## 2 Material and Methods
### Performance Metrics Overview  
The proposed model was evaluated in terms of precision, recall, F1-score, accuracy, and ROC (AUC) curve. This study proposes the following formulas for evaluating machine learning performance metrics:  
* Precision (Positive Predictive Value): Precision is the ratio of the number of true positive predictions to the total number of positive predictions [44] (defined as Equation (1)). \[\text{Precision}=\frac{\text{True Positives}}{\text{True Positives}+\text{ False Positives}}\] (1)* Recall (Sensitivity or True Positive Rate): Recall is the ratio of the prediction of true positives to the total number of actual positives [45] (defined as Equation (2)). \[\text{Recall}=\frac{\text{True Positives}}{\text{True Positives}+\text{False Negatives}}\] (2)
* F1-Score: The F1 score is calculated as the harmonic mean of precision and recall, balancing the two (defined as Equation (3) [46]). \[\text{F1-Score}=\frac{2\times\text{Precision}\times\text{Recall}}{\text{ Precision}+\text{Recall}}\] (3)
* Accuracy: The accuracy of a prediction is determined by the ratio of correct predictions to the total number of predictions made [47] (defined as Equation (4)). \[\text{Accuracy}=\frac{\text{True Positives}+\text{True Negatives}}{\text{ Total Instances}}\] (4)
* Receiver Operating Characteristic (ROC) Curve and Area Under the Curve (AUC): ROC curves graphically represent tradeoffs between sensitivity (true positive rates) and specificity (true negative rates) at different cutoffs. The AUC, which summarizes the performance of the classifier at different cut-offs, is the area under the ROC curve. ROC Curve: The ROC curve plots the true positive rate (sensitivity) against the false positive rate (1--specificity) at various threshold values. The AUC formula is a measure of the area under the ROC curve [44]. In this study, the classification process for the three specified classes--\"broken\", \"clean\", and \"dirty\"--was conducted using the structured table provided in Figure 2. This table systematically compares the actual ground truth (actual situation) with the model's predictions, enabling a detailed classification performance evaluation. Key metrics such as true positive (TP), false negative (FN), and true negative (TN) are explicitly outlined for each class through combinatorial scenarios. * True Positive (TP): Represents cases where a class is correctly identified. For instance, the \"Broken-Broken (TP)\" entry denotes cases in which genuinely broken items are accurately classified as broken by the model. Similarly, \"Clean-Clean (TP)\" and \"Dirty-Dirty (TP)\" reflect successful predictions for the clean and dirty classes, respectively. * False Negative (FN): Occurs when instances belonging to a specific class are misclassified into other courses. For the \"Broken\" class, FN is calculated as the sum of \"Broken-Clean\" and \"Broken-Dirty\" cases, indicating broken items incorrectly labeled as clean or dirty. The same logic applies to the FN values for the \"Clean\" and \"Dirty\" classes. * True Negative (TN): Refers to the correct identification of instances not belonging to a target class. For example, the TN value for the \"Broken\" class aggregates all correctly classified non-broken cases, such as \"Clean-Clean\", \"Clean-Dirty\", \"Dirty-Clean\", and \"Dirty-Dirty\" combinations. The table resembles a multi-class confusion matrix, highlighting critical performance metrics (e.g., accuracy, precision, specificity) for evaluating the classifier. Misclassification patterns, such as \"Dirty-Broken\" or \"Clean-Dirty\", reveal where the model struggles, pinpointing areas for refinement. For instance, frequent confusion between \"Clean\" and \"Dirty\" may suggest overlapping features or insufficient training data for these classes. This structured analysis aids in balancing the model's optimization, ensuring reliable predictions across all classes.