2020/11/08 by Patanè, Giuseppe · 4 citations
Computer Science · Physics and Astronomy · #Advanced Graph Neural Networks #Bayesian Modeling and Causal Inference #Complex Network Analysis Techniques #FOS: Computer and information sciences #Graphics (cs.GR) #Machine Learning (cs.LG)
paper · pdf · doi:10.48550/arxiv.2011.04055
openalex publication_date 2020/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Data are represented as graphs in a wide range of applications, such as Computer Vision (e.g., images) and Graphics (e.g., 3D meshes), network analysis (e.g., social networks), and bio-informatics (e.g., molecules). In this context, our overall goal is the definition of novel Fourier-based and graph filters induced by rational polynomials for graph processing, which generalise polynomial filters and the Fourier transform to non-Euclidean domains. For the efficient evaluation of discrete spectral Fourier-based and wavelet operators, we introduce a spectrum-free approach, which requires the solution of a small set of sparse, symmetric, well-conditioned linear systems and is oblivious of the evaluation of the Laplacian or kernel spectrum. Approximating arbitrary graph filters with rational polynomials provides a more accurate and numerically stable alternative with respect to polynomials. To achieve these goals, we also study the link between spectral operators, wavelets, and filtered convolution with integral operators induced by spectral kernels. According to our tests, main advantages of the proposed approach are (i) its generality with respect to the input data (e.g., graphs, 3D shapes), applications (e.g., signal reconstruction and smoothing, shape correspondence), and filters (e.g., polynomial, rational polynomial), and (ii) a spectrum-free computation with a generally low computational cost and storage overhead.