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.

Manifold regularization semi-supervised learning is a powerful graph-based semi-supervised learning method. However, the performance of semi-supervised learning methods based on manifold regularization depends to some extent on the quality of the manifold graph and unlabeled samples. Intuitively speaking, the quality of the graph directly affects the final classification performance of the model. In response to the above problems, this paper first proposed an adaptive safety semi-supervised learning framework. The framework implements the weight assignment of the self-similarity graph during the model learning process. In order to adapt to the learning needs, accelerate the learning speed, and avoid the impact of the curse of dimensionality, the framework also optimizes the features of each sample point through an automatic weighting mechanism to extract effective features and eliminate redundant information in the learning task. In addition, the framework defines an adaptive risk measurement mechanism for the uncertainty and potential risks of unlabeled samples to determine the degree of risk of unlabeled samples. Finally, a new adaptive safe semi-supervised extreme learning machine was proposed. Comprehensive experimental results across various class imbalance scenarios demonstrated that our proposed method outperforms other methods in terms of classification accuracy, and other critical performance metrics.