{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:GRPSLDUII4NNQJUX6P36TIDRD7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a087ce549d96f304f032776eb211e347c8d508d4619f4ec3dd5e69a28b06f117","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-06-05T09:14:25Z","title_canon_sha256":"9db5fc4d44e26a16caade35e0b938bfeb00e5d3e3442dfd89fd14c794522f0a0"},"schema_version":"1.0","source":{"id":"2506.04786","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.04786","created_at":"2026-07-05T12:05:17Z"},{"alias_kind":"arxiv_version","alias_value":"2506.04786v2","created_at":"2026-07-05T12:05:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.04786","created_at":"2026-07-05T12:05:17Z"},{"alias_kind":"pith_short_12","alias_value":"GRPSLDUII4NN","created_at":"2026-07-05T12:05:17Z"},{"alias_kind":"pith_short_16","alias_value":"GRPSLDUII4NNQJUX","created_at":"2026-07-05T12:05:17Z"},{"alias_kind":"pith_short_8","alias_value":"GRPSLDUI","created_at":"2026-07-05T12:05:17Z"}],"graph_snapshots":[{"event_id":"sha256:7ba1cfa8f67fc97ca5cbe2f93b7a3a9d49fcb4bec66e3634265504a64f6c5c0e","target":"graph","created_at":"2026-07-05T12:05:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.04786/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Vector Quantization (VQ) is a widely used technique in machine learning and data compression, valued for its simplicity and interpretability. Among hard VQ methods, $k$-medoids clustering and Kernel Density Estimation (KDE) approaches represent two prominent yet seemingly unrelated paradigms -- one distance-based, the other rooted in probability density matching. In this paper, we investigate their connection through the lens of Quadratic Unconstrained Binary Optimization (QUBO). We compare a heuristic QUBO formulation for $k$-medoids, which balances centrality and diversity, with a principled","authors_text":"Christian Bauckhage, Sascha M\\\"ucke, Thore Gerlach","cross_cats":["quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-06-05T09:14:25Z","title":"Kernel $k$-Medoids as General Vector Quantization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04786","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3a0e86ed080da7b40c9c4b9fb17fead5fa4d87a821d0f63d1992f00df56c8802","target":"record","created_at":"2026-07-05T12:05:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a087ce549d96f304f032776eb211e347c8d508d4619f4ec3dd5e69a28b06f117","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-06-05T09:14:25Z","title_canon_sha256":"9db5fc4d44e26a16caade35e0b938bfeb00e5d3e3442dfd89fd14c794522f0a0"},"schema_version":"1.0","source":{"id":"2506.04786","kind":"arxiv","version":2}},"canonical_sha256":"345f258e88471ad82697f3f7e9a0711fd2ec3a54b5f2c5195ac89265a601feef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"345f258e88471ad82697f3f7e9a0711fd2ec3a54b5f2c5195ac89265a601feef","first_computed_at":"2026-07-05T12:05:17.321638Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:05:17.321638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5fKUR5cOMVDUXK+8qke+XvVsQsRZm+2beIGGWYV6XLUMcMrz6NWLa2OrNSewnHjgrKHUDqWOlYeubV65wWPpAA==","signature_status":"signed_v1","signed_at":"2026-07-05T12:05:17.322219Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.04786","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a0e86ed080da7b40c9c4b9fb17fead5fa4d87a821d0f63d1992f00df56c8802","sha256:7ba1cfa8f67fc97ca5cbe2f93b7a3a9d49fcb4bec66e3634265504a64f6c5c0e"],"state_sha256":"316613c0b8ac1b4d3fa80505a4559f3f2cbc4f724ea52dc63bce5eee8240d6c4"}