{"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/linear-partial-gromov-wasserstein-embedding","title":"Linear Partial Gromov-Wasserstein Embedding","arxiv_id":"2410.16669","date":"2024-10-22","proceeding":null,"authors":["Yikun Bai","Abihith Kothapalli","Hengrong Du","Rocio Diaz Martin","Soheil Kolouri"],"abstract":"The Gromov-Wasserstein (GW) problem, a variant of the classical optimal transport (OT) problem, has attracted growing interest in the machine learning and data science communities due to its ability to quantify similarity between measures in different metric spaces. However, like the classical OT problem, GW imposes an equal mass constraint between measures, which restricts its application in many machine learning tasks. To address this limitation, the partial Gromov-Wasserstein (PGW) problem has been introduced. It relaxes the equal mass constraint, allowing the comparison of general positive Radon measures. Despite this, both GW and PGW face significant computational challenges due to their non-convex nature. To overcome these challenges, we propose the linear partial Gromov-Wasserstein (LPGW) embedding, a linearized embedding technique for the PGW problem. For $K$ different metric measure spaces, the pairwise computation of the PGW distance requires solving the PGW problem ${O}(K^2)$ times. In contrast, the proposed linearization technique reduces this to ${O}(K)$ times. Similar to the linearization technique for the classical OT problem, we prove that LPGW defines a valid metric for metric measure spaces. Finally, we demonstrate the effectiveness of LPGW in practical applications such as shape retrieval and learning with transport-based embeddings, showing that LPGW preserves the advantages of PGW in partial matching while significantly enhancing computational efficiency. The code is available at https://github.com/mint-vu/Linearized_Partial_Gromov_Wasserstein.","url_abs":"https://arxiv.org/abs/2410.16669v3","url_pdf":"https://arxiv.org/pdf/2410.16669v3.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":"linear-partial-gromov-wasserstein-embedding","repo_url":"https://github.com/mint-vu/linearized_partial_gromov_wasserstein","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"computational-efficiency","task_name":"Computational Efficiency"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2410.16669","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2410.16669"}},"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. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"deterministic:regex_extraction","url":"https://github.com/mint-vu/Linearized_Partial_","reach":{"status":"gone","observed_at":"2026-09-17","how":"tree_404+repo_404"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/mint-vu/linearized_partial_gromov_wasserstein","reach":null}],"summary":{"ran_draft_wrong":2,"ran_fixture":1,"unverified":2},"by_repo_kind":{"official":{"samples":5,"ran":3,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":5,"samples":[{"code_sha256_prefix":"81453c042b786248","entry":"HKExpMonge","repo":"mint-vu/linearized_partial_gromov_wasserstein","repo_kind":"official","path":"lib/HK/LinHK.py","file_url":"https://github.com/mint-vu/linearized_partial_gromov_wasserstein/blob/HEAD/lib/HK/LinHK.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"81453c042b786248"}},{"code_sha256_prefix":"27d50176d89873cb","entry":"HKLog","repo":"mint-vu/linearized_partial_gromov_wasserstein","repo_kind":"official","path":"lib/HK/LinHK.py","file_url":"https://github.com/mint-vu/linearized_partial_gromov_wasserstein/blob/HEAD/lib/HK/LinHK.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"27d50176d89873cb"}},{"code_sha256_prefix":"8361f15bc2a5e3e0","entry":"extractMongeData","repo":"mint-vu/linearized_partial_gromov_wasserstein","repo_kind":"official","path":"lib/HK/LinHK.py","file_url":"https://github.com/mint-vu/linearized_partial_gromov_wasserstein/blob/HEAD/lib/HK/LinHK.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"8361f15bc2a5e3e0"}},{"code_sha256_prefix":"61506143c11a9dc0","entry":"LPGW_embedding","repo":"mint-vu/linearized_partial_gromov_wasserstein","repo_kind":"official","path":"lib/linear_gromov.py","file_url":"https://github.com/mint-vu/linearized_partial_gromov_wasserstein/blob/HEAD/lib/linear_gromov.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"61506143c11a9dc0"}},{"code_sha256_prefix":"496dc9a62b3a4511","entry":"X_to_C","repo":"mint-vu/linearized_partial_gromov_wasserstein","repo_kind":"official","path":"lib/linear_gromov.py","file_url":"https://github.com/mint-vu/linearized_partial_gromov_wasserstein/blob/HEAD/lib/linear_gromov.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"496dc9a62b3a4511"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}