{"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/a-functional-representation-for-graph","title":"A Functional Representation for Graph Matching","arxiv_id":"1901.05179","date":"2019-01-16","proceeding":null,"authors":["Fu-Dong Wang","Gui-Song Xia","Nan Xue","Yi-Peng Zhang","Marcello Pelillo"],"abstract":"Graph matching is an important and persistent problem in computer vision and\npattern recognition for finding node-to-node correspondence between\ngraph-structured data. However, as widely used, graph matching that\nincorporates pairwise constraints can be formulated as a quadratic assignment\nproblem (QAP), which is NP-complete and results in intrinsic computational\ndifficulties. In this paper, we present a functional representation for graph\nmatching (FRGM) that aims to provide more geometric insights on the problem and\nreduce the space and time complexities of corresponding algorithms. To achieve\nthese goals, we represent a graph endowed with edge attributes by a linear\nfunction space equipped with a functional such as inner product or metric, that\nhas an explicit geometric meaning. Consequently, the correspondence between\ngraphs can be represented as a linear representation map of that functional.\nSpecifically, we reformulate the linear functional representation map as a new\nparameterization for Euclidean graph matching, which is associative with\ngeometric parameters for graphs under rigid or nonrigid deformations. This\nallows us to estimate the correspondence and geometric deformations\nsimultaneously. The use of the representation of edge attributes rather than\nthe affinity matrix enables us to reduce the space complexity by two orders of\nmagnitudes. Furthermore, we propose an efficient optimization strategy with low\ntime complexity to optimize the objective function. The experimental results on\nboth synthetic and real-world datasets demonstrate that the proposed FRGM can\nachieve state-of-the-art performance.","url_abs":"http://arxiv.org/abs/1901.05179v1","url_pdf":"http://arxiv.org/pdf/1901.05179v1.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":"a-functional-representation-for-graph","repo_url":"https://github.com/wangfudong/FRGM","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[{"task_slug":"graph-matching","task_name":"Graph Matching"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1901.05179","atlas_url":"https://app.syntology.ai/?focus=1901.05179","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}