## 2 Description of the Proposed Method  
### Detection and Evaluation of the Stress in the Phonation Signal Based on the GMM Classifier  
The GMM-based classification works in the following way: the input data investigated are approximated by a linear combination of Gaussian probability density functions. They are used to calculate the covariance matrix as well as the vectors of means and weights. Next, the clustering operation organizes objects into groups whose members are similar in some way. The \(k\)-means algorithm determining the centers is used for GMM parameters initialization. This procedure is repeated several times until a minimum deviation of the input data sorted in \(k\) clusters \(S=\{S_{1},\,S_{2},\,\ldots,\,S_{k}\}\) is found. Subsequently, the iteration algorithm of expectation-maximization determines the maximum likelihood of the GMM [19]. The number of mixtures (\(N_{\text{MIX}}\)) and the number of iterations (\(N_{\text{ITER}}\)) have an influence on the execution of the training algorithm--mainly on the time duration of this process and on the GMM accuracy. The GMM classifier returns the probability/score (\(T\), \(n\))--for the model \(SM_{\text{n}}\) (\(n\)) corresponding to each of \(N\) output classes using the feature vector \(T\) from the processed signal. The normalized scores (in the range from 0 to 1) obtained in this way are further processed in the classification/detection/evaluation procedures. The proposed method uses partially normalized GMM scores obtained during the classification process for three output classes:  
* \(C_{\text{1N}}\) for the normal speech represented by a neutral state and emotions with positive valence and low arousal,
* \(C_{\text{2S}}\) for the stressed speech modeled by emotions with negative pleasure and high arousal,
* \(C_{\text{3O}}\) comprising the remaining two of six primary emotions (sadness having negative pleasure with low arousal and joy as a positive emotion with high arousal). The developed stress evaluation system analyzes the input phonation signal of five basic vowels (\"a\", \"e\", \"i\", \"o\", and \"u\") obtained from voice records together with the PPG signal sensed in \(M\) measuring phases \(MF_{1}\), \(MF_{2}\),... \(MF_{\text{M}}\). During the GMM classification we obtain \(M\) output matrices of normalized scores with dimension \(P\times N\), i.e., for \(P\) processed input frames of the analyzed phonation signal and for each of \(N\) output classes--see the block diagram in Figure 1. Then, the relative occurrence parameters \(RO_{\text{C1N},\,\text{C2S},\,\text{C3O}}\) [%] are calculated as partial winners of \(C_{\text{1N}}\), \(C_{\text{2S}}\), \(C_{\text{3O}}\) classes (with maximum probability scores) separately for each of the analyzed vowels recorded in the \(MF_{1}\) to \(MF_{\text{M}}\) measuring phases. Then, summary mean values of the \(C_{\text{1N}}\) and \(C_{\text{2S}}\) class occurrence percentage (\(\overline{RO_{\text{C1N}}}\), \(\overline{RO_{\text{C2S}}}\)) quantify differences between measuring phases. The stress factor in [%] is defined as  
\[L_{\text{STRESS}}\ (n)=\overline{RO_{\text{C2S}}}\ (n)-\overline{RO_{\text{C2S}}} \ (1)\ \ \ \text{for}\ 1\ \leq\ n\ \leq\ M \tag{1}\]This practically corresponds to the mean percentage occurrence for the \(C_{\text{2S}}\) class relative to the first recording phase as the baseline--which means \(L_{\text{STRESS}}\) (1) = 0. The same methodology is used for \(L_{\text{NORMAL}}\) [%] calculation  
\[L_{\text{NORMAL}}\ (n)=\overline{RO_{\text{CIN}}}\ (n)-\overline{RO_{\text{CIN}}}\ (1)\ \ \ \text{for}\ 1\ \leq\ n\ \leq\ M, \tag{2}\]  
which expresses changes corresponding to the normal speech type.