## 4 Experimental Results and Discussion
### Comparison with Existing Methods  
The proposed method was compared with existing fault diagnosis models to evaluate its performance. The compared models included the convolutional autoencoder (CAE) [35], CNN [36], and MSMM [29] models. Details of the methods and their parameter adjustments can be summarized as follows:  
* CAE: The input image size was \(32\times 32\). The encoder contained two convolutional layers. The first and second convolutional layers had 20 kernels of size \(3\times 3\) and one kernel of size \(3\times 3\), respectively. A pooling layer was added after each layer. The decoder included two deconvolutional layers with the same convolutional kernel size. The network used the Adam optimizer and rectified linear unit (ReLU) activation function, with an initial learning rate of 0.001 and a maximum iteration number of 100. * CNN: The input image size was \(32\times 32\). The model structure included convolutional, batch normalization, ReLU activation function, max pooling, fully connected, and SoftMax layers. The convolutional layers had 20 kernels of dimensions \(5\times 5\). Network training used a stochastic gradient descent with momentum (SGDM) optimizer. The initial learning rate was 0.001 and the number of iterations was 100. * MSMM: The training and testing datasets input to the model were two-dimensional images of size \(32\times 32\). This model was applied to the fault diagnosis problem of turnouts based on current signals. The feature matrix obtained from the data preprocessing was used as the input to train the classifier. All the hyperparameters involved were selected through cross-validation. The details of the hyperparameter settings and tune ranges in the models are listed in Table 2. The learning rate, batch size, and number of epochs are represented as \(r\), \(b\), and \(e\), respectively. The MSMM parameters are \(C\) and \(\tau\). The model was applied to the problem of current signal-based turnout fault diagnosis, and the image matrix features obtained from data preprocessing were used as inputs to train the classifier. To evaluate the performance of these methods, a ten-fold cross-validation method was adopted. Cross-validation is a widely used model evaluation method in machine learning. In k-fold cross-validation, the dataset is divided into k random subsets, with one subset chosen as the testing set and the remaining subsets used as the training set in each iteration [37]. This process helps mitigate the adverse effects caused by imbalanceddata partitioning in a single split, leading to a more reliable and accurate assessment of the model's performance. By averaging the results of multiple evaluations, cross-validation provides a more comprehensive and robust estimation of the model's effectiveness [38]. The advantages of cross-validation are particularly evident in small-scale datasets, where the impact of imbalanced partitioning is more pronounced. For each class of samples, we randomly selected 500 to form the dataset. The accuracy, precision, and F1-score of the different methods were compared and analyzed using 10-fold cross-validation. The results are shown in Table 3 and Figure 6.  
In Table 3, the average testing and training accuracy, precision, and F1-score of the four models are presented. The results show that the proposed PL-MSMM method outperforms the other methods in terms of accuracy, precision, and F1-score. The comparative results between matrix learning models (MSMM and PL-MSMM) and non-matrix learning models (CAE and CNN) indicate that the inclusion of structural information from 2D images significantly enhances diagnostic performance. Matrix learning models, which consider the structural information of the input data, have demonstrated superior results. Figure 6a-d show the testing accuracy, precision, and F1-score when applying 10-fold cross-validation to the four models. It can be seen that the minimum accuracy of PL-MSMM is 98.22% and the maximum accuracy is 99.56%. The overall average classification accuracy can reach 98.67%.