{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/decimated-framelet-system-on-graphs-and-fast","title":"Decimated Framelet System on Graphs and Fast G-Framelet Transforms","arxiv_id":"2012.06922","date":"2020-12-12","proceeding":null,"authors":["Xuebin Zheng","Bingxin Zhou","Yu Guang Wang","Xiaosheng Zhuang"],"abstract":"Graph representation learning has many real-world applications, from super-resolution imaging, 3D computer vision to drug repurposing, protein classification, social networks analysis. An adequate representation of graph data is vital to the learning performance of a statistical or machine learning model for graph-structured data. In this paper, we propose a novel multiscale representation system for graph data, called decimated framelets, which form a localized tight frame on the graph. The decimated framelet system allows storage of the graph data representation on a coarse-grained chain and processes the graph data at multi scales where at each scale, the data is stored at a subgraph. Based on this, we then establish decimated G-framelet transforms for the decomposition and reconstruction of the graph data at multi resolutions via a constructive data-driven filter bank. The graph framelets are built on a chain-based orthonormal basis that supports fast graph Fourier transforms. From this, we give a fast algorithm for the decimated G-framelet transforms, or FGT, that has linear computational complexity O(N) for a graph of size N. The theory of decimated framelets and FGT is verified with numerical examples for random graphs. The effectiveness is demonstrated by real-world applications, including multiresolution analysis for traffic network, and graph neural networks for graph classification tasks.","url_abs":"https://arxiv.org/abs/2012.06922v2","url_pdf":"https://arxiv.org/pdf/2012.06922v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"decimated-framelet-system-on-graphs-and-fast","repo_url":"https://github.com/YuGuangWang/FGT","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"graph-classification","task_name":"Graph Classification"},{"task_slug":"graph-representation-learning","task_name":"Graph Representation Learning"},{"task_slug":"representation-learning","task_name":"Representation Learning"},{"task_slug":"super-resolution","task_name":"Super-Resolution"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2012.06922","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2012.06922"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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