arXiv subjects

Feiyue Zhao

Publications and source records attributed to Feiyue Zhao.

5 recordsLinked to original sources

arXiv2026

Generalized Linear Graph Representation: A Compact Operator Space for Graph Signal Processing and Graph Neural Networks

Graph Signal Processing (GSP) and Graph Neural Networks (GNNs) rely fundamentally on the matrix representation of the underlying graph topology. This representation defines key operators such as the graph Fourier transform, spectral filtering, and convolution. Existing parameterized operator families interpolate only partial subsets of classical graph matrices, while broader formulations become non-compact when representing transition-type operators, limiting both theoretical analysis and stable learning. To address this issue, we propose the Generalized Linear Graph Representation (GLGR), denoted by $\mathbf{Q}_{\alpha,l}$, as a compact two-parameter operator family defined on a bounded linear domain. GLGR unifies major classical operators together with transition-type operators without requiring asymptotic parameters. Theoretically, we show that $\mathbf{Q}_{\alpha,l}$ admits a variational decomposition balancing local smoothness and global degree-weighted energy, derive spectral perturbation bounds, and establish graph-aware sufficient conditions for positive semi-definiteness. Building on this formulation, we develop Adaptive GLGR Convolution (AG-Conv), which makes the propagation operator itself learnable within end-to-end GNNs. Experiments on graph classification and node classification benchmarks show that GLGR improves both fixed-operator representation search and adaptive graph learning across multiple backbones.

eess.SP↗

arXiv2026

A Unified Fractional Spectral Framework for Spatiotemporal Graph Signals: Bi-Fractional Transform and Geodesic Coupling

Graph signal processing extends spectral analysis to data supported on irregular domains. Existing fractional transforms for two-dimensional graph signals, including the two-dimensional graph fractional Fourier transform (GFRFT), typically impose a shared fractional order across dimensions, which limits adaptivity to heterogeneous spatiotemporal spectra. To address this limitation, we propose the two-dimensional graph bi-fractional Fourier transform, which assigns independent fractional orders to the factor graphs of a Cartesian product, enabling decoupled spectral control while preserving separability, unitarity, and invertibility. To further resolve the basis ambiguity in temporal fractional analysis, we develop a geodesic-coupled GFRFT by constructing a coupling path along the principal geodesic on the unitary manifold, thereby unifying graph-induced and discrete temporal bases with guaranteed unitarity and a closed-form inverse. Building on these transforms, we derive a differentiable Wiener-type filtering framework with a hybrid optimization strategy: the fractional orders are learned end-to-end from data, while the coupling parameter is fixed as a structural regularizer. Experiments on real-world time-varying graph datasets and dynamic image restoration tasks demonstrate consistent gains over state-of-the-art fractional transforms and competitive learning-based baselines.

eess.SP↗

arXiv2026

FGFRFT: Fast Graph Fractional Fourier Transform via Exact Spectral Splitting and Fourier-Series Approximation

The graph fractional Fourier transform (GFRFT) for unitary graph Fourier transform (GFT) matrices can be interpreted through the scalar function $e^{j\alpha\theta}$ on the unit circle. Under the principal branch, its Fourier-series representation encounters an intrinsic obstruction at the spectral point $\lambda=-1$ for non-integer orders. To address this issue, we propose a fast graph fractional Fourier transform (FGFRFT) based on exact spectral splitting: the $\lambda=-1$ component is treated exactly, and the complementary component is approximated by a truncated Fourier series in integer powers of the GFT matrix. This construction yields an offline--online implementation that reduces the online complexity of repeated operator updates from $O(N^3)$ to $O(2LN^2)$ for truncation order $L$, while preserving differentiability with respect to the transform order. We further derive truncation-error bounds, approximate unitarity and additivity, and reconstruction-error bounds. Experiments on approximation accuracy, transform-order learning, image denoising, and point-cloud denoising show that FGFRFT provides substantial online acceleration while remaining close to the exact GFRFT under the tested settings.

eess.SP↗

arXiv2025

Rotation-Parameterized Graph Fractional Fourier Transform: Definition, Properties, and Optimal Filtering

Graph spectral representations are fundamental in graph signal processing, providing a rigorous frameworkforanalyzing graph-structured data. The graph fractional Fourier transform (GFRFT) extends the graph Fourier transform (GFT) through a fractional-order parameter, enabling flexible spectral analysis with mathematical consistency. The angular graph Fourier transform (AGFT) further introduces angular control by rotating GFT eigenvectors; however, existing constructions may fail to reduce exactly to the GFT at zero angle, weakening theoretical consistency and interpretability. To address these complementary limitations, namely the lack of rotation-based basis control in GFRFT and the defective zero-angle degeneracy of AGFT, this paper proposes the rotation-parameterized graph fractional Fourier transform (RP-GFRFT), which unifies fractional order and rotation-parameterized spectral analysis. A degeneracy preserving rotation matrix family is constructed to guarantee exact GFT reduction at zero angle. TwoRP-GFRFTvariants,I-RP-GFRFTandII-RP-GFRFT,arethenformulated, with theoretical analyses confirming their unitarity, invertibility, reduction behavior, and smooth parameter dependence. The fractional order and rotation angle are jointly optimized for adaptive graph spectral filtering. Experiments on real-world signals, images, and point clouds demonstrate that RP-GFRFT improves denoising accuracy, reconstruction quality, and feature preservation over GFRFT, AGFT, and representative filtering baselines.

stat.ML↗

arXiv2025

Hierarchical Graph Feature Enhancement with Adaptive Frequency Modulation for Visual Recognition

Convolutional neural networks (CNNs) have demonstrated strong performance in visual recognition tasks, but their inherent reliance on regular grid structures limits their capacity to model complex topological relationships and non-local semantics within images. To address this limita tion, we propose the hierarchical graph feature enhancement (HGFE), a novel framework that integrates graph-based rea soning into CNNs to enhance both structural awareness and feature representation. HGFE builds two complementary levels of graph structures: intra-window graph convolution to cap ture local spatial dependencies and inter-window supernode interactions to model global semantic relationships. Moreover, we introduce an adaptive frequency modulation module that dynamically balances low-frequency and high-frequency signal propagation, preserving critical edge and texture information while mitigating over-smoothing. The proposed HGFE module is lightweight, end-to-end trainable, and can be seamlessly integrated into standard CNN backbone networks. Extensive experiments on CIFAR-100 (classification), PASCAL VOC, and VisDrone (detection), as well as CrackSeg and CarParts (segmentation), validated the effectiveness of the HGFE in improving structural representation and enhancing overall recognition performance.

cs.CV↗