# ChaMTeC: CHAnnel Mixing and Temporal Convolution Network for Time-Series Anomaly Detection
## 5 Experimental Results and Performance Evaluation
### Coverage-Based Point-Adjusted F1-Score (\(F1_{CPA}\))  
We use the _Coverage-Based Point-Adjusted F1-Score (\(F1_{CPA}\))_ to get around the drawbacks of \(F1_{PA}\). This method refines true positive evaluation by requiring a minimum overlap ratio between predicted and actual anomaly segments. A predicted anomaly is only regarded as a true positive in this method if it satisfies a predetermined coverage threshold.  
\[\text{Precision}_{CPA}=\frac{\sum_{i}|A_{i}\cap P_{i}|}{\sum_{i}|P_{i}|} \tag{26}\]  
\[\text{Recall}_{CPA}=\frac{\sum_{i}|A_{i}\cap P_{i}|}{\sum_{i}|A_{i}|} \tag{27}\]  
where  
* \(A_{i}\) represents the ground-truth anomaly segments.
* \(P_{i}\) denotes the predicted anomaly segments.
* \(|A_{i}\cap P_{i}|\) is the length of the intersection between the predicted and ground-truth anomaly segments.
* \(|P_{i}|\) is the total predicted anomaly duration.
* \(|A_{i}|\) is the total ground-truth anomaly duration.  
Using these coverage-based definitions, the final \(F1_{CPA}\) score is computed as follows:  
\[F1_{CPA}=2\times\frac{\text{Precision}_{CPA}\times\text{Recall}_{CPA}}{ \text{Precision}_{CPA}+\text{Recall}_{CPA}} \tag{28}\]  
By penalizing predictions that do not adequately cover the actual anomaly period, this metric guarantees a more realistic evaluation. \(F1_{CPA}\) offers a more stringent evaluation of the model's capacity to capture anomalies as continuous events, in contrast to \(F1_{PA}\), which has the potential to distort performance by favoring scattered detections.  
Our dataset, WaterLog\({}^{*}\), is particularly well suited for evaluating anomaly detection methods due to its unique characteristics. Unlike many public benchmarks that contain frequent and densely packed anomalies, WaterLog\({}^{*}\) features sparse and isolated anomaly regions. This sparsity mirrors real-world scenarios where anomalies are rare and often localized, making it a more challenging and realistic candidate for evaluation. By leveraging this dataset, we can better distinguish between methods that perform well in detecting sparse anomalies and those that rely on frequent anomaly occurrences. Table 4 demonstrates that \(F_{1}\) and \(F_{1 CPA}\) give the same results because WaterLog\({}^{*}\) does not contain large anomaly regions; on the other hand, adjustments in the other datasets have a huge effect on the results, as seen in Table 5. To evaluate the effectiveness of our proposed anomaly detection approach, we conduct an ablation study on two benchmark datasets: the _MSL dataset_ and _WaterLog dataset_. We compare the performance of five state-of-the-art methods--**LMSAutoTSF**[20], **iTransformer**[21], **TimeMixer**[22], **PatchTST**[23], and **AnomalyTransformer**[5]--under two thresholding approaches: _Fixed Thresholding_ and _Sliding Window Thresholding_ (_thFactor_ = _2.0_). For a comprehensive evaluation, we utilize three metrics: \(F_{1}\), \(F_{1 PA}\), and \(F_{1 CPA}\). Additionally, we evaluate two variants of our proposed architecture with and without an attention (w/o) mechanism to analyze the impact of attention components, as detailed in all tables containing results.