Inspired by graph-based methodologies, we introduce a novel graph-spanning algorithm designed to identify changes in both offline and online data across low to high dimensions. This versatile approach is applicable to Euclidean and graph-structured data with unknown distributions, while maintaining control over error probabilities. Theoretically, we demonstrate that the algorithm achieves high detection power when the magnitude of the change surpasses the lower bound of the minimax separation rate, which scales on the order of $\sqrt{nd}$. Our method outperforms other techniques in terms of accuracy for both Gaussian and non-Gaussian data. Notably, it maintains strong detection power even with small observation windows, making it particularly effective for online environments where timely and precise change detection is critical.

翻译：受图基方法启发，我们提出了一种新颖的图跨距算法，用于在低维至高维数据中检测离线和在线数据的变点。该通用方法适用于分布未知的欧几里得数据和图结构数据，同时能有效控制错误概率。理论上，我们证明当变点幅度超过极小极大分离率下界（其量级为$\sqrt{nd}$）时，该算法具有高检测效能。在高斯与非高斯数据场景中，本方法在检测精度上均优于现有技术。值得注意的是，即使在较小观测窗口下，算法仍能保持强大的检测能力，这使其在需要及时精准变点检测的在线环境中具有显著优势。