## 4 Experiments and Results
### Acoustic Data-Driven Subword Units  
This section describes the seven subword units obtained in the previous and proposed methods. Table 1 shows the based-units, clustering samples, and clustering methods for deriving each unit. As the subword unit, we first used the grapheme units of Table 1(a). The Korean language is written in Hangul, a syllabic unit character that consists of initial, medial, and final sounds. Here, Hangul creates 11,172 (= 19 \(\times\) 21 \(\times\) (27 + 1)) syllables by combining 19 initial consonants, 21 medial vowels, and 27 final consonants (including no final consonant). The total number of unique letter units that have eliminated duplicate consonants from the initial and final consonants is 52 (including silence). In this paper, we call the unique letter units the grapheme units. The phoneme units of Table 1(b), on the other hand, typically consist of 40 phonemes, including silence. Here, the phoneme unit is derived from a grapheme-to-phoneme converter [33; 34] and has acoustically high discrimination despite having a smaller number than the grapheme units. However, the phonemes in spontaneous \begin{table}
\begin{tabular}{l l c c} \hline \hline
**Subword Unit** & **Based-Unit** & **Clustering Samples** & **Clustering Method** \\ \hline (a) Grapheme-52 & Grapheme & - & - \\ (b) Phoneme-40 & Phoneme & - & - \\ (c) Pho-LTV-Kmeans-120 [9] & Phoneme & Latent vectors & k-Means \\ (d) Gra-MFCC-Tree-120 [11] & Grapheme & MFCC vectors & Decision tree \\ (e) Pho-MFCC-Tree-120 & Phoneme & MFCC vectors & Decision tree \\ (f) Pho-LTV-Tree-120 (_proposal_) & Phoneme & Latent vectors & Decision tree \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of the subword units obtained in the various methods. speech still possess acoustically ambiguous units. In Korean consonants, the phonemes /_b/l_, /_d_, and /_g_/ are a typical set of similar consonants, and their corresponding double-consonants, /_b_\({}^{h}\)/_, /_t_\({}^{e}\)/, and /_k_\({}^{f}\)/, also have similar sounds. In Korean vowels, the phonemes /_e_/ and /_e_/ are the two most similar vowels. Note that ordinary Koreans usually do not distinguish the two phonemes /_e_/ and /_e_/ in daily life. Next, we extracted the Pho-LTV-Kmeans-120 units of Table 1(c) using the method proposed in a previous study [9]. This previous study first extracted fixed-length latent vectors from broadcast data in the same way we proposed in Section 3. Then, the authors used the k-means clustering algorithm and built a new phoneme set by gathering the clustered vectors. On the other hand, our study used decision tree-based clustering instead of k-means clustering. This clustering method is the main difference between the proposed method and this previous study [9], where the number of clusters (_k_) was determined by speech recognition experiments. On the other hand, in this paper, we selected the optimal number of clusters using the Davies-Bouldin (DB) index [35], which is an evaluation measure of the clustering algorithm. Here, the DB index is calculated using Equations (6-8) below:  
\[DB=\frac{1}{N}\sum_{i=1}^{N}\max_{j\
eq i}\frac{S_{i}+S_{j}}{M_{i,j}} \tag{6}\]  
\[S_{i}=\left(\frac{1}{T_{i}}\sum_{j=1}^{T_{i}}\left|x_{j}-\mu_{i}\right|^{2} \right)^{\frac{1}{2}} \tag{7}\]  
\[M_{i,j}=\left\|\mu_{i}-\mu_{j}\right\|_{2}=\left(\sum_{k=1}^{n}\left|\mu_{k,i }-\mu_{k,j}\right|^{2}\right)^{\frac{1}{2}} \tag{8}\]  
In Equation (6), \(S_{i}\) is a measure of scatter within the _i_-th cluster, and \(M_{i,j}\) is a measure of cluster separation between the _n_-dimensional _i_-th cluster and the _j_-th cluster. Here, the measure of scatter (\(S_{i}\)) is denoted as in Equation (7) and indicates the average distance between the _j_-th latent vector \(x_{j}\) and the centroid \(A_{i}\) in the _i_-th cluster with \(T_{i}\) latent vectors. The measure of separation (\(M_{i,j}\)) is denoted as in Equation (8) and indicates the distance between centroid \(A_{i}\) of the _i_-th cluster and centroid \(A_{j}\) of the _j_-th cluster.