## 3 Results and Discussion
### Qualitative Analysis of the Proposed Technique
#### 3.2.2 Synthesis of the Simple Model  
The validity of the proposed simple model was checked on the test dataset described in Section 3.1. \begin{table}
\begin{tabular}{c c c c} \hline
**Emotional** & **FACS** & **Synthetic Model, X = \(\left(x_{i}\right)_{i=1}^{3}\)** & **Simple Model, X = \(\left(x_{i}\right)_{i=1}^{7}\)** \\ \hline \multirow{5}{*}{Anger} & \multirow{5}{*}{(1) lowered eyebrows (AU4); upper eyelids (AU5); (2) raised lower eyelids (AU23).} & (1) squinting eyes (lowered upper eyelid and raised lower eyelid); (2) lowered eyebrows; (3) tight lips. & (1) the mouth is closed; (2) the corners of the lips are raised; (3) eyes are squinted; (4) eyebrows (bridge of the nose) are drawn together; (5) eyebrows are lowered; (6) outer corners of the eyebrows are lowered; (7) the corners of the eyebrows are lowered. \\ \cline{2-3}  & \multirow{5}{*}{(1) lowered eyebrows are raised (AU1); upper eyelids (AU5); (3) lowered eyebrows (AU4); (4) raised upper eyelids (AU5); (5) raised lower eyelids (AU7); (6) lips are stretched (AU20); (7) drooping jaw (AU26).} & (1) the mouth is ajar; (2) the corners of the lips are down; (3) eyes are wide open; (4) eyebrows (nose bridge) are brought together; (5) eyebrows are lowered; (6) outer corners of the eyebrows are lowered; (7) the corners of the eyebrows are lowered. \\ \cline{2-3}  & \multirow{5}{*}{(1) the cheeks are raised (AU6); raised lower eyelids; (2) eyebrows in normal (3) stretched lips.} & (1) the mouth is ajar or open; (2) the corners of the lips are raised; (3) eyes are squinted or open; (4) eyebrows (nose bridge) are normal; (5) eyebrows are raised up or normal; (6) outer corners of eyebrows are raised up or normal; (7) inner eyebrows corners are raised up or normal. \\ \cline{2-3}  & \multirow{5}{*}{(1) the cheeks are raised (R12A); (2) the corners of the lips are turned out (R14A).} & (1) the mouth is closed; (2) the corners of the lips are down; (3) eyes are squinted or open; (4) eyebrows (nose bridge) are normal; (5) eyebrows are normal; (6) outer corners of eyebrows are normal; (7) internal corners of eyebrows are normal. \\ \cline{2-3}  & \multirow{5}{*}{(1) the inner parts of the eyebrows are raised (AU1); (2) lowered eyebrows (AU4); (3) lowered corners of the lips (AU15).} & (1) upper and lower eyelids are lowered; (2) eyebrows are lowered; (3) lips are compressed. \\ \cline{2-3}  & \multirow{5}{*}{(2) lowered eyebrows (AU4); (3) lowered corners of the lips (AU15).} & (1) upper and lower eyelids are lowered; (2) eyebrows are lowered; (3) eyebrows are lowered; (5) eyebrows are lowered; (6) outer corners of the eyebrows are lowered or normal; (7) inner eyebrows are lowered or normal. \\ \cline{2-3}  & \multirow{5}{*}{(3) lowered eye  
Based on the images of the corresponding emotions from the given dataset, according to Table 2, features \(x_{1}\), \(x_{2}\), and \(x_{3}\) are formed at the appropriate intervals. The generated input data were visualized for five emotional states (Anger, Fear, Joy, Neutral, and Sadness) in two-dimensional space using MDS and visualized in Figure 10.  
As can be seen from Figure 10a, the synthesized data are grouped by emotions, which confirms the ability of the proposed model to be used for the classification of emotional states. Next, following the steps of the proposed hyperplane classification method (using visual analytics and the \"human-in-the-loop\" principle), piecewise linear separators for classes corresponding to emotional states are specified (Figure 10b), and hyperplane parameters are obtained. With the help of the obtained parameters of hyperplanes, a decision tree was built for hyperplane classification of mimic manifestations of emotional states. Next, we provide a concise comparative analysis of two emotions based on our synthetic model. For example, as can be seen in Figure 10b, the classes of emotions Anger and Sadness can be visually divided into two groups each.