## 3 Research Methodology
### Evaluation Metrics for Monolingual and Bilingual Speech Recognition  
#### 3.1.1 Word Error Rate and Character Error Rate  
English speech recognition systems predominantly employ the WER as a yardstick to evaluate performance [49; 50]. WER quantifies the discrepancies between the system-generated transcription and the reference transcript by measuring word substitutions, deletions, and insertions. Expressed as a percentage of the total words in the reference transcript, a lower WER signifies higher system accuracy. This metric is widely recognized for its simplicity, intuitiveness, and comprehensive evaluation of ASR performance, encompassing both individual word accuracy and overall transcript quality.  
WER is instrumental in benchmarking different speech recognition systems and monitoring their performance improvements over time. On the other hand, the CER is the preferred performance evaluation metric for Mandarin speech recognition. Mandarin ASR systems typically utilize modeling units such as phonemes, characters, and words, whereas English ASR systems often rely on phonemes, international phonetic symbols, and subwords. When comparing a Mandarin ASR transcript to a reference, CER measures character-level discrepancies, including substitutions, deletions, and insertions. This metric is particularly suited to Mandarin due to its unique character-based writing system and distinct linguistic structure. Consequently, while WER is ideal for evaluating English ASR systems, CER is more appropriate for assessing the performance of Mandarin ASR systems. The WER/CER is calculated as follows:  
\[WER/CER=\frac{S_{W/C}+D_{W/C}+I_{W/C}}{N_{W/C}}. \tag{1}\]  
Here, \(S_{W/C}\), \(D_{W/C}\), and \(I_{W/C}\) represent the numbers of word/character substitutions, deletions, and insertions, respectively, while \(N_{W/C}\) is the total number of words/characters in the reference. Both WER and CER can be calculated using the Levenshtein distance (LD) method, also known as the edit distance algorithm, introduced by [PERSON] in 1965 [51]. This approach defines the minimum number of edits needed to transform one string into another, providing a robust framework for evaluating ASR performance across different languages and systems. The edit distance of two strings \(a\) and \(b\) can be mathematically expressed as follows:  
\[lev_{a,b}(i,j)=\left\{\begin{array}{ll}max(i,j)&\text{if}\min(i,j)=0,\\ \\ min\left\{\begin{array}{ll}lev_{a,b}(i-1,j  
case is reached. The final result, \(lev_{|a||,|b|}\), is the total edit distance between the entire strings \(a\) and \(b\). This distance measures how many edits (insertions, deletions, or substitutions) are needed to change the hypothesis sequence into the reference sequence.  
For each transcribed word, we compute the LD, which measures the differences between two strings in terms of substitutions, deletions, and insertions [51]. This distance metric is widely used in linguistic research, such as for assessing phonetic distances between languages and language varieties [52; 53]. In the context of speech recognition, LD serves as a metric for evaluating the phonetic distance between the ground truth and the generated transcriptions, thereby providing a comprehensive measure of system accuracy.