## 4 Experimental Results and Analysis
### Verification for Automatic Language Identification Using R-Vector
#### 4.3.2 Analysis of Computation Complexity  
As mentioned in Section 3.2, we expect the proposed R-vector-based approach allows LID operating directly on user devices that have limited hardware resources. For this reason, we compared our approach with the conventional approaches in terms of computation complexity. We used two measures for the comparison: the number of parameters required in a training phase and computational intensity regarding a testing phase. Table 10 summarizes the results analyzed on the basis of a two-class LID task.  
As known commonly, the CNN-based approach requires the highest number of parameters and computational intensity. As addressed in Figure 9, the CNN-based LID processes seven layers including three layers for feature extraction, three layers for classification, and one layer for softmax. The overall number of parameters to be estimated is calculated as 198,912, comprising 1792 parameters in feature extraction layers (\(64\times 4+128\times 4+256\times 4\)), 196,608 parameters in classification layers (256 \(\times\) 256 \(\times\) 3), and 512 parameters in softmax layers (256 \(\times\) 2). The more that the size of convolution filters or the number of layers increases, the more the number of parameters. In terms of computational intensity, the CNN-based LID requires about 500,000 computations which are obtained by considering the filter size, the number of input channels, and the input size. Feature extraction layers need 315,392 computations (\(64\times 13\times 64+128\times 64\times 16+256\times 128\times 4\)), and classification layers and a softmax layer conduct 197,120 computations (\(256\times 256\times 3+256\times 2\)).  
In the i-vector-based approach, the number of parameters depends on the number of UBM mixtures, the dimension of the input feature, and the i-vector dimension. When using 128 mixtures, 13-dimensional MFCCs, and 10-dimensional i-vectors, the total number of parameters is calculated as 39,936 = \(128\times 13+128\times 169+128\times 13\times 10\). During recognition, 19,968 computations are required: 3328 for UBM processing and 16,640 for i-vector processing.  
Finally, the R-vector-based approach has the lowest computation complexity. A dominant processing of this approach is to construct GMMs used for consonantal and vocalic intervals. In this study, 13-dimensional GMM mixtures were optimally defined. Thus, the number of parameters is only \(2366=13\times 13+13\times 169\), and the computational intensity is regarded as 345 computations consisting of \(338=13\times 13\times 2\) for interval detection and 7 for R-vector estimation.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Number of Parameters** & **Computational Intensity** \\ \hline CNN & 198,912 & 512,512 \\ i-vector & 39,936 & 19,968 \\ R-vector & 2366 & 345 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Computation complexity of LID approaches for a two-class LID task.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Baseline Approaches** & **ER (\%)** & **Proposed Approaches** & **ER (\%)** \\ \hline CNN & 65.16 & R-vector with SVM & 66.80 \\ i-vector & 65.41 & R-vector with i-vector & 65.66 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Performance (Error Rate (ER)) of three-class LID experiments on the 2011 NIST LRE test set.