## 2 Description of the Proposed Method
### Creation of Gaussian Mixture Models for Pleasure-Arousal Classes  
The proposed evaluation method is based on the determination and statistical analysis of distances between originals (from a speaker) and the tested synthetic speech in the P-A space with the help of the GMM classifier. The data investigated are approximated  
Figure 1: 2D diagram of emotion distribution in the P-A space and corresponding quadrant categorization with importance weights.  
by a linear combination of Gaussian probability density functions [25]. They are used to calculate the covariance matrix as well as the vectors of means and weights. Next, the clustering operation is performed to organize objects into groups whose members are similar in some way. Two basic algorithms may be used in this clustering process:  
1. \(k\)-means clustering--dividing the objects into \(k\) clusters so that some metric relative to the centroids of the clusters is minimized,
2. spectral clustering--finding data points as nodes of a connected graph and partitioning this graph into sub-graph clusters based on their spectral decomposition [26].  
In practice, for initialization of the GMM model parameters the \(k\)-means algorithm determining the centers is usually used--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 is used to determine the maximum likelihood of the GMM. 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 accuracy of the output GMMs obtained.  
The preparation as well as evaluation phases begin with the analysis of the input sentences yielding various speech/sound properties. Four types of signal features are determined in the proposed system: time duration, prosodic, basic spectral and supplementary spectral parameters. The analyzed signal is processed in overlapping segments. The determined pitch (F0) contour can be divided into \(N\) voiced parts and \(N+1\) unvoiced parts of various durations to obtain different types of time duration (TDUR) features [27]. Apart from the TDUR features, the contours of F0 and signal energy are used to determine standard prosodic (PROS) parameters. Other types of signal features are spectral features (SPEC1), computed using the spectral and cepstral analysis of each input frame, and spectral high-level statistical parameters (SPEC2). The representative statistical values (median, range, standard deviation--std, relative maximum and minimum, etc.) of these features compose the input vector of \(N_{\text{FEAT}}\) features for GMM processing. The speech and non-speech sounds are used for the creation and training of the output GMM models specified by the number of Pleasure classes \(N_{\text{FC}}\) and Arousal classes \(N_{\text{AC}}\)--see the block diagram in Figure 2.  
During the classification process, the input vectors from the analyzed sentence are passed to the GMM classifier block to obtain the scores (\(T\), \(m\)) that are subsequently  
Figure 2: Block diagram of the preparation phase—creation and training of GMMs for P-A classes.  
quantized to discrete levels corresponding to \(N_{\text{PC}}/N_{\text{AC}}\) output P-A classes. This approach is carried out for each of M frames of the analyzed sentence to obtain output vectors of winner P-A classes--see the block diagram in Figure 3.