## 4 Results
### Effectiveness of Our Criteria
#### 4.3.1 Effective Analysis Based on the Fault Diagnosis Results  
We verify the effectiveness of feature selection based on the accuracy of composite fault diagnosis. We discuss the accuracy for single features and the feature subset. In the verification, we formulate the criteria for deciding the selection threshold. We also analyze the results of different feature selection approaches. The effectiveness for single features is the basis for determining the quality of the feature set. We have evaluated the effectiveness for each feature in the feature set and obtained the accuracy of solely relying on any single feature to diagnose composite faults. As shown in Table 3, the accuracy for single features is all above 50%, better than the random probability results. This shows that every feature can be used for composite fault diagnosis, but the resulting accuracy does not satisfy the requirements in real application. We base our further study on the results in Table 3 and build the original feature set (including 20 features) and propose an approach which obtains high accuracy with fewer features. To obtain maximum accuracy with minimum features, we have designed the criteria for threshold selection. Specifically, we rank the centrality indicators of features in the CFN network and increase the number of input features in the DNN according to the ranking. Then we obtain the accuracy of composite fault diagnosis with different numbers of features. We will base our analysis on the accuracy of composite fault diagnosis and the accuracy gain. Figure 5(a) shows how the accuracy changes with the size of the feature subset. The accuracy first rises and then drops. The maximum accuracy for different centralities corresponds to different sizes of the optimal subset (referred to here as the optimal number of features). Specifically, for degree and betweenness centrality, the optimal number of features is 10; and for closeness and PageRank centrality, that number is 9. When the optimal number of features is reached, the accuracy will either remain or decrease. Meanwhile, Figure 5(b) shows how the accuracy gain changes with the size of the feature subset. Overall, the accuracy gain first shrinks and then expands amongst volatilities, and the volatilities eventually become minor. When the number of features reach a certain threshold, more features do not improve the diagnosis and may even hamper the diagnosis. All this verifies that feature selection is necessary as more features do not always improve the results. The model with an appropriate number of features is better than the one with all features in fault diagnosis. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Features** & **Acc** & **Features** & **Acc** & **Features** & **Acc** & **Features** & **Acc** \\ \hline fea1 & 0.703 & fea6 & 0.747 & fea11 & 0.685 & fea16 & 0.703 \\ fea2 & 0.777 & fea7 & 0.707 & fea12 & 0.688 & fea17 & 0.672 \\ fea3 & 0.737 & fea8 & 0.667 & fea13 & 0.67 & fea18 & 0.702 \\ fea4 & 0.747 & fea9 & 0.733 & fea14 & 0.687 & fea19 & 0.672 \\ fea5 & 0.767 & fea10 & 0.676 & fea15 & 0.703 & fea20 & 0.675 \\ \hline \hline \end{tabular}  
* Acc indicates the accuracy of composite fault diagnosis.  
\end{table} 
Table 3: Accuracy of composite fault diagnosis for single features. To verify the superiority of the proposed method, we contrast the performance of different selection approaches from the two viewpoints below. In practice, we use the feature subset obtained by different selection approaches as the input for the DNN and get the accuracy of composite fault as the foundation for comparison. Results are shown in Table 4. On the one hand, we contrast the accuracy of the optimal feature subset by using different centrality indicators of the CFN network. We find that the accuracy of our methods is over 94% for composite fault diagnosis, which is a 4% improvement over the results without feature selections. On the other hand, a number of various classical feature selection methodologies are contrasted, including IAMB, RF, SelectKBest.