## 4 Experiments and Discussion
### Validation of Proposed Voice Trigger Approach
#### 4.2.2 Results and Discussion
While learning the CNN-based models, we empirically set other hyperparameters as follows: batch size of input features, 800; learning rate, 0.001; and number of epochs, 500. The entire learning process was executed using the Pytorch framework [38]. Table 2 presents the trigger word detection results of five participants in terms of EER. All approaches demonstrated much better performance compared to the results shown in Table 1 because they were evaluated on clean speech data in this experiment. The CNN-based method slightly outperformed the proposed approach for most participants, providing approximately 1% relative improvement. Next, we investigated the detection accuracy for each trigger word. As shown in Figure 15, the CNN method provided better accuracy compared to the MMSE-based approach. However, the performance gap differed according to the trigger words. For the \"Charlie\" trigger word, the proposed approach missed only three utterances compared to the CNN-based approach. As confirmed in Figure 14, this result demonstrates different performance according to trigger words, e.g., \"Charlie\" and \"alpha\" provided better accuracy than the other trigger words. The experimental results for the two approaches indicate that the CNN-based approach provides relatively reliable performance; however, the difference is not significant. Although more sophisticated approaches employing DNNs have been reported to improve the correctness of trigger word detection, such computationally intensive algorithms would be highly inefficient on a user device that continuously monitors incoming speech signals and determines if the signals are trigger words. To consider the difference between the two approaches in terms of computational complexity, we attempted to analyze \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Approach**} & \multicolumn{5}{c}{**Equal Error Rate (\%)**} \\ \cline{2-7}  & **Priticipant1** & **Particip2** & **Particip3** & **Particip4** & **Particip5** & **Average** \\ \hline CNN-based & 4.32 & 3.76 & 4.93 & 7.29 & 4.68 & 4.99 \\ Proposed & 5.78 & 5.12 & 4.84 & 8.61 & 5.43 & 5.96 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: EER (%) of trigger word detection. Figure 15: Detection accuracy of each trigger word. the number of parameters required in the training phase and the quantity of computation required during the decoding phase. Table 3 summarizes the results. CNN-based approaches require a number of parameters and have high computational intensity. As shown in Figure 11, the CNN-based detection processes seven layers (i.e., three layers for feature extraction, three layers for classification, and one layer for softmax). The overall number of parameters to be estimated was calculated as 199,936, including 1792 parameters in the feature extraction layers (\(64\times 4+128\times 4+256\times 4\)), 196,608 parameters in the classification layers (\(256\times 256\times 3\)), and 1536 parameters in the softmax layer (\(256\times 6\)). Note that the number of parameters increases with increasing numbers of convolution filters and layers. In terms of computational intensity during the decoding phase, the CNN-based model required greater than 500,000 computations, which were obtained by considering filter size, the number of input channels, and the input size. The feature extraction layers required 315,392 computations (\(64\times 13\times 64+128\times 64\times 16+256\times 128\times 4\)), and the classification and softmax layers performed 198,144 computations (\(256\times 256\times 3+256\times 6\)). In the proposed approach with statistic modeling (e.g., the HMM), the parameters to be estimated during the training phase comprise the mean and variance of each GMM in each state and a transition probability matrix. When trained with a sufficient number of HMM parameters, eight states and 32 GMMs could handle utterances passing through the duration filtering process.