Control barrier functions (CBFs) provide a principled framework for safety-critical control, but their construction typically requires an explicit and differentiable description of the safe or unsafe region. It becomes challenging for data-defined unsafe regions that may evolve over time. This paper proposes SafeLink, a data-driven CBF construction and adaptation method based on a cost-sensitive random vector functional link (RVFL) network. SafeLink introduces asymmetric misclassification costs to promote conservative unsafe-region representation while preserving a closed-form solution. We establish the Lipschitz continuity of the learned CBF and its derivatives, and derive sufficient conditions for conservative unsafe-region coverage and the corresponding interval-wise safety guarantees. Analytical updates are further developed for adjusting the misclassification cost and for incrementally adding or decrementally removing samples, avoiding full retraining when the unsafe region changes. Experiments on a two-link manipulator demonstrate that SafeLink rapidly adapts to evolving unsafe regions, enables collision-free target reaching, and achieves substantially lower update runtimes than baselines.

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