{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:Y5BVFSLOCLVP7FQ72CCKGTQMBE","short_pith_number":"pith:Y5BVFSLO","canonical_record":{"source":{"id":"1111.2111","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-11-09T06:39:17Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"1ed5ba3889ed65255678cad7c87116c37eea6e764c2a95530ed5f3a79ad2ab35","abstract_canon_sha256":"451dd237e670ac7e1784957d721b1cfb40a299e540c19b197efdeda948103552"},"schema_version":"1.0"},"canonical_sha256":"c74352c96e12eaff961fd084a34e0c09048e48a9e18f6a4a2a29b5fbd6ce431e","source":{"kind":"arxiv","id":"1111.2111","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2111","created_at":"2026-05-18T04:07:07Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2111v2","created_at":"2026-05-18T04:07:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2111","created_at":"2026-05-18T04:07:07Z"},{"alias_kind":"pith_short_12","alias_value":"Y5BVFSLOCLVP","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Y5BVFSLOCLVP7FQ7","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Y5BVFSLO","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:Y5BVFSLOCLVP7FQ72CCKGTQMBE","target":"record","payload":{"canonical_record":{"source":{"id":"1111.2111","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-11-09T06:39:17Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"1ed5ba3889ed65255678cad7c87116c37eea6e764c2a95530ed5f3a79ad2ab35","abstract_canon_sha256":"451dd237e670ac7e1784957d721b1cfb40a299e540c19b197efdeda948103552"},"schema_version":"1.0"},"canonical_sha256":"c74352c96e12eaff961fd084a34e0c09048e48a9e18f6a4a2a29b5fbd6ce431e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:07.516914Z","signature_b64":"U2EjPZteQvZnsYvJtcBp+7hKvCcefBPlxnhvcJbpyV5ZYDlWCEPzzbEKa2cS06F18Ptxc9GFtDRl4mFv4amGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c74352c96e12eaff961fd084a34e0c09048e48a9e18f6a4a2a29b5fbd6ce431e","last_reissued_at":"2026-05-18T04:07:07.516218Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:07.516218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.2111","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":"2026-05-18T04:07:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0vA8O/86yYiI+U2NZlYJz/lmm//X40LiIVOlyggBCZ5lsqfz/k45qdckGu8dx5HvtVjNr8EVbfPLbSCNEo5OAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:26:29.010367Z"},"content_sha256":"a49dee73d3351682538537adcbca28951b23d0bc5a0f07d4e0baff477607a3d0","schema_version":"1.0","event_id":"sha256:a49dee73d3351682538537adcbca28951b23d0bc5a0f07d4e0baff477607a3d0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:Y5BVFSLOCLVP7FQ72CCKGTQMBE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generic Multiplicative Methods for Implementing Machine Learning Algorithms on MapReduce","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Nello Cristianini, Peter Flach, Song Liu","submitted_at":"2011-11-09T06:39:17Z","abstract_excerpt":"In this paper we introduce a generic model for multiplicative algorithms which is suitable for the MapReduce parallel programming paradigm. We implement three typical machine learning algorithms to demonstrate how similarity comparison, gradient descent, power method and other classic learning techniques fit this model well. Two versions of large-scale matrix multiplication are discussed in this paper, and different methods are developed for both cases with regard to their unique computational characteristics and problem settings. In contrast to earlier research, we focus on fundamental linear"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2111","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":"2026-05-18T04:07:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KqoyNFZ6b/H6Fg2L9Uyw8R7woF1mN8Cp4Qmbw+EJeBBgTbmO5vbyXs0d/xqmiuNFM4QVnWlqNS2ynELeeyWsAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:26:29.010986Z"},"content_sha256":"2293056b75fb2c9e9095f36f089fbfe558f0c90c6b6231bdda9acd9bb6a210ce","schema_version":"1.0","event_id":"sha256:2293056b75fb2c9e9095f36f089fbfe558f0c90c6b6231bdda9acd9bb6a210ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y5BVFSLOCLVP7FQ72CCKGTQMBE/bundle.json","state_url":"https://pith.science/pith/Y5BVFSLOCLVP7FQ72CCKGTQMBE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y5BVFSLOCLVP7FQ72CCKGTQMBE/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":"2026-05-27T18:26:29Z","links":{"resolver":"https://pith.science/pith/Y5BVFSLOCLVP7FQ72CCKGTQMBE","bundle":"https://pith.science/pith/Y5BVFSLOCLVP7FQ72CCKGTQMBE/bundle.json","state":"https://pith.science/pith/Y5BVFSLOCLVP7FQ72CCKGTQMBE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y5BVFSLOCLVP7FQ72CCKGTQMBE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Y5BVFSLOCLVP7FQ72CCKGTQMBE","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":"451dd237e670ac7e1784957d721b1cfb40a299e540c19b197efdeda948103552","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-11-09T06:39:17Z","title_canon_sha256":"1ed5ba3889ed65255678cad7c87116c37eea6e764c2a95530ed5f3a79ad2ab35"},"schema_version":"1.0","source":{"id":"1111.2111","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2111","created_at":"2026-05-18T04:07:07Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2111v2","created_at":"2026-05-18T04:07:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2111","created_at":"2026-05-18T04:07:07Z"},{"alias_kind":"pith_short_12","alias_value":"Y5BVFSLOCLVP","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Y5BVFSLOCLVP7FQ7","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Y5BVFSLO","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:2293056b75fb2c9e9095f36f089fbfe558f0c90c6b6231bdda9acd9bb6a210ce","target":"graph","created_at":"2026-05-18T04:07:07Z","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 introduce a generic model for multiplicative algorithms which is suitable for the MapReduce parallel programming paradigm. We implement three typical machine learning algorithms to demonstrate how similarity comparison, gradient descent, power method and other classic learning techniques fit this model well. Two versions of large-scale matrix multiplication are discussed in this paper, and different methods are developed for both cases with regard to their unique computational characteristics and problem settings. In contrast to earlier research, we focus on fundamental linear","authors_text":"Nello Cristianini, Peter Flach, Song Liu","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-11-09T06:39:17Z","title":"Generic Multiplicative Methods for Implementing Machine Learning Algorithms on MapReduce"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2111","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:a49dee73d3351682538537adcbca28951b23d0bc5a0f07d4e0baff477607a3d0","target":"record","created_at":"2026-05-18T04:07:07Z","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":"451dd237e670ac7e1784957d721b1cfb40a299e540c19b197efdeda948103552","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-11-09T06:39:17Z","title_canon_sha256":"1ed5ba3889ed65255678cad7c87116c37eea6e764c2a95530ed5f3a79ad2ab35"},"schema_version":"1.0","source":{"id":"1111.2111","kind":"arxiv","version":2}},"canonical_sha256":"c74352c96e12eaff961fd084a34e0c09048e48a9e18f6a4a2a29b5fbd6ce431e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c74352c96e12eaff961fd084a34e0c09048e48a9e18f6a4a2a29b5fbd6ce431e","first_computed_at":"2026-05-18T04:07:07.516218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:07.516218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U2EjPZteQvZnsYvJtcBp+7hKvCcefBPlxnhvcJbpyV5ZYDlWCEPzzbEKa2cS06F18Ptxc9GFtDRl4mFv4amGAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:07.516914Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.2111","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a49dee73d3351682538537adcbca28951b23d0bc5a0f07d4e0baff477607a3d0","sha256:2293056b75fb2c9e9095f36f089fbfe558f0c90c6b6231bdda9acd9bb6a210ce"],"state_sha256":"dcd696f94da71e240c0f0bd97aa0997916f205dd0fff7f9d82d148e0687f1c81"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cJecyFGY0dALNMjuRF5BBglh2vTREaEfkm8rV5zL/8MPgcqkk0A3YE5uSu9HxNbqmIrQLLqz/EUOUNhJnChvBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T18:26:29.014071Z","bundle_sha256":"0f2bfe256dfbf6aa999e4f72c8a1205754d75861c38473436fed1204a1291fb9"}}