🤖 AI Summary
This study addresses the challenges of detecting distribution drift in high-dimensional data streams, which are often hindered by excessive computational costs, loss of geometric structure, and unstable cluster identities. The authors propose a framework that tracks local statistics based on a fixed Voronoi tessellation and introduces a rotation- and reflection-invariant drift metric to enable robust detection under coordinate transformations while preserving the intrinsic geometry of high-dimensional manifolds. By modeling drift propagation through graph-theoretic constructs, incorporating an O(N) efficient update mechanism, and leveraging product quantization for scalability to ultra-high-dimensional settings, the method significantly reduces computational overhead and false positives. Experimental results demonstrate its effectiveness in lowering computational burden, minimizing spurious alerts, and providing spatial localization of drift occurrences.
📝 Abstract
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.