Filter Learning for Subgraphs: Algebras and Performance Risk Bounds
Graph signal processing tasks that leverage spectral information typically assume access to the complete graph topology, which is often unavailable in practice. We propose a systematic framework for subgraph filter learning (SFL), where subgraph-supported operators approximate ambient graph filters under partial observations. We formulate SFL as a statistical learning problem in which optimal subgraph operators are inherently data-dependent. To address the difficulty of directly estimating such operators, we develop a subgraph filter algebra based on distance-aware Laplacian constructions, defining a structured and controllable class of filters for effective approximation. We further esta...
| Authors | Purui Zhang, Feng Ji, Yanan Zhao et al. |
|---|---|
| Primary category | cs.LG |
| Published | 23 July 2026 |
| Last updated at source | 23 July 2026 |
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