{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:F5TXYUZTA26WX5X6QVSHSNH2GL","short_pith_number":"pith:F5TXYUZT","canonical_record":{"source":{"id":"1903.06877","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-03-16T04:18:33Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"c39e00d847a00e49b0e78e3dd988e775331d0b72d3aab6edece0f3cde97a1195","abstract_canon_sha256":"608cf67cd4d1a1b255b53a131306d2daa570f8a6314080872118933d97d3e002"},"schema_version":"1.0"},"canonical_sha256":"2f677c533306bd6bf6fe85647934fa32e174e3aeb5d5517970f2990281038950","source":{"kind":"arxiv","id":"1903.06877","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.06877","created_at":"2026-05-17T23:51:08Z"},{"alias_kind":"arxiv_version","alias_value":"1903.06877v1","created_at":"2026-05-17T23:51:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.06877","created_at":"2026-05-17T23:51:08Z"},{"alias_kind":"pith_short_12","alias_value":"F5TXYUZTA26W","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"F5TXYUZTA26WX5X6","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"F5TXYUZT","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:F5TXYUZTA26WX5X6QVSHSNH2GL","target":"record","payload":{"canonical_record":{"source":{"id":"1903.06877","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-03-16T04:18:33Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"c39e00d847a00e49b0e78e3dd988e775331d0b72d3aab6edece0f3cde97a1195","abstract_canon_sha256":"608cf67cd4d1a1b255b53a131306d2daa570f8a6314080872118933d97d3e002"},"schema_version":"1.0"},"canonical_sha256":"2f677c533306bd6bf6fe85647934fa32e174e3aeb5d5517970f2990281038950","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:08.731143Z","signature_b64":"6yxOBCfkIxsk5uvaqV/3zACBOk4V1NaU6fSwXdDu4/L6fmmD3vCJoonuGd74joShQifmCLa9ZFdHOF1UIiLACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f677c533306bd6bf6fe85647934fa32e174e3aeb5d5517970f2990281038950","last_reissued_at":"2026-05-17T23:51:08.730465Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:08.730465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.06877","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":"2026-05-17T23:51:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J80cbDuojxBC93gQYv4bHvC3rkEZ49jsWpIWkN9MOps43HmmN8sI2HFpkrZXQk8nLE3mQebNFUVMCRPL7Ww/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:51:53.713888Z"},"content_sha256":"777649695bc6baebac1970f9901c61fa6f5a88584b266684fbc63ab7c566ca7e","schema_version":"1.0","event_id":"sha256:777649695bc6baebac1970f9901c61fa6f5a88584b266684fbc63ab7c566ca7e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:F5TXYUZTA26WX5X6QVSHSNH2GL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spherical Principal Component Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Gongguo Tang, Hua Wang, Kai Liu, Qiuwei Li","submitted_at":"2019-03-16T04:18:33Z","abstract_excerpt":"Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in some fields, angle distance is known to be more important and critical for analysis. In this paper, we propose a method by adding constraints on factors to unify the Euclidean distance and angle distance. However, due to the nonconvexity of the objective and constraints, the optimized solution is not easy to obtain. We propose an alternating linearized mini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06877","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":"2026-05-17T23:51:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kRm7kWcxxOOMP+lJ0WXz0EOnAKuWAKrIXgOrHd+I8faEjjuzXXvnMUVU2b/Q90Bx1h05Lg0UdIV7FniQcaJbBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:51:53.714255Z"},"content_sha256":"98aeb40fde7e69065e5f07affd9a78749f6fd34537829dcf57e8674c6b0f9a86","schema_version":"1.0","event_id":"sha256:98aeb40fde7e69065e5f07affd9a78749f6fd34537829dcf57e8674c6b0f9a86"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F5TXYUZTA26WX5X6QVSHSNH2GL/bundle.json","state_url":"https://pith.science/pith/F5TXYUZTA26WX5X6QVSHSNH2GL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F5TXYUZTA26WX5X6QVSHSNH2GL/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":"2026-06-05T21:51:53Z","links":{"resolver":"https://pith.science/pith/F5TXYUZTA26WX5X6QVSHSNH2GL","bundle":"https://pith.science/pith/F5TXYUZTA26WX5X6QVSHSNH2GL/bundle.json","state":"https://pith.science/pith/F5TXYUZTA26WX5X6QVSHSNH2GL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F5TXYUZTA26WX5X6QVSHSNH2GL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:F5TXYUZTA26WX5X6QVSHSNH2GL","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":"608cf67cd4d1a1b255b53a131306d2daa570f8a6314080872118933d97d3e002","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-03-16T04:18:33Z","title_canon_sha256":"c39e00d847a00e49b0e78e3dd988e775331d0b72d3aab6edece0f3cde97a1195"},"schema_version":"1.0","source":{"id":"1903.06877","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.06877","created_at":"2026-05-17T23:51:08Z"},{"alias_kind":"arxiv_version","alias_value":"1903.06877v1","created_at":"2026-05-17T23:51:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.06877","created_at":"2026-05-17T23:51:08Z"},{"alias_kind":"pith_short_12","alias_value":"F5TXYUZTA26W","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"F5TXYUZTA26WX5X6","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"F5TXYUZT","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:98aeb40fde7e69065e5f07affd9a78749f6fd34537829dcf57e8674c6b0f9a86","target":"graph","created_at":"2026-05-17T23:51:08Z","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":"Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in some fields, angle distance is known to be more important and critical for analysis. In this paper, we propose a method by adding constraints on factors to unify the Euclidean distance and angle distance. However, due to the nonconvexity of the objective and constraints, the optimized solution is not easy to obtain. We propose an alternating linearized mini","authors_text":"Gongguo Tang, Hua Wang, Kai Liu, Qiuwei Li","cross_cats":["math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-03-16T04:18:33Z","title":"Spherical Principal Component Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06877","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":"sha256:777649695bc6baebac1970f9901c61fa6f5a88584b266684fbc63ab7c566ca7e","target":"record","created_at":"2026-05-17T23:51:08Z","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":"608cf67cd4d1a1b255b53a131306d2daa570f8a6314080872118933d97d3e002","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-03-16T04:18:33Z","title_canon_sha256":"c39e00d847a00e49b0e78e3dd988e775331d0b72d3aab6edece0f3cde97a1195"},"schema_version":"1.0","source":{"id":"1903.06877","kind":"arxiv","version":1}},"canonical_sha256":"2f677c533306bd6bf6fe85647934fa32e174e3aeb5d5517970f2990281038950","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f677c533306bd6bf6fe85647934fa32e174e3aeb5d5517970f2990281038950","first_computed_at":"2026-05-17T23:51:08.730465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:08.730465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6yxOBCfkIxsk5uvaqV/3zACBOk4V1NaU6fSwXdDu4/L6fmmD3vCJoonuGd74joShQifmCLa9ZFdHOF1UIiLACA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:08.731143Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.06877","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:777649695bc6baebac1970f9901c61fa6f5a88584b266684fbc63ab7c566ca7e","sha256:98aeb40fde7e69065e5f07affd9a78749f6fd34537829dcf57e8674c6b0f9a86"],"state_sha256":"f38616dac429fbcdddf65e73b1c68df1b2ba32e8aefde73482705351e6cd5479"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jSl2svcp9GPmz8J+KkNsL1CySbfBaQyyW136ddW5whU7mwJPB/azSr97wMMBwe9ukNT2xzw6tZlVcbxMJuVuDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T21:51:53.716488Z","bundle_sha256":"2f9f14de46c73fcd8d96ee3368425286ff25cf8d34f90d83e590a2c182a47df6"}}