{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QUXGD2I3I7HV2DWV4BZSY3K5MN","short_pith_number":"pith:QUXGD2I3","canonical_record":{"source":{"id":"1610.04929","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-10-16T23:37:26Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"43954e13d9772bea9d609d12d484c31a393d1fbc7d140c81a144b3fdcb944c73","abstract_canon_sha256":"d85ee775774642a159c58acb15dba51efa72725ff68a68a7bc0e7c1e0c80eb52"},"schema_version":"1.0"},"canonical_sha256":"852e61e91b47cf5d0ed5e0732c6d5d63743c238b0036956ee82e8978f7fef031","source":{"kind":"arxiv","id":"1610.04929","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04929","created_at":"2026-05-18T01:02:06Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04929v1","created_at":"2026-05-18T01:02:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04929","created_at":"2026-05-18T01:02:06Z"},{"alias_kind":"pith_short_12","alias_value":"QUXGD2I3I7HV","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"QUXGD2I3I7HV2DWV","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"QUXGD2I3","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QUXGD2I3I7HV2DWV4BZSY3K5MN","target":"record","payload":{"canonical_record":{"source":{"id":"1610.04929","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-10-16T23:37:26Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"43954e13d9772bea9d609d12d484c31a393d1fbc7d140c81a144b3fdcb944c73","abstract_canon_sha256":"d85ee775774642a159c58acb15dba51efa72725ff68a68a7bc0e7c1e0c80eb52"},"schema_version":"1.0"},"canonical_sha256":"852e61e91b47cf5d0ed5e0732c6d5d63743c238b0036956ee82e8978f7fef031","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:06.699858Z","signature_b64":"iZNPDTgqw8ueog23aeHh6quVlagAOFHab8DWJJbb5RNFJySZ3Pb/oP6yc3MX7EpnUE7FxiaFDK7HQE9w4q23AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"852e61e91b47cf5d0ed5e0732c6d5d63743c238b0036956ee82e8978f7fef031","last_reissued_at":"2026-05-18T01:02:06.699358Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:06.699358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.04929","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:02:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L4T7PKwzMXeob/TYEF0VzlbD2AiUix3yOwmOtZ5HO/B82jbkLqXw+Y9WXWDi+ipPVgcNlwGfxR+yAkQRepJoDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T00:20:32.441272Z"},"content_sha256":"5888416bfadf24944f6cf4c926c6c0cc55a35a7a5b32b303e58a3d6225f213ce","schema_version":"1.0","event_id":"sha256:5888416bfadf24944f6cf4c926c6c0cc55a35a7a5b32b303e58a3d6225f213ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QUXGD2I3I7HV2DWV4BZSY3K5MN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Probabilistic Dimensionality Reduction via Structure Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Li Wang","submitted_at":"2016-10-16T23:37:26Z","abstract_excerpt":"We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth skeleton of embedding points in a low-dimensional space from high-dimensional noisy data. The formulation of the new model can be equivalently interpreted as two coupled learning problem, i.e., structure learning and the learning of projection matrix. This interpretation motivates the learning of the embedding points that can directly form an explicit graph str"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04929","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:02:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"65+Ty/yZo0Lc/Y7jnU0i5dJx7v0e7qWCA8F05RUgCdixrr23v01OSejEBVBO1L7f55kTB7HTA92p2c5hf40GCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T00:20:32.442012Z"},"content_sha256":"c3046c60c87e185ed5ec181b68a5c720336e6c28c157f0ebe38bf661141e8c10","schema_version":"1.0","event_id":"sha256:c3046c60c87e185ed5ec181b68a5c720336e6c28c157f0ebe38bf661141e8c10"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QUXGD2I3I7HV2DWV4BZSY3K5MN/bundle.json","state_url":"https://pith.science/pith/QUXGD2I3I7HV2DWV4BZSY3K5MN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QUXGD2I3I7HV2DWV4BZSY3K5MN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T00:20:32Z","links":{"resolver":"https://pith.science/pith/QUXGD2I3I7HV2DWV4BZSY3K5MN","bundle":"https://pith.science/pith/QUXGD2I3I7HV2DWV4BZSY3K5MN/bundle.json","state":"https://pith.science/pith/QUXGD2I3I7HV2DWV4BZSY3K5MN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QUXGD2I3I7HV2DWV4BZSY3K5MN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QUXGD2I3I7HV2DWV4BZSY3K5MN","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":"d85ee775774642a159c58acb15dba51efa72725ff68a68a7bc0e7c1e0c80eb52","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-10-16T23:37:26Z","title_canon_sha256":"43954e13d9772bea9d609d12d484c31a393d1fbc7d140c81a144b3fdcb944c73"},"schema_version":"1.0","source":{"id":"1610.04929","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04929","created_at":"2026-05-18T01:02:06Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04929v1","created_at":"2026-05-18T01:02:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04929","created_at":"2026-05-18T01:02:06Z"},{"alias_kind":"pith_short_12","alias_value":"QUXGD2I3I7HV","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"QUXGD2I3I7HV2DWV","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"QUXGD2I3","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:c3046c60c87e185ed5ec181b68a5c720336e6c28c157f0ebe38bf661141e8c10","target":"graph","created_at":"2026-05-18T01:02:06Z","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"},"paper":{"abstract_excerpt":"We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth skeleton of embedding points in a low-dimensional space from high-dimensional noisy data. The formulation of the new model can be equivalently interpreted as two coupled learning problem, i.e., structure learning and the learning of projection matrix. This interpretation motivates the learning of the embedding points that can directly form an explicit graph str","authors_text":"Li Wang","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-10-16T23:37:26Z","title":"Probabilistic Dimensionality Reduction via Structure Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04929","kind":"arxiv","version":1},"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":"sha256:5888416bfadf24944f6cf4c926c6c0cc55a35a7a5b32b303e58a3d6225f213ce","target":"record","created_at":"2026-05-18T01:02:06Z","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":"d85ee775774642a159c58acb15dba51efa72725ff68a68a7bc0e7c1e0c80eb52","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-10-16T23:37:26Z","title_canon_sha256":"43954e13d9772bea9d609d12d484c31a393d1fbc7d140c81a144b3fdcb944c73"},"schema_version":"1.0","source":{"id":"1610.04929","kind":"arxiv","version":1}},"canonical_sha256":"852e61e91b47cf5d0ed5e0732c6d5d63743c238b0036956ee82e8978f7fef031","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"852e61e91b47cf5d0ed5e0732c6d5d63743c238b0036956ee82e8978f7fef031","first_computed_at":"2026-05-18T01:02:06.699358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:06.699358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iZNPDTgqw8ueog23aeHh6quVlagAOFHab8DWJJbb5RNFJySZ3Pb/oP6yc3MX7EpnUE7FxiaFDK7HQE9w4q23AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:06.699858Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.04929","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5888416bfadf24944f6cf4c926c6c0cc55a35a7a5b32b303e58a3d6225f213ce","sha256:c3046c60c87e185ed5ec181b68a5c720336e6c28c157f0ebe38bf661141e8c10"],"state_sha256":"218bfd8a89bd190f9740548e1f1911f96d210ec25d5aa07836b9409a2c9d06a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X78Vq/JT8RwmqGhpQx4Gl2h5BFid9BaAwET2DmC2Pak5R/Mrgw5Gqat4V+aGeHfnBAvRg4Nh9W897LneJxSxBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T00:20:32.446687Z","bundle_sha256":"bdd2b5c7f071d66570a49c72d510af29f917ec6ea9a8b8d7c62fcf22a791c3d5"}}