Data-Driven Graph Filters via Adaptive Spectral Shaping

2026-02-03

AI Summary

This work addresses the challenge that traditional graph filters struggle to simultaneously achieve interpretability, scalability, and cross-graph generalization when processing heterogeneous graph signals. The authors propose an adaptive spectral shaping framework that learns reusable baseline spectral kernels and modulates them with a small number of Gaussian components to construct multi-peak, multi-scale filters. By employing Chebyshev expansions instead of explicit eigendecomposition, the method enables efficient computation. The introduced TASS mechanism facilitates few-shot adaptation across graphs using a fixed set of baseline kernels, significantly enhancing transfer stability. Experiments demonstrate that the proposed approach achieves substantially lower reconstruction errors than fixed wavelet and linear filter banks on multiple synthetic graph benchmarks, while maintaining both interpretability and strong cross-graph generalization capabilities.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

We introduce Adaptive Spectral Shaping, a data-driven framework for graph filtering that learns a reusable baseline spectral kernel and modulates it with a small set of Gaussian factors. The resulting multi-peak, multi-scale responses allocate energy to heterogeneous regions of the Laplacian spectrum while remaining interpretable via explicit centers and bandwidths. To scale, we implement filters with Chebyshev polynomial expansions, avoiding eigendecompositions. We further propose Transferable Adaptive Spectral Shaping (TASS): the baseline kernel is learned on source graphs and, on a target graph, kept fixed while only the shaping parameters are adapted, enabling few-shot transfer under matched compute. Across controlled synthetic benchmarks spanning graph families and signal regimes, Adaptive Spectral Shaping reduces reconstruction error relative to fixed-prototype wavelets and learned linear banks, and TASS yields consistent positive transfer. The framework provides compact spectral modules that plug into graph signal processing pipelines and graph neural networks, combining scalability, interpretability, and cross-graph generalization.

Problem

• graph filtering
• spectral shaping
• data-driven
• transferability
• interpretability

Innovation

• Adaptive Spectral Shaping
• Graph Filtering
• Chebyshev Approximation
• Transferable Learning
• Interpretable Spectral Kernels