{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ABM7OPDYPDE3X5YXR7KTMWK567","short_pith_number":"pith:ABM7OPDY","canonical_record":{"source":{"id":"1506.04389","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-14T13:19:38Z","cross_cats_sorted":[],"title_canon_sha256":"26e641a277d81279871335034ffcb621e88d16c9f62d0e4cf020ba5768310117","abstract_canon_sha256":"b24df0371fc1b0fc8d4c33975591fc2c7c309b4080a7c249ad9e5f048a66f6f1"},"schema_version":"1.0"},"canonical_sha256":"0059f73c7878c9bbf7178fd536595df7c3d4de9fe52cd819d37c7de91cf44ca0","source":{"kind":"arxiv","id":"1506.04389","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.04389","created_at":"2026-05-18T01:37:48Z"},{"alias_kind":"arxiv_version","alias_value":"1506.04389v2","created_at":"2026-05-18T01:37:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04389","created_at":"2026-05-18T01:37:48Z"},{"alias_kind":"pith_short_12","alias_value":"ABM7OPDYPDE3","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ABM7OPDYPDE3X5YX","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ABM7OPDY","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ABM7OPDYPDE3X5YXR7KTMWK567","target":"record","payload":{"canonical_record":{"source":{"id":"1506.04389","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-14T13:19:38Z","cross_cats_sorted":[],"title_canon_sha256":"26e641a277d81279871335034ffcb621e88d16c9f62d0e4cf020ba5768310117","abstract_canon_sha256":"b24df0371fc1b0fc8d4c33975591fc2c7c309b4080a7c249ad9e5f048a66f6f1"},"schema_version":"1.0"},"canonical_sha256":"0059f73c7878c9bbf7178fd536595df7c3d4de9fe52cd819d37c7de91cf44ca0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:48.743765Z","signature_b64":"K+2D0JVyzTUTL370HFxsZzLnJKex4K4LkxEriE6KNCRJPQ6Ad+UhQmN9F/d2URA0xCVX/O28NcPRwKEIoTXYDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0059f73c7878c9bbf7178fd536595df7c3d4de9fe52cd819d37c7de91cf44ca0","last_reissued_at":"2026-05-18T01:37:48.743130Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:48.743130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.04389","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":"2026-05-18T01:37:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PftMdjEglZ9mCSnpYm8jnmqjKeIkDGSLv1/RniAQkKB4SgAGojhBexQ3OX/T8dLxvkiwLhaZOcYg0l5KtV5wCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:25:44.051141Z"},"content_sha256":"aeccdd743f374fa8baca596d2967bba8b7787b040a4f0bd7f775714851f12d80","schema_version":"1.0","event_id":"sha256:aeccdd743f374fa8baca596d2967bba8b7787b040a4f0bd7f775714851f12d80"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ABM7OPDYPDE3X5YXR7KTMWK567","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Online Matrix Factorization via Broyden Updates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"\\\"Omer Deniz Aky{\\i}ld{\\i}z","submitted_at":"2015-06-14T13:19:38Z","abstract_excerpt":"In this paper, we propose an online algorithm to compute matrix factorizations. Proposed algorithm updates the dictionary matrix and associated coefficients using a single observation at each time. The algorithm performs low-rank updates to dictionary matrix. We derive the algorithm by defining a simple objective function to minimize whenever an observation is arrived. We extend the algorithm further for handling missing data. We also provide a mini-batch extension which enables to compute the matrix factorization on big datasets. We demonstrate the efficiency of our algorithm on a real datase"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04389","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":"2026-05-18T01:37:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gKW81j7SyHhY6XXqJvRDbUUZkj822UJsyVfNXCzyv7DGnVg6FY024vt4OusIGOxEGu8FsYEubJhvogUC6iF+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:25:44.051856Z"},"content_sha256":"9b839350edea7f40c9f959c48f8d15bd01cce99a3fd2cb16d93cfca995d9b2b4","schema_version":"1.0","event_id":"sha256:9b839350edea7f40c9f959c48f8d15bd01cce99a3fd2cb16d93cfca995d9b2b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ABM7OPDYPDE3X5YXR7KTMWK567/bundle.json","state_url":"https://pith.science/pith/ABM7OPDYPDE3X5YXR7KTMWK567/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ABM7OPDYPDE3X5YXR7KTMWK567/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":"2026-05-26T20:25:44Z","links":{"resolver":"https://pith.science/pith/ABM7OPDYPDE3X5YXR7KTMWK567","bundle":"https://pith.science/pith/ABM7OPDYPDE3X5YXR7KTMWK567/bundle.json","state":"https://pith.science/pith/ABM7OPDYPDE3X5YXR7KTMWK567/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ABM7OPDYPDE3X5YXR7KTMWK567/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ABM7OPDYPDE3X5YXR7KTMWK567","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":"b24df0371fc1b0fc8d4c33975591fc2c7c309b4080a7c249ad9e5f048a66f6f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-14T13:19:38Z","title_canon_sha256":"26e641a277d81279871335034ffcb621e88d16c9f62d0e4cf020ba5768310117"},"schema_version":"1.0","source":{"id":"1506.04389","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.04389","created_at":"2026-05-18T01:37:48Z"},{"alias_kind":"arxiv_version","alias_value":"1506.04389v2","created_at":"2026-05-18T01:37:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04389","created_at":"2026-05-18T01:37:48Z"},{"alias_kind":"pith_short_12","alias_value":"ABM7OPDYPDE3","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ABM7OPDYPDE3X5YX","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ABM7OPDY","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:9b839350edea7f40c9f959c48f8d15bd01cce99a3fd2cb16d93cfca995d9b2b4","target":"graph","created_at":"2026-05-18T01:37:48Z","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":"In this paper, we propose an online algorithm to compute matrix factorizations. Proposed algorithm updates the dictionary matrix and associated coefficients using a single observation at each time. The algorithm performs low-rank updates to dictionary matrix. We derive the algorithm by defining a simple objective function to minimize whenever an observation is arrived. We extend the algorithm further for handling missing data. We also provide a mini-batch extension which enables to compute the matrix factorization on big datasets. We demonstrate the efficiency of our algorithm on a real datase","authors_text":"\\\"Omer Deniz Aky{\\i}ld{\\i}z","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-14T13:19:38Z","title":"Online Matrix Factorization via Broyden Updates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04389","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:aeccdd743f374fa8baca596d2967bba8b7787b040a4f0bd7f775714851f12d80","target":"record","created_at":"2026-05-18T01:37:48Z","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":"b24df0371fc1b0fc8d4c33975591fc2c7c309b4080a7c249ad9e5f048a66f6f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-14T13:19:38Z","title_canon_sha256":"26e641a277d81279871335034ffcb621e88d16c9f62d0e4cf020ba5768310117"},"schema_version":"1.0","source":{"id":"1506.04389","kind":"arxiv","version":2}},"canonical_sha256":"0059f73c7878c9bbf7178fd536595df7c3d4de9fe52cd819d37c7de91cf44ca0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0059f73c7878c9bbf7178fd536595df7c3d4de9fe52cd819d37c7de91cf44ca0","first_computed_at":"2026-05-18T01:37:48.743130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:48.743130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K+2D0JVyzTUTL370HFxsZzLnJKex4K4LkxEriE6KNCRJPQ6Ad+UhQmN9F/d2URA0xCVX/O28NcPRwKEIoTXYDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:48.743765Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.04389","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aeccdd743f374fa8baca596d2967bba8b7787b040a4f0bd7f775714851f12d80","sha256:9b839350edea7f40c9f959c48f8d15bd01cce99a3fd2cb16d93cfca995d9b2b4"],"state_sha256":"483c39168bcc3866e5a89bf0704bcdf6b7d4ad5832af694822ad9b1d56d785cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HZlRaUfoQT1tkMBl0nGS/H0hDIqkkUAtbaChbqamyBv5KDGcL7r7mUz3MRg4wRfXLnokDPM2nBtNE0+Xyn7kAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T20:25:44.055526Z","bundle_sha256":"c03952d7096dd2211c0a5ce0590122e59c7cc9845eabf13f9fdc7c8d15a9f0a7"}}