###### Abstract
Deep learning with automatic features has experienced rapid development in recent years [5; 18; 19; 20]. [PERSON] et al. [21] developed an unsupervised railway turnout fault detection method using a deep autoencoder. [PERSON] et al. [22] proposed an autoencoder-based fault diagnosis method for railway turnout. [PERSON] et al. [23] proposed a dual-scale neural network-based fault diagnosis method to solve the data scarcity problem in labeled fault data. The method used a one-dimensional vibration signal as the input. These methods effectively mitigate the limitations associated with expert experience. However, the data processing or model in these studies ignores the structural information of the time series data, resulting in the loss of spatial structure-related information and subsequently impacting the method's performance [24; 25]. In recent years, matrix-based machine learning has gained attention as a pattern recognition method that utilizes matrix data as inputs [26]. Relative to vector-based pattern recognition and deep learning methods for railway turnout fault diagnosis, matrix-based machine learning can preserve the structural information of the time series data. Additionally, unlike distance measurement methods that heavily rely on standard curves, this approach is not constrained by predefined curves, enhancing its adaptability to diverse  
Figure 1: Turnout structural schematic. datasets. [PERSON] et al. [27] introduced a support matrix machine (SMM) that employs the hinge loss, Frobenius norm, and kernel norm to integrate the structural information of the input matrix. Support vector machine (SVM) is designed for vector inputs. However, when dealing with matrix data, it is necessary to reshape the matrix into a vector, which may result in the loss of structural information. In contrast, SMM operates directly on matrix data, preserving the inherent structural information. SMM extends the concept of SVM to matrices and utilizes the hinge loss, Frobenius norm, and kernel norm to integrate the structural information of the input matrix. This enables SMM to capture the dependencies and relationships between different elements of the matrix. Subsequently, many improved SMMs have been developed to enhance performance in various classification scenarios. [PERSON] et al. [28] presented a least squares interactive SMM to improve computational efficiency and address the SMM problem in multi-quadratic programming. [PERSON] et al. [29] built upon the objective function that combines multiclass hinge loss and regularization terms. However, these models tend to be sensitive to noise, which is attributed to the integration of hinge loss functions. Fault diagnosis is a multiclassification problem. Datasets for industrial scenarios generally contain a lot of noise. To solve the limitation in noise-sensitivity and enhance the performance of MSMM for fault diagnosis problems, we design a pinball loss function-based [30] MSMM called the PL-MSMM. We then employ PL-MSMM to diagnose turnout faults. The main contributions of this study can be summarized as follows:  
1. A multiclass classifier with a pinball loss function is designed, namely PL-MSMM. Industrial datasets often contain noise. This classifier is better equipped to handle noisy data, making it well-suited for real-world industrial scenarios. 2. A railway turnouts fault diagnosis method with monitoring signal images and the designed PL-MSMM is proposed. It does not rely on the standard curve and takes into account the spatial structure of the time series monitoring signal, giving it better generalizability and performance. 3. The proposed method is validated using a real-field current dataset. The experimental results demonstrate its efficiency as a turnout fault diagnosis framework in practical scenarios. The remainder of this paper is structured as follows. The proposed classifier is presented in Section 2. The proposed diagnostic method is described in Section 3. The testing of the proposed method using field data is discussed in Section 4.