通过自适应谱形变，让图滤波器更灵活、可解释且跨图通用。
Data-Driven Graph Filters via Adaptive Spectral Shaping
- 学习基础谱核并用高斯因子动态调节，生成多峰多尺度响应。
- 在合成数据上重构误差低于固定波基和可学习线性滤波器组。
- 支持少样本迁移，适合部署在图神经网络和信号处理流程中。
我们提出自适应谱形变（Adaptive Spectral Shaping），一种数据驱动的图滤波框架，通过学习一个可复用的基础谱核，并用少量高斯因子对其进行调制，实现对拉普拉斯谱中异质区域的能量分配。所得响应具有多个峰值和多尺度特性，同时保持可通过显式中心与带宽解释的可读性。为提升效率，采用切比雪夫多项式展开实现滤波器，避免特征分解。进一步提出可迁移的自适应谱形变（TASS）：在源图上学习基础核，目标图上固定该核仅调整调制参数，实现在匹配计算量下的少样本迁移。在涵盖不同图族与信号场景的受控合成基准测试中，该方法相比固定原型波基和可学习线性滤波器组显著降低重建误差，且TASS展现出持续正向迁移效果。该框架提供紧凑的谱模块，可无缝嵌入图信号处理流水线与图神经网络，兼具可扩展性、可解释性与跨图泛化能力。
原文摘要 · Abstract (English)
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.
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