## 2 Description of the Proposed Method
### Description of the Proposed Automatic Evaluation System  
The functional structure of the proposed automatic system can be divided into the preparation and the main evaluation parts. Within the preparation part, the following two operations are preformed:  
1. Creation and training of GMM models [25] of \(N_{\text{PC}}\) Pleasure classes and \(N_{\text{AC}}\) Arousal classes using the material from the speech and sound databases. 2. These GMM models are used in the preliminary classification process to determine the individual coordinates [_Pco(k)_, _Aco(k)_] of the original sentences in the P-A space and the resulting 2D center position [\(C_{\text{PO}}\), \(C_{\text{AO}}\)] as: \[\left[C_{\text{PO}},\ \ C_{\text{AO}}\ \right]=\left[\frac{1}{k}\sum_{k=1}^{K} \text{Pco}(k),\frac{1}{k}\sum_{k=1}^{K}\text{Aco}(k)\right],\] (1) where \(1\leq k\leq K\) and \(K\) is the total number of the processed original sentences. The main evaluation part consists of the GMM classification operations applied on the synthetic speech sentences produced by different synthesis methods _Synt1_, _Synt2_, _Synt3_... etc. Output values representing their actual position in the P-A space are subsequently processed to obtain the final evaluation order (_FEO_) decision as shown in the block diagram in Figure 4. The whole evaluation process can be described by the following five operations:  
1. GMM-based classification of analyzed sentences to obtain their actual positions in the P-A space coordinates [_Pc(n)_, _Ac(n)_] for all \(N\) analyzed sentences in relation to the center [\(C_{\text{PO}}\), \(C_{\text{AO}}\)]--see a visualization in an example in Figure 5a. 2. Calculation of relative coordinates [\(P^{\prime}c(n)\), _A^{\prime}c(n)\)_] = [_Pc(n)_-_C_PO, _Ac(n)_-_C_AO] with respect to the center of originals [\(C_{\text{PO}}\), \(C_{\text{AO}}\)]--see an example in Figure 5b. 3. Calculation of the final normalized sum vector (FV) using the coordinates [\(P^{\prime}c(n)\), _A^{\prime}c(n)\)_]: the FV begins in the center [\(0\), \(0\)] and ends at the point [\(FV_{\text{PN}}\), \(FV_{\text{AN}}\)] given by: \[\left[\ \ FV_{\text{PN}},\ \ \ FV_{\text{AN}}\ \right]=\left[\sum_{n=1}^{N}P^{ \prime}c(n)/N,\sum_{n=1}^{N}A^{\prime}c(n)/N\right],\] (2) where \(N\) is the total number of the processed synthetic sentences. The FV vector can be also expressed in the polar coordinates by its magnitude (\(M_{\text{FV}}\)) and angle (\(\phi_{\text{FV}}\)) in degrees: \[M_{\text{FV}}=\sqrt{\left(FV_{\text{PN}}\right)^{2}+\left(FV_{\text{AN}} \right)^{2}},\phi_{\text{FV}}=\left(\text{Arctg}(FV_{\text{AN}}/FV_{\text{PN }})/\pi\right)\cdot 180\] (3)  
Figure 3: Block diagram of the GMM classification in the P-A space. The FV obtained is subsequently localized inside four emotional quadrants \(EQ_{1}\)-\(EQ_{4}\) around the center of originals (see Figure 5c) with a corresponding emotional meaning in relation to the 2D emotional space (compare with the diagram in Figure 1). 1. Determination of the summary distribution parameters (SDP) from the FV magnitude and angle for all \(N_{\text{TST}}\) tested synthesis types as: \[\text{SDP}(i)=M_{\text{FV}}(i)*IW_{\text{EQ1}-4}(\phi_{\text{FV}}(i))\quad 1 \leq i\leq N_{\text{TST}},\] (4)  
Figure 4: Block diagram of the evaluation part processing using synthetic speech sentences. Figure 5: Visualization of localized positions of synthetic speech sentences for \(N=50\): (**a**) sentence locations in the P-A space, (**b**) relative locations around the center of originals, (**c**) the resulting normalized FV with determined vector magnitude and phase items belonging to quadrants \(EQ_{1-4}\). where \(IW_{\text{EQ1-4}}\) are the importance weight functions depending on the quadrants \(\text{EQ}_{1-4}\) determined from the FV angle values (see Figure 1):  
\[\text{EQ}_{1-4}=\left\{