{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:E3YKYHJ5N65XBDHUGR33ZM3RNT","short_pith_number":"pith:E3YKYHJ5","schema_version":"1.0","canonical_sha256":"26f0ac1d3d6fbb708cf43477bcb3716cfd7250c9a34031aa6f0208132b8f996c","source":{"kind":"arxiv","id":"2502.07510","version":2},"attestation_state":"computed","paper":{"title":"Joint Metric Space Embedding by Unbalanced OT with Gromov-Wasserstein Marginal Penalization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Florian Beier, Gabriele Steidl, Moritz Piening, Robert Beinert","submitted_at":"2025-02-11T12:28:47Z","abstract_excerpt":"We propose a new approach for unsupervised alignment of heterogeneous datasets, which maps data from two different domains without any known correspondences to a common metric space. Our method is based on an unbalanced optimal transport problem with Gromov-Wasserstein marginal penalization. It can be seen as a counterpart to the recently introduced joint multidimensional scaling method. We prove that there exists a minimizer of our functional and that for penalization parameters going to infinity, the corresponding sequence of minimizers converges to a minimizer of the so-called embedded Wass"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2502.07510","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-02-11T12:28:47Z","cross_cats_sorted":[],"title_canon_sha256":"a88874b6536212e1fac94e63e68b0a07cb2494ab5b6870c19ce764f7a918bc6a","abstract_canon_sha256":"30db0f591eb416cbab21b96aa906fcbff90feafd11bbdf596159932e3499b725"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:02:18.000559Z","signature_b64":"NVFkxCnloxCk+1WQCiPOZyBhLUFBnoEIVFILMZBTVMUoGbaI1nV/31eJMDNETAUYm8X1U5EPCBZHCrpmJZV0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26f0ac1d3d6fbb708cf43477bcb3716cfd7250c9a34031aa6f0208132b8f996c","last_reissued_at":"2026-07-05T11:02:18.000099Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:02:18.000099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Joint Metric Space Embedding by Unbalanced OT with Gromov-Wasserstein Marginal Penalization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Florian Beier, Gabriele Steidl, Moritz Piening, Robert Beinert","submitted_at":"2025-02-11T12:28:47Z","abstract_excerpt":"We propose a new approach for unsupervised alignment of heterogeneous datasets, which maps data from two different domains without any known correspondences to a common metric space. Our method is based on an unbalanced optimal transport problem with Gromov-Wasserstein marginal penalization. It can be seen as a counterpart to the recently introduced joint multidimensional scaling method. We prove that there exists a minimizer of our functional and that for penalization parameters going to infinity, the corresponding sequence of minimizers converges to a minimizer of the so-called embedded Wass"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.07510","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.07510/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2502.07510","created_at":"2026-07-05T11:02:18.000154+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.07510v2","created_at":"2026-07-05T11:02:18.000154+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.07510","created_at":"2026-07-05T11:02:18.000154+00:00"},{"alias_kind":"pith_short_12","alias_value":"E3YKYHJ5N65X","created_at":"2026-07-05T11:02:18.000154+00:00"},{"alias_kind":"pith_short_16","alias_value":"E3YKYHJ5N65XBDHU","created_at":"2026-07-05T11:02:18.000154+00:00"},{"alias_kind":"pith_short_8","alias_value":"E3YKYHJ5","created_at":"2026-07-05T11:02:18.000154+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/E3YKYHJ5N65XBDHUGR33ZM3RNT","json":"https://pith.science/pith/E3YKYHJ5N65XBDHUGR33ZM3RNT.json","graph_json":"https://pith.science/api/pith-number/E3YKYHJ5N65XBDHUGR33ZM3RNT/graph.json","events_json":"https://pith.science/api/pith-number/E3YKYHJ5N65XBDHUGR33ZM3RNT/events.json","paper":"https://pith.science/paper/E3YKYHJ5"},"agent_actions":{"view_html":"https://pith.science/pith/E3YKYHJ5N65XBDHUGR33ZM3RNT","download_json":"https://pith.science/pith/E3YKYHJ5N65XBDHUGR33ZM3RNT.json","view_paper":"https://pith.science/paper/E3YKYHJ5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.07510&json=true","fetch_graph":"https://pith.science/api/pith-number/E3YKYHJ5N65XBDHUGR33ZM3RNT/graph.json","fetch_events":"https://pith.science/api/pith-number/E3YKYHJ5N65XBDHUGR33ZM3RNT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E3YKYHJ5N65XBDHUGR33ZM3RNT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E3YKYHJ5N65XBDHUGR33ZM3RNT/action/storage_attestation","attest_author":"https://pith.science/pith/E3YKYHJ5N65XBDHUGR33ZM3RNT/action/author_attestation","sign_citation":"https://pith.science/pith/E3YKYHJ5N65XBDHUGR33ZM3RNT/action/citation_signature","submit_replication":"https://pith.science/pith/E3YKYHJ5N65XBDHUGR33ZM3RNT/action/replication_record"}},"created_at":"2026-07-05T11:02:18.000154+00:00","updated_at":"2026-07-05T11:02:18.000154+00:00"}