提出可旋转不变的几何无监督漂移检测框架,有效应对高维数据流挑战。
ARGUS: Adaptive Rotation-Invariant Geometric Unsupervised System
- 基于固定空间划分追踪局部统计量,避免全局比较与投影失真。
- 计算复杂度降为O(N),支持单元级漂移定位,且在旋转下保持稳定。
- 适用于高维数据(d>500)的分布式漂移监测,适合工业级实时系统。
高维数据流中的分布漂移检测面临根本性挑战:全局比较方法扩展性差,投影方法丢失几何结构,重聚类方法存在身份不稳定性。本文提出Argus,将漂移检测重新定义为在数据流形的固定空间划分上追踪局部统计量。主要贡献有四:第一,证明在标准正交基上的Voronoi剖分可生成对正交变换(旋转与反射)不变的漂移度量;第二,该框架在每快照下实现O(N)复杂度,同时提供单元级的分布变化定位;第三,提出图论特征刻画漂移传播,区分一致漂移与孤立扰动;第四,引入产品量化剖分,通过将空间分解为独立子空间并聚合子空间漂移信号,实现d>500的高维扩展。论文建立理论基础,证明不变性,并通过实验验证其在坐标旋转下正确识别漂移,而现有方法产生误报。该剖分方法为分布监控提供了保留高维结构、无成对比较负担的几何化基础。
原文摘要 · Abstract (English)
Detecting distributional drift in high-dimensional data streams presents fundamental challenges: global comparison methods scale poorly, projection-based approaches lose geometric structure, and re-clustering methods suffer from identity instability. This paper introduces Argus, A framework that reconceptualizes drift detection as tracking local statistics over a fixed spatial partition of the data manifold. The key contributions are fourfold. First, it is proved that Voronoi tessellations over canonical orthonormal frames yield drift metrics that are invariant to orthogonal transformations. The rotations and reflections that preserve Euclidean geometry. Second, it is established that this framework achieves O(N) complexity per snapshot while providing cell-level spatial localization of distributional change. Third, a graph-theoretic characterization of drift propagation is developed that distinguishes coherent distributional shifts from isolated perturbations. Fourth, product quantization tessellation is introduced for scaling to very high dimensions (d>500) by decomposing the space into independent subspaces and aggregating drift signals across subspaces. This paper formalizes the theoretical foundations, proves invariance properties, and presents experimental validation demonstrating that the framework correctly identifies drift under coordinate rotation while existing methods produce false positives. The tessellated approach offers a principled geometric foundation for distribution monitoring that preserves high-dimensional structure without the computational burden of pairwise comparisons.
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