Joint Graph Rewiring and Feature Denoising via Spectral Resonance
Jonas Linkerh\"agner, Cheng Shi, Ivan Dokmani\'c
TL;DR
This paper introduces JDR, an algorithm that jointly denoises node features and rewires graphs by aligning spectral spaces, significantly improving GNN performance on noisy, real-world graph data.
Contribution
The paper presents a novel joint denoising and rewiring algorithm for graphs that handles heterophily and is theoretically justified, outperforming existing methods.
Findings
JDR improves node classification accuracy on synthetic and real-world datasets.
The method effectively handles graphs with varying levels of homophily and heterophily.
Theoretical analysis supports the algorithm's effectiveness in stylized settings.
Abstract
When learning from graph data, the graph and the node features both give noisy information about the node labels. In this paper we propose an algorithm to jointly denoise the features and rewire the graph (JDR), which improves the performance of downstream node classification graph neural nets (GNNs). JDR works by aligning the leading spectral spaces of graph and feature matrices. It approximately solves the associated non-convex optimization problem in a way that handles graphs with multiple classes and different levels of homophily or heterophily. We theoretically justify JDR in a stylized setting and show that it consistently outperforms existing rewiring methods on a wide range of synthetic and real-world node classification tasks.
Peer Reviews
Decision·ICLR 2025 Oral
The primary novelty of JDR lies in its combined optimization of graph structure and node feature alignment, enhancing data quality by maximizing alignment between the spectral components of the graph and feature matrices. This unified approach addresses both structural and feature-level noise simultaneously, which is rare among existing methods that typically target these types of noise separately. A key concept introduced is “spectral resonance,” where optimal alignment between the graph’s lead
JDR depends on the availability of informative node features for effective rewiring and denoising, which restricts its applicability to settings with substantial node feature information; this reliance could limit its effectiveness in networks that primarily encode structural data. The algorithm’s design is also tailored to node-level tasks, making it less suited for graph-level tasks like graph classification, where global structure matters more than node-specific features
1. The proposed method is general and can be applied to a wide range of GNNs for downstream classification tasks. 2. The proposed method jointly considers graph rewiring and feature denoising. 3. The proposed method improves the performance of a numer of GNNs on a number of popular datasets in the experiments.
1. The solution is somewhat incremental and its novelty is low, although it appears to be sound. 2. There is no theoretical guarantee on the degree of improvement using JDR. 3. The experiments were conducted on a small number of datasets that cannot be considered as an evidence that the proposed method is really effective.
- This paper uses cSBMs as a key framework to build intuition about the graph rewiring and denoising problem, providing the theoretical foundation for the alignment target. - The empirical verification using synthetic data is clear. - The method is evaluated on both homophilic graphs and heterophilic graphs, showing its generalizability.
- The proposed method involves graph structure matrix and graph feature matrix decomposition, which can be computationally challenging on extremely large real-world graph data, limiting the practicability of the proposed method. - As the SVD decomposition can have time complexity of $O(N^3)$, it may be not accurate to say the proposed JDR has time complexity of $O(N)$
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Taxonomy
TopicsAdvanced Computing and Algorithms