In this study, we introduced an innovative and robust semi-supervised learning strategy tailored for high-dimensional data categorization. This strategy encompasses several pivotal symmetry elements. To begin, we implemented a risk regularization factor to gauge the uncertainty and possible hazards linked to unlabeled samples within semi-supervised learning. Additionally, we defined a unique non-second-order statistical indicator, termed $C_p$-Loss, within the kernel domain. This $C_p$-Loss feature is characterized by symmetry and bounded non-negativity, efficiently minimizing the influence of noise points and anomalies on the model's efficacy. Furthermore, we developed a robust safe semi-supervised extreme learning machine (RS3ELM), grounded on this educational framework. We derived the generalization boundary of RS3ELM utilizing Rademacher complexity. The optimization of the output weight matrix in RS3ELM is executed via a fixed point iteration technique, with our theoretical exposition encompassing RS3ELM's convergence and computational complexity. Through empirical analysis on various benchmark datasets, we demonstrated RS3ELM's proficiency and compared it against multiple leading-edge semi-supervised learning models.