# Fault Diagnosis of Railway Point Machines Using the Locally Connected Autoencoder
## 4 Fault Data Analysis
### Feature Representations of Different Approaches  
To visualize the feature representations, similar to the work in [30], we map the representations in the multidimensional space to a two-dimensional plane using the kernel PCA method [31]. Kernel PCA transforms the data into the high-dimensional feature space and uses a Mercer kernel to reduce the dimension. Unless otherwise stated, the dimension reduction method used in this paper is the kernel PCA method.  
Figure 5 shows the activations of the hidden representations of the baseline method and the contrast autoencoder-based methods for all 3300 sequences in \(\mathbb{S}\). The normal classes are labeled as Class 1, Class 2 and Class 3, respectively. The fault class is flagged as Class -1. As can be seen in Figure 5, the principal components of Featurebased are more mixed compared to the autoencoder-based methods. This is because the hand-engineering feature extraction approach has difficulties handling the nonlinear data. Further, for the autoencoder-based methods, the current signals related to healthy point machines have a wide distribution, whereas the signals related to defective point machines have a more confined distribution, which may cause a decline of the effectiveness of the outlier detection. The latter is caused by violating a fundamental hypothesis in the local density-based method (such as the LOF algorithm) and the one class-based method (such as the ABOD algorithm [32]). The hypothesis is that in the feature space, the normal samples have higher density, whereas the abnormal samples have lower density [33].  
The final feature representations of the proposed scheme without the weighting strategy are reported in Figure 6, where the number of the hidden units is set to 35. An overlapped window method [34] is adopted in the analysis, where the step size \(S_{tr}\) changes from 20 to 40. Considering that the sequence length differs in Cu-3300, we preset a length parameter \(L_{\text{pre}}\) to ensure the same length of sequences. To be more specific, if the length of \(\mathbf{s}_{n}\) is less than \(L_{\text{pre}}\), we pad the signals up to \(L_{\text{pre}}\); when the length of \(\mathbf{s}_{n}\) is greater than \(L_{\text{pre}}\), the extra part is intercepted. Compared to the other autoencoder-based methods shown in Figure 5, the locally connected autoencoder performs slightly better, as the fault signal has a more dispersed distribution. The results demonstrate the great ability of the proposed method in automatically learning the useful features from the raw current signals. It also can be seen that the changes of \(M_{\text{loc}}\) and \(S_{\text{tr}}\) do not reduce the effectiveness of the proposed scheme, where the robustness is verified.  
Figure 7 provides the feature representations of the proposed scheme, where \(L=10\) and \(\alpha=0.1\). Similar to Figure 6, the proposed scheme can achieve superior performance for the representation learning in the field of the point machine fault diagnosis. Note that using the weighting strategy, the densities of the feature representations of both the normal and fault signals are observed to be increased. The increase of the densities of both the normal and fault signals can be explained that the locally connected autoencoder with the weighting strategy incorporated can produce more effective representations. In Section 4.2, observe that the weighting strategy can effectively improve the detection accuracy, especially for those cases when the number of the neighbor points is relatively small. This is reasonable, as the increase of the densities of the feature representations caused by the weighting strategy is larger for the normal data than for the fault data. Also note that in this strategy, the weights of the informative signals are increased and the reason is similar to that of the adaboost algorithm [35].