{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TSX2AGLRFC2SK3LNRPOQYHEREA","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":"9116fb44d5f886bd60f715236f9bde8864d0529c5aadccadf810d65aeca312b4","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-12-07T22:02:33Z","title_canon_sha256":"b68957f83aeee115e4c64089138bf9b408f3d03eb0d9a348ea8132ea3aefcc4b"},"schema_version":"1.0","source":{"id":"1412.2404","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2404","created_at":"2026-05-18T01:17:33Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2404v3","created_at":"2026-05-18T01:17:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2404","created_at":"2026-05-18T01:17:33Z"},{"alias_kind":"pith_short_12","alias_value":"TSX2AGLRFC2S","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TSX2AGLRFC2SK3LN","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TSX2AGLR","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:c90d435aca0a797f432b5ec7be2a0a1ac5bec9cce6d5fec7b443ebbaf1ead067","target":"graph","created_at":"2026-05-18T01:17:33Z","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":"Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have not been well studied. Our key contribution is to show that $2K$ projection vectors are sufficient for the independence preservation of any $K$ class data sampled from a union of independent subspaces. It is this non-trivial observation that we use for designing our dimensionality reduction technique. In this paper, we propose a novel dimensionality reductio","authors_text":"Devansh Arpit, Ifeoma Nwogu, Venu Govindaraju","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-12-07T22:02:33Z","title":"Dimensionality Reduction with Subspace Structure Preservation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2404","kind":"arxiv","version":3},"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":"sha256:85d2ebb81740b42f8aebf8096d5b163c806da7df05706ecb298902c73c3565ce","target":"record","created_at":"2026-05-18T01:17:33Z","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":"9116fb44d5f886bd60f715236f9bde8864d0529c5aadccadf810d65aeca312b4","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-12-07T22:02:33Z","title_canon_sha256":"b68957f83aeee115e4c64089138bf9b408f3d03eb0d9a348ea8132ea3aefcc4b"},"schema_version":"1.0","source":{"id":"1412.2404","kind":"arxiv","version":3}},"canonical_sha256":"9cafa0197128b5256d6d8bdd0c1c912031e99327a0121083942a27f5f5f92cdd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cafa0197128b5256d6d8bdd0c1c912031e99327a0121083942a27f5f5f92cdd","first_computed_at":"2026-05-18T01:17:33.294349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:33.294349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KbtnrUWfngZ17tKqZRoMzbaV0+WEAEme9pZvgOMx+01wynJgc6bDtHXobdpV2xLbiOccT6aU+7z0FPMo6C56CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:33.295053Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.2404","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85d2ebb81740b42f8aebf8096d5b163c806da7df05706ecb298902c73c3565ce","sha256:c90d435aca0a797f432b5ec7be2a0a1ac5bec9cce6d5fec7b443ebbaf1ead067"],"state_sha256":"51c407d4219ff2c226b54ce726a72a537e998ddd671a6a5ca9a63a9850e9d609"}