# A Multi-Leak Identification Scheme Using Multi-Classification for Water Distribution Infrastructure
## 3 Performance Evaluation of Different Classifier Scenarios
### Performance Evaluation of the MC-MLI  
The performance of the proposed MC-MLI is evaluated in terms of average accuracy, sensitivity, specificity, and detection time. In this experiment, all classification schemes are evaluated under the same scenario, i.e., the same training data, same testing data, and the same leak scenario. Three (3) schemes are compared, namely prime multi-class classification (prime MCC), multi-class classification with the adaptive kernel (MCC + AK), prime multi-classification (prime MC), and multi-classification with the adaptive kernel (MC + AK) (the proposed MC-MLI). The multi-class classification refers to one multi-class classifier. The multi-classification refers to multiple binary classifiers. The prime classification means the classifier does not comprise any adaptive kernel or MCDM.  
As shown in Figure 4, the proposed MC-MLI achieves the best performances: 96.1% accuracy, 96.9% sensitivity, 95.3% specificity, and 5.3 s detection time. The comparison of prime MCC and MCC + AK reveals that the adaptive kernel significantly improves detection accuracy, sensitivity and specificity by >15%. The main drawback of multi-class classification is low accuracy, and thus the performance of MCC + AK is limited. The performance of multi-class classification degrades with the increasing number of classes. This renders serious challenges for multi-leak detection. For instance, if there are 10 pipe sections and 10 potential leak points, the number of leak combinations will be 1023, and thus 1023 classes will be needed for the multi-class classifier. Furthermore, multi-class approaches are inflexible in that the entire detection system need to be re-trained when a new pipe section is connected.  
Multi-classification is proposed to overcome the captioned challenges. The multi-classification can break down an entire pipeline system into numerous pipe sections. A unique classifier is assigned to each pipe section. This facilitates classifier customization for every pipe. Furthermore, it is not necessary to re-train the entire detection system when the new pipe section is connected. A new classifier will be assigned and customized to the new pipe section. This facilitates the management of WDI. The result demonstrates that prime MC achieves higher accuracy, sensitivity and specificity than that of prime MCC. The performance of the prime MC is close to MCC + AK. This proves that multi-classification accomplishes better identification performances than multi-class classification. However, the detection time of prime MC is much longer than that of other schemes due to the complex feature vector. The proposed MC-MLI solves the problem by determining the best feature combination for every classifier by MCDM. Owing to weighting assignment for  
Figure 4: Performance evaluation of the proposed MC-MLI (**a**) Comparisons of average accuracy, sensitivity, and specificity; (**b**) Comparisons of average detection time. * Note: MC + AK is actually the proposed MC-MLI scheme.  
feature importance levels, MC-MLI using adaptive kernel improves accuracy, sensitivity and specificity by >15% compared to the prime MC.