## 3 Results and Discussion
### Quantitative Comparison of the Proposed Technique with the Analogs
Comparatively, Model_5 outperforms all other models in terms of Accuracy (82.42% and 74.55%), indicating its better overall ability to identify emotional states. In addition, Model_5 demonstrated high Precision, Recall, and F1-Score values for all emotions, which emphasizes its balanced performance. High Precision indicates that the model has fewer false positives, and high Recall indicates fewer false negatives. In general, a high F1-Score also indicates that Model_5 maintains a balance between Precision and Recall, suggesting that it is successfully applicable to emotion recognition in security-critical systems. The key aspect that positively distinguishes Model_5 for the task at hand is its ability to successfully process the emotion Fear. Stable operation of Model_5 with this emotion can be especially valuable in video surveillance systems that meet security requirements, where accurate identification of the emotional state Fear can allow for the swift and efficient localization of a group of targeted individuals in a crowd. Evaluation of the effectiveness of the proposed technique (Model_5) in comparison with analogs was performed by pairwise comparison of the results of the technique with modern identification models that achieved high performance on both datasets. According to Figures 13-15, we can see that the proposed technique (Model_5) outperforms the state-of-the-art identification models in the following indicators:  
* Accuracy--by 2.20% and 0.91% (hereinafter, the first value corresponds to the FER+small dataset, the second to the ADFES-small dataset). * Precision--by 2.30% for the FER+small dataset. * Recall--by 2.21% and 0.91%. * F1-Score--by 2.26% and 0.47%. * False positive rate--by 0.55% and 0.23%. * False negative rate--by 2.21% and 0.91%. The practical implications of these results lie in the technique's (Model_5) automation of input conversion. The technique turns low-resolution video frames of human faces (704 \(\times\) 480) into output data identifying groups exhibiting sudden negative emotional shifts. The unique combination of a new facial expression representation model, geometric interpretation method, and enhanced hyperplane classification strategy resulted in a high classification accuracy of human emotional states (up to 82.42%). Using the technique gives security personnel a reliable tool to understand crowd dynamics and predict potential security risks during large gatherings. In conclusion, the proposed technique showed decent and balanced characteristics in all statistical indicators. The technique shows excellent accuracy and recall, providing a low number of false positives and negative results. Its overall accuracy across all emotional states is superior to its peers, and its stable performance across all emotions, especially the Fear emotion, makes it suitable for deployment in video surveillance systems that meet security requirements. The strengths of the proposed techniques include ease of use, high accuracy of emotional state identification, and a high level of interpretability of classification results.