## 5 Evaluation of the Performance of Existing Applications  
Performance metrics are usually measured at the frame or pixel level concerning the ground truth data in datasets. If an abnormal event is identified in a frame, it is categorized as abnormal. The frame-level criterion considers only the entire frame. Instead of merely determining whether a frame contains abnormal events, the pixel-level analysis seeks to identify anomalous events within the frame. Therefore, the pixel-level criterion is better for assessing the quality of an algorithm [86]. In pixel-level evaluations, the locations of the detected objects are crucial. In rare cases, the detection can be performed at the clip level. However, this criterion is not preferred because it needs to provide sufficient evaluation details. In anomaly detection studies, most models use the Receiver Operating Characteristic Curve (ROC) and its associated Area Under the Curve (AUC) as metrics. These metrics can be calculated by using a confusion matrix. Table 14 shows the general structure of the confusion matrix and related evaluation measures. In addition, as seen in Figure 8, the ROC curve shows the correlation between the false positive and true positive rates for different parameter cut-off values. Another metric used in models is the Equal Error Rate (EER). The EER selects the best threshold on the ROC curve to maximize the TPR and minimize the FPR. However, according to recent studies [87; 88], EER evaluation criteria result in a severely unbalanced sample of normal and abnormal events. The performance comparison of framework-level applications using the AUC and EER is summarized in Table 15. The methods were published between 2016 and 2023. \begin{table}
\begin{tabular}{c c c} \hline
**Clip-Level** & **Frame-Level** & **Pixel-Level** \\ \hline UCF-Crime & Avenue & Avenue \\  & UCF-Crime & ShanghaiTech \\  & UMN & UCSD Ped1/ Ped2 \\  & ShanghaiTech & \\  & UCSD Ped1/ Ped2 \\  & Subway Entrance/Exit & \\ \hline \end{tabular}
\end{table} 
Table 13: Based on ground truth labeling. \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{Actual Class} \\ \cline{2-3}  & True & False \\ \cline{2-3} Predicted Class & True & True Positives & False Positives \\  & & (TPs) & (FPs) \\ \hline False & False Negatives & True Negatives \\  & & (FNs) & (TNs) \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Confusion matrix and related evaluation measures. AUC of 93.8%. However, the ConvAE method [90] had the worst result with an AUC of 70.2% and an EER of 25.1%. For the Subway Exit dataset, the NNC [95] method demonstrated the best performance with an AUC of 95.1%. The second-best method was HMCF [109] with an AUC of 94.2%. The worst-performing method on this dataset was ConvAE [90] with an AUC of 80.7% and an EER of 9.9%. For the Subway Exit dataset, the NNC method [95] showed the best performance with an AUC of 95.1%. The HMCF method [109] achieved the second-best result with an AUC of 94.2%. However, the ConvAE method [90] had the worst result with an AUC of 80.7% and an EER of 9.9%. For the UCSD Ped1 dataset, the reconstruction-based DR-STN method [116] exhibited the best performance with an AUC of 98.8%. The second-best method was decoupled Arch. [111] with an AUC of 95.1%. The worst-performing method on this dataset was S-RBM [92] with an AUC of 70.2%. For the UCSD Ped2 dataset, the reconstruction-based DMAD [118] method achieved the best performance with an AUC of 99.7%. The second-best method was AMSRC [117] with an AUC of 99.3%, and no EER value was reported. The worst-performing method on this dataset was 3D gradients+conv5 [88] with an AUC of 82.2%. For the Shanghai Tech dataset, the self-reasoning method [107] showed the best performance with an AUC of 84.1%. The multi-task L. method [110] had the second-best result with an AUC of 83.5%, but the sRNN-AE method [98] had the worst result with an AUC of 69.6%. Finally, for the UCF-Crime dataset, the EADN method [115] demonstrated the best performance with an AUC of 98.0%.