Learning Higher-Order Structure from Incomplete Spatiotemporal Data: Multi-Scale Hypergraph Laplacians with Neural Refinement

2026-05-17

AI Summary

This work addresses the challenge of structured missing data in sensor networks—arising from device calibration, localized failures, or new deployments—which exhibits complex higher-order group dependencies that traditional imputation methods struggle to capture. To this end, the authors propose a Multi-Scale Hypergraph Laplacian (MSHL) framework that first constructs multi-scale hypergraphs based on topological and residual correlations to model such high-order structures, followed by a hypergraph-conditioned residual network for nonlinear refinement. This approach uniquely integrates multi-scale hypergraph modeling with neural fine-tuning, enabling it to learn group-conservation patterns beyond the representational capacity of conventional graph models. The method significantly outperforms existing graph-based baselines when higher-order structures are identifiable, while maintaining competitive performance otherwise. Extensive experiments across five missing-data scenarios on two real-world traffic networks demonstrate its superiority, robustness, and theoretical guarantees.

Abstract

Sensor networks increasingly govern modern infrastructure, yet the data they lose are rarely missing in the uniform-random patterns assumed by standard imputation benchmarks. Loop detectors go offline during calibration, roadside cabinets silence clusters of nearby sensors, and newly installed instruments provide no history. Such failures create structured absences whose values are constrained by higher-order relations among groups of sensors, not merely by pairwise proximity. Existing low-rank and graph-based methods often miss this collective structure and can fail when missingness becomes coherent. We introduce Multi-Scale Hypergraph Laplacians (MSHL), a two-stage framework for learning higher-order structure from incomplete spatiotemporal observations. The Discovery stage builds a multi-scale hypergraph from complementary topology and residual-correlation evidence, with an observation-only selector that adapts to the supported interaction scale. The Refinement stage adds a small hypergraph-conditioned residual network that is safe by construction: it learns nonlinear corrections where informative residual features exist and defers to the linear estimate where they do not. We prove that MSHL represents group-conservation patterns inaccessible to pairwise graph priors, adapts to the best fixed scale up to a logarithmic factor, transfers this advantage to held-out imputation error, and admits a one-sided refinement guarantee. On two real traffic networks evaluated across scattered cell missingness, contiguous block outages, and whole-sensor blackouts at five rates, MSHL improves over a pairwise-graph baseline whenever higher-order structure is identifiable and otherwise matches it within sampling noise. The results point to a broader principle for reliable infrastructure learning: missing data should be treated not as isolated entries to fill, but as evidence of structure to discover.

Problem

• higher-order structure
• incomplete spatiotemporal data
• structured missingness
• hypergraph
• sensor networks

Innovation

• hypergraph
• spatiotemporal imputation
• higher-order structure
• multi-scale learning
• structured missingness