ARGUS: Adaptive Rotation-Invariant Geometric Unsupervised System

TL;DR

Argus introduces a geometric, rotation-invariant framework for detecting distributional drift in high-dimensional data streams, combining theoretical invariance proofs with scalable, localized change detection methods.

Contribution

It formalizes a novel, invariant drift detection method using Voronoi tessellations, achieving O(N) complexity and high-dimensional scalability with theoretical guarantees.

Findings

Successfully detects drift under coordinate rotations.

Maintains high-dimensional structure without pairwise comparisons.

Scales to dimensions greater than 500 with product quantization.

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.