Traditional fault diagnosis methods struggle to handle fault data, with complex data characteristics such as high dimensions and large noise. Deep learning is a promising solution, which typically works well only when labeled fault data are available. To address these problems, a robust unsupervised fault diagnosis using machine learning is proposed in this paper. First, a special dimension reduction method for the high-dimensional fault data is designed. Second, the extracted features are enhanced by incorporating nonlinear information through the learning of a graph structure. Third, to alleviate the problem of reduced fault-diagnosis accuracy attributed to noise and outliers, $l_{2,1}$-norm and typicality-aware constraints are introduced from the perspective of model optimization, respectively. Finally, this paper provides comprehensive theoretical and experimental evidence supporting the effectiveness and robustness of the proposed method. The experiments on both the benchmark Tennessee-Eastman process and a real hot-steel milling process show that the proposed method exhibits better robustness compared to other methods, maintaining high diagnostic accuracy even in the presence of outliers or noise.