# Fault Diagnosis of Railway Point Machines Using the Locally Connected Autoencoder
## 4 Fault Data Analysis
### Analysis Results of Fault Diagnosis  
The results of the fault diagnosis are discussed in this subsection. As mentioned above, the LOF algorithm is employed for high robustness and easy implementation. A core parameter is the number of nearest neighbors in defining the outlier factor of the current signal, which is defined as \(k\) in this paper. Figure 5: 2D projection of the final feature representations. (**a**) FeatureBased; (**b**) FeatureBased Method with PCA; (**c**) SPDAE-80; (**d**) STDAE-150-50; (**e**) GRU-40; (**f**) GRU-70. The comparison of fault diagnosis of different schemes is reported in Figure 8, which shows the receiver operating characteristic (ROC) curves. The horizontal axis and the vertical axis of Figure 8 are the false positive rate and true positive rate, respectively. These curves are used to visualize the performance of the fault detection effect, as they measure the ability to produce good relative sample scores that serve to discriminate positive and negative samples [36]. To quantitatively measure the performance, the area under curve (AUC) is calculated. Bigger AUC values indicate better performances of the fault diagnosis scheme. For the analysis, \(\alpha\) and \(L\) are set as 0.1 and 10, respectively. The proposed scheme with \(M_{\text{loc}}=20\) and \(S_{\text{tr}}=20\) is named as Weight-I, whereas the proposed scheme with \(M_{\text{loc}}=30\) and \(S_{\text{tr}}=30\) is abbreviated as Weight-II. The corresponding schemes without the weighting strategy are termed as Average-I and Average-II, respectively. As can be seen in Figure 8, the parameter \(k\) is set to 60, 80, 100, 140, and 190. The value of \(k\) changes from 60 to 200. The optimal results of all the schemes are shown in Figure 8a. The figure shows that the locally connected autoencoder outperforms the other schemes as it has the highest AUC value of 0.981. The locally connected autoencoder without weighting strategy has the second best performance with  
Figure 9 shows the impact of \(\alpha\) and \(L\) on the fault detection results of the locally connected autoencoder when the number of the hidden units is set equal to 35 and the values of \(M_{\text{loc}}\) and \(S_{\text{tr}}\) are both set to 30. From Figure 9, we observe that the locally connected autoencoder with the weighting strategy incorporated performs better than the scheme without the weight strategy. This is because this strategy enhances the densities of the feature representations of the normal signals, resulting in a stable performance of the fault diagnosis task. This fault analysis result also verifies the analysis of Figure 7. One can also find that, when \(k\) is relativity small, the superiority of the proposed scheme is more notable, as the gaps of the AUC scores of the proposed scheme and the other schemes are larger. It is especially important as it is difficult to set appropriate values of \(k\) in advance in actual fault diagnosis tasks. If a relativity small value of \(k\) is selected, the proposed scheme retains a good performance while the other schemes suffer significant deterioration. When the value of \(k\) increases to 120, the AUC scores are very close of the proposed scheme with or without the weighting strategy. Besides, both suffer a performance reduction when \(k\) further increases. It also can be seen that the larger value of \(\alpha\) causes the performance deterioration, which can be considered as \"the overfitting phenomenon\". The setting of \(L\) also has an influence on the detection accuracy when \(k\) is small. The delicate adjustment of \(L\) is helpful to improve the performance. Our analysis result is consistent with the analysis in the original paper of [PERSON] [26]. Figure 8: Receiver operating characteristic (ROC) curves and AUCs of different schemes. (**a**) optimal; (**b**) \(k=60\); (**c**) \(k=80\); (**d**) \(k=100\); (**e**) \(k=140\); (**f**) \(k=190\).