, a language indicating the higher value than the other language showed a similar rhythmic direction introduced in previous linguistics studies such as [12] and [30], excluding Varco-V and nPVI-V, in which Korean was selected as a language giving the higher values. In fact, the two metrics convey insufficient language property, as they indicated relatively low significance levels. Figure 6 describes the results of distribution of rhythm metrics for English and Korean. Although there exist overlapped quantiles for two languages, most metrics indicated a significant distance for median values between the languages, giving characteristics discriminating languages. It is interesting to observe that two metrics (Varco-V and nPVI-V) that indicated different tendencies from previous linguistics studies in the significance results (Table 3) showed highly overlapped quantiles and similar median values. The metrics also exhibited significant outliers compared to other metrics, thus giving few discriminative characteristics. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**SiTEC Corpus**} & \multicolumn{3}{c}{**Mozilla Corpus**} \\ \hline LANGUAGE & English & Korean & Chinese & Spanish & English \\ CODE & EN & KO & CN & SP & EN \\ Number of UTTERANCES & 4902 & 4906 & 6234 & 6225 & 6226 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Description of speech corpora used for evaluation. SiTEC: Speech information TEchnology & industry promotion Center. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **\%V** & **\(\Delta\)V** & **\(\Delta\)C** & **Varco-V** & **Varco-C** & **nPVI-V** & **rPVI-C** \\ \hline \(>1\) & KO & KO & EN & KO & EN & KO & EN \\ Sig. 2 & *** & *** & *** & *** & *** & *** & *** \\ \hline \hline \end{tabular}  
* A language with the higher value than the other. 2 Significance levels: \(<\)0.001 ***, \(<\)0.01 ***, \(<\)0.05 *.  
\end{table} 
Table 3: Significance results with Linear Mixed Effects (LME) for English and Korean.