## 4 Experiments and Results
### Results of Acoustic Data-Driven Subword Units  
We first confirmed the performance of the Pho-LTV-Kmeans units obtained by using the previous method [9]. Table 4 shows the performance of the units after increasing the number of clusters from 40 to 160. As a result, we confirmed the best performance in 120 clusters, as expected in the DB index comparison experiment. In the News, Web, and SPT evaluation data, the Pho-LTV-Kmeans-120 unit showed 15.9%, 8.9%, and 7.0% better performance than the phoneme unit. The performance presented in Table 4 has a higher overall WER than the performance presented in the previous study [9]. This is because, here, the number of decoding units in the language model is 1.8 million words, which is much larger than the 81 thousand words used in the previous study [9]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Units** & **AM** & **News** & **Web** & **SPT** \\ \hline \multirow{3}{*}{Grapheme-52} & CI-GMM-HMM & 39.6 & 59.1 & 92.9 \\  & CD-GMM-HMM & 23.4 & 35.3 & 74.9 \\  & CD-LSTM-HMM & 17.7 & 22.1 & 53.6 \\ \hline \multirow{3}{*}{Phoneme-40} & CI-GMM-HMM & 36.8 & 57.1 & 92.2 \\  & CD-GMM-HMM & 22.1 & 34.2 & 74.6 \\ \cline{1-1}  & CD-LSTM-HMM & **15.7** & **20.3** & **52.6** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Word error rate (%) of the grapheme unit and the phoneme unit. Table 5 shows the performance of the subword units derived from each method. Here, the number of subword units derived by each method was 120, which presented the best performance in the Pho-LTV-Kmeans experiments. As argued in a previous study [11], the Gra-MFCC-Tree-120 offers significantly better performance improvement than the grapheme unit. In addition, we observed that units derived from large amounts of speech data can achieve similar performance to a phoneme unit. In a previous study [11], the phoneme-like units performed more poorly than the phoneme units, but in our experiments, the Gra-MFCC-Tree-120 performed better than the phoneme units. This is due to our use of an LSTM-based AM, which was trained by about 1000 h of speech data, unlike the previous study, which used a GMM-based AM, trained by a small amounts of speech data. On the other hand, the Pho-MFCC-Tree-120, which is derived from the phoneme unit rather than the grapheme unit, showed higher performance than the Gra-MFCC-Tree-120. However, the Pho-MFCC-Tree-120 unit showed lower performance than the Pho-LTV-Kmeans-120 unit obtained by using segment-level latent vectors instead of the frame-level feature vectors. We finally confirmed the performance of the Pho-LTV-Tree-120 derived by using the proposed method. The proposed unit showed a relative performance improvement of 17.8% in the News evaluation data--similar to the AM training data--and a significant improvement of 11.1% and 8.9% in the Web and SPT evaluation data with different domains. Moreover, the proposed unit showed higher performance than the subword units derived by other methods. This is because, unlike previous studies [9; 11], we used segment-level vectors instead of frame-level vectors as samples for clustering and performed the decision tree-based clustering instead of k-means clustering. Table 5 shows the performance difference between the latent vectors and the feature vectors by comparing the performance between Pho-LTV-Tree-120 and Pho-MFCC-Tree-120. We can also observe the performance difference between k-means clustering and decision tree-based clustering by comparing the performance between Pho-LTV-Kmeans-120 and Pho-LTV-Tree-120. In the matched-pairs sentence segment word-error test using the National Institute of Standards and Technology Scoring Toolkit (SCTK) [36], the proposed method yielded a p-value less than 0.001 compared with other methods, including the 'Pho-LTV-Kmeans-120' method [9]. This justifies the statistical significance of the proposed method. As a result, we confirmed that the subword unit,