{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UMPQCNA6GNNOOY7RXUZKOSDHPK","short_pith_number":"pith:UMPQCNA6","canonical_record":{"source":{"id":"1504.01777","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2015-04-07T23:18:34Z","cross_cats_sorted":[],"title_canon_sha256":"54d4147cf811ea1881ed1711cbf6728a699f38ce5baa89a1a62bbe72ee3805e7","abstract_canon_sha256":"e9cbbd09c7635d3b4eb523abb77fd33236797f3b2f47ea045a5433c9324c27c0"},"schema_version":"1.0"},"canonical_sha256":"a31f01341e335ae763f1bd32a748677a9eaca5cfeb243e9e0e568226eee92fe4","source":{"kind":"arxiv","id":"1504.01777","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01777","created_at":"2026-05-18T02:17:32Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01777v2","created_at":"2026-05-18T02:17:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01777","created_at":"2026-05-18T02:17:32Z"},{"alias_kind":"pith_short_12","alias_value":"UMPQCNA6GNNO","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UMPQCNA6GNNOOY7R","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UMPQCNA6","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UMPQCNA6GNNOOY7RXUZKOSDHPK","target":"record","payload":{"canonical_record":{"source":{"id":"1504.01777","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2015-04-07T23:18:34Z","cross_cats_sorted":[],"title_canon_sha256":"54d4147cf811ea1881ed1711cbf6728a699f38ce5baa89a1a62bbe72ee3805e7","abstract_canon_sha256":"e9cbbd09c7635d3b4eb523abb77fd33236797f3b2f47ea045a5433c9324c27c0"},"schema_version":"1.0"},"canonical_sha256":"a31f01341e335ae763f1bd32a748677a9eaca5cfeb243e9e0e568226eee92fe4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:32.949622Z","signature_b64":"VPa5TjEi4/GRaVmZpiUjfSth3SNn9g0jCpQ9fd6uxfwbEW1VDQ6yCgiViuamTLjV51DSxgBolWfeznzEcp0pBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a31f01341e335ae763f1bd32a748677a9eaca5cfeb243e9e0e568226eee92fe4","last_reissued_at":"2026-05-18T02:17:32.948920Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:32.948920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.01777","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:17:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SKoXn2P3vxiI9Sbdp44queMKRUtwNN062kKlY4y+KPsoVEB90KHpxStlsGXOVfT8IoyQBmJ9cYOhctjPu6nMBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T10:23:58.525713Z"},"content_sha256":"7d0cff7ddcc1c4b6cd1ec8e938fe67e6b1e5c61a88ac42caaed7584f8c67c5a1","schema_version":"1.0","event_id":"sha256:7d0cff7ddcc1c4b6cd1ec8e938fe67e6b1e5c61a88ac42caaed7584f8c67c5a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UMPQCNA6GNNOOY7RXUZKOSDHPK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Heterogeneous Tensor Decomposition for Clustering via Manifold Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CV","authors_text":"Bamdev Mishra, Baocai Yin, Junbin Gao, Xia Hong, Yanfeng Sun","submitted_at":"2015-04-07T23:18:34Z","abstract_excerpt":"Tensors or multiarray data are generalizations of matrices. Tensor clustering has become a very important research topic due to the intrinsically rich structures in real-world multiarray datasets. Subspace clustering based on vectorizing multiarray data has been extensively researched. However, vectorization of tensorial data does not exploit complete structure information. In this paper, we propose a subspace clustering algorithm without adopting any vectorization process. Our approach is based on a novel heterogeneous Tucker decomposition model. In contrast to existing techniques, we propose"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01777","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":""},"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":"2026-05-18T02:17:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Swwn7n1n7B2cWksJs7FRL3ke9e1iQOeYODquR/zfuhNOGqWer7aYtymjE2Q6kEB1/X2lkZibL2Pto6DeABqDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T10:23:58.526071Z"},"content_sha256":"36dc4e2d0fe270845ff5290e1b1ff63ce2de31fe0b9a5bc78d6ca2da57b32d1c","schema_version":"1.0","event_id":"sha256:36dc4e2d0fe270845ff5290e1b1ff63ce2de31fe0b9a5bc78d6ca2da57b32d1c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UMPQCNA6GNNOOY7RXUZKOSDHPK/bundle.json","state_url":"https://pith.science/pith/UMPQCNA6GNNOOY7RXUZKOSDHPK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UMPQCNA6GNNOOY7RXUZKOSDHPK/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":"2026-06-02T10:23:58Z","links":{"resolver":"https://pith.science/pith/UMPQCNA6GNNOOY7RXUZKOSDHPK","bundle":"https://pith.science/pith/UMPQCNA6GNNOOY7RXUZKOSDHPK/bundle.json","state":"https://pith.science/pith/UMPQCNA6GNNOOY7RXUZKOSDHPK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UMPQCNA6GNNOOY7RXUZKOSDHPK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UMPQCNA6GNNOOY7RXUZKOSDHPK","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":"e9cbbd09c7635d3b4eb523abb77fd33236797f3b2f47ea045a5433c9324c27c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2015-04-07T23:18:34Z","title_canon_sha256":"54d4147cf811ea1881ed1711cbf6728a699f38ce5baa89a1a62bbe72ee3805e7"},"schema_version":"1.0","source":{"id":"1504.01777","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01777","created_at":"2026-05-18T02:17:32Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01777v2","created_at":"2026-05-18T02:17:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01777","created_at":"2026-05-18T02:17:32Z"},{"alias_kind":"pith_short_12","alias_value":"UMPQCNA6GNNO","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UMPQCNA6GNNOOY7R","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UMPQCNA6","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:36dc4e2d0fe270845ff5290e1b1ff63ce2de31fe0b9a5bc78d6ca2da57b32d1c","target":"graph","created_at":"2026-05-18T02:17:32Z","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":"Tensors or multiarray data are generalizations of matrices. Tensor clustering has become a very important research topic due to the intrinsically rich structures in real-world multiarray datasets. Subspace clustering based on vectorizing multiarray data has been extensively researched. However, vectorization of tensorial data does not exploit complete structure information. In this paper, we propose a subspace clustering algorithm without adopting any vectorization process. Our approach is based on a novel heterogeneous Tucker decomposition model. In contrast to existing techniques, we propose","authors_text":"Bamdev Mishra, Baocai Yin, Junbin Gao, Xia Hong, Yanfeng Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2015-04-07T23:18:34Z","title":"Heterogeneous Tensor Decomposition for Clustering via Manifold Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01777","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":"sha256:7d0cff7ddcc1c4b6cd1ec8e938fe67e6b1e5c61a88ac42caaed7584f8c67c5a1","target":"record","created_at":"2026-05-18T02:17:32Z","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":"e9cbbd09c7635d3b4eb523abb77fd33236797f3b2f47ea045a5433c9324c27c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2015-04-07T23:18:34Z","title_canon_sha256":"54d4147cf811ea1881ed1711cbf6728a699f38ce5baa89a1a62bbe72ee3805e7"},"schema_version":"1.0","source":{"id":"1504.01777","kind":"arxiv","version":2}},"canonical_sha256":"a31f01341e335ae763f1bd32a748677a9eaca5cfeb243e9e0e568226eee92fe4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a31f01341e335ae763f1bd32a748677a9eaca5cfeb243e9e0e568226eee92fe4","first_computed_at":"2026-05-18T02:17:32.948920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:32.948920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VPa5TjEi4/GRaVmZpiUjfSth3SNn9g0jCpQ9fd6uxfwbEW1VDQ6yCgiViuamTLjV51DSxgBolWfeznzEcp0pBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:32.949622Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01777","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d0cff7ddcc1c4b6cd1ec8e938fe67e6b1e5c61a88ac42caaed7584f8c67c5a1","sha256:36dc4e2d0fe270845ff5290e1b1ff63ce2de31fe0b9a5bc78d6ca2da57b32d1c"],"state_sha256":"e58818e75392a63454119c39731ee6beea151f63de67baa1491157aa729ecfeb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gJDekj4BU1PiYeMAd+DUcuSE0X+DgAHjvFgdVSL/nhsnt9523WNfHh1TJcg5HXyjBHDDGiMh6lgDl1VhuA4CBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T10:23:58.528120Z","bundle_sha256":"a2231de6db80619fba214352fbbeeacbd6472e6be5e7c636c5768672cb02afbf"}}