# Graph-based Semi-Supervised & Active Learning for Edge Flows

arXiv: https://arxiv.org/abs/1905.07451 · HTML: https://mlsanity.com/paper/1905.07451/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 May 2019.

## Built on by (most cited first, 25 of 25)

- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Principled Simplicial Neural Networks for Trajectory Prediction](https://mlsanity.com/paper/2102.10058/) (2021)
- [Signal Processing on Cell Complexes](https://mlsanity.com/paper/2110.05614/) (2021)
- [Simplicial Convolutional Filters](https://mlsanity.com/paper/2201.11720/) (2022)
- [Hodge-Compositional Edge Gaussian Processes](https://mlsanity.com/paper/2310.19450/) (2023)
- [Finite Impulse Response Filters for Simplicial Complexes](https://mlsanity.com/paper/2103.12587/) (2021)
- [Signal processing on simplicial complexes](https://mlsanity.com/paper/2106.07471/) (2021)
- [The decomposition of the higher-order homology embedding constructed from the k-Laplacian](https://mlsanity.com/paper/2107.10970/) (2021)
- [Convolutional Filtering in Simplicial Complexes](https://mlsanity.com/paper/2201.12584/) (2022)
- [Cycle Invariant Positional Encoding for Graph Representation Learning](https://mlsanity.com/paper/2311.14333/) (2023)
- [FastGAS: Fast Graph-based Annotation Selection for In-Context Learning](https://mlsanity.com/paper/2406.03730/) (2024)
- [Helmholtzian Eigenmap: Topological feature discovery & edge flow learning from point cloud data](https://mlsanity.com/paper/2103.07626/) (2021)
- [Representing Edge Flows on Graphs via Sparse Cell Complexes](https://mlsanity.com/paper/2309.01632/) (2023)
- [Outlier Detection for Trajectories via Flow-embeddings](https://mlsanity.com/paper/2111.13235/) (2021)
- [Imputation of Time-varying Edge Flows in Graphs by Multilinear Kernel Regression and Manifold Learning](https://mlsanity.com/paper/2409.05135/) (2024)
- [Graph Classification Gaussian Processes via Hodgelet Spectral Features](https://mlsanity.com/paper/2410.10546/) (2024)
- [Matched Topological Subspace Detector](https://mlsanity.com/paper/2504.05892/) (2025)
- [Free Energy Node Embedding via Generalized Skip-gram with Negative Sampling](https://mlsanity.com/paper/2105.09182/) (2021)
- [Graph Neural Networks for Edge Signals: Orientation Equivariance and Invariance](https://mlsanity.com/paper/2410.16935/) (2024)
- [Topological Trajectory Classification and Landmark Inference on Simplicial Complexes](https://mlsanity.com/paper/2412.03145/) (2024)
- [Stationarity and Spectral Characterization of Random Signals on Simplicial Complexes](https://mlsanity.com/paper/2602.03055/) (2026)
- [Windowed Fourier Analysis for Signal Processing on Graph Bundles](https://mlsanity.com/paper/2302.05592/) (2023)
- [Sensor Placement for Learning in Flow Networks](https://mlsanity.com/paper/2401.02438/) (2023)
- [FlowSymm: Physics Aware, Symmetry Preserving Graph Attention for Network Flow Completion](https://mlsanity.com/paper/2601.22317/) (2026)
- [Gauge-Invariant, Parameter-Insensitive Regularization for Potential Recovery from Flow on Directed Graphs](https://mlsanity.com/paper/2607.13609/) (2026)

## Abstract (arXiv)

We present a graph-based semi-supervised learning (SSL) method for learning edge flows defined on a graph. Specifically, given flow measurements on a subset of edges, we want to predict the flows on the remaining edges. To this end, we develop a computational framework that imposes certain constraints on the overall flows, such as (approximate) flow conservation. These constraints render our approach different from classical graph-based SSL for vertex labels, which posits that tightly connected nodes share similar labels and leverages the graph structure accordingly to extrapolate from a few vertex labels to the unlabeled vertices. We derive bounds for our method's reconstruction error and demonstrate its strong performance on synthetic and real-world flow networks from transportation, physical infrastructure, and the Web. Furthermore, we provide two active learning algorithms for selecting informative edges on which to measure flow, which has applications for optimal sensor deployment. The first strategy selects edges to minimize the reconstruction error bound and works well on flows that are approximately divergence-free. The second approach clusters the graph and selects bottleneck edges that cross cluster-boundaries, which works well on flows with global trends.