The switch machine, an essential element of railway infrastructure, is crucial in maintaining the safety of railway operations. Traditional methods for fault diagnosis are constrained by their dependence on extensive labeled datasets. Semi-supervised learning (SSL), although a promising solution to the scarcity of samples, faces challenges such as the imbalance of pseudo-labels and inadequate data representation. In response, this paper presents the Semi-Supervised Adaptive Matrix Machine (SAMM) model, designed for the fault diagnosis of switch machine. SAMM amalgamates semi-supervised learning with adaptive technologies, leveraging adaptive low-rank regularizer to discern the fundamental links between the rows and columns of matrix data and applying adaptive penalty items to correct imbalances across sample categories. This model methodically enlarges its labeled dataset using probabilistic outputs and semi-supervised, automatically adjusting parameters to accommodate diverse data distributions and structural nuances. The SAMM model's optimization process employs the alternating direction method of multipliers (ADMM) to identify solutions efficiently. Experimental evidence from a dataset containing current signals from switch machines indicates that SAMM outperforms existing baseline models, demonstrating its exceptional status diagnostic capabilities in situations where labeled samples are scarce. Consequently, SAMM offers an innovative and effective approach to semi-supervised classification tasks involving matrix data.