{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:7TYEKQC5XSV24MZCMSAEAMPAJA","short_pith_number":"pith:7TYEKQC5","schema_version":"1.0","canonical_sha256":"fcf045405dbcabae332264804031e04810f0e3df4654e84f2756850c1ff0932c","source":{"kind":"arxiv","id":"1406.2646","version":1},"attestation_state":"computed","paper":{"title":"Learning with Cross-Kernels and Ideal PCA","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Franz J Kir\\'aly, Louis Theran, Martin Kreuzer","submitted_at":"2014-06-10T17:48:58Z","abstract_excerpt":"We describe how cross-kernel matrices, that is, kernel matrices between the data and a custom chosen set of `feature spanning points' can be used for learning. The main potential of cross-kernels lies in the fact that (a) only one side of the matrix scales with the number of data points, and (b) cross-kernels, as opposed to the usual kernel matrices, can be used to certify for the data manifold. Our theoretical framework, which is based on a duality involving the feature space and vanishing ideals, indicates that cross-kernels have the potential to be used for any kind of kernel learning. We p"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1406.2646","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-06-10T17:48:58Z","cross_cats_sorted":["math.AC","stat.ML"],"title_canon_sha256":"46df9180c0309abdc71901289db51e748bad97386131b703aeb91941f5175f75","abstract_canon_sha256":"95ea6103f630db0cdacd8359f2a7fc1c85b6174e461d4401e7565abbcec84a68"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:01.240443Z","signature_b64":"3RngJxGPawu+fFkHFQWLR3CccK8tIyGJaNMyclY+340rTNpwsJ1Y360btwT7JQMw8J6HFl5jJXDn6mTQvm+5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fcf045405dbcabae332264804031e04810f0e3df4654e84f2756850c1ff0932c","last_reissued_at":"2026-05-18T02:50:01.239953Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:01.239953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Learning with Cross-Kernels and Ideal PCA","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Franz J Kir\\'aly, Louis Theran, Martin Kreuzer","submitted_at":"2014-06-10T17:48:58Z","abstract_excerpt":"We describe how cross-kernel matrices, that is, kernel matrices between the data and a custom chosen set of `feature spanning points' can be used for learning. The main potential of cross-kernels lies in the fact that (a) only one side of the matrix scales with the number of data points, and (b) cross-kernels, as opposed to the usual kernel matrices, can be used to certify for the data manifold. Our theoretical framework, which is based on a duality involving the feature space and vanishing ideals, indicates that cross-kernels have the potential to be used for any kind of kernel learning. We p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2646","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1406.2646","created_at":"2026-05-18T02:50:01.240018+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.2646v1","created_at":"2026-05-18T02:50:01.240018+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2646","created_at":"2026-05-18T02:50:01.240018+00:00"},{"alias_kind":"pith_short_12","alias_value":"7TYEKQC5XSV2","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"7TYEKQC5XSV24MZC","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"7TYEKQC5","created_at":"2026-05-18T12:28:19.803747+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7TYEKQC5XSV24MZCMSAEAMPAJA","json":"https://pith.science/pith/7TYEKQC5XSV24MZCMSAEAMPAJA.json","graph_json":"https://pith.science/api/pith-number/7TYEKQC5XSV24MZCMSAEAMPAJA/graph.json","events_json":"https://pith.science/api/pith-number/7TYEKQC5XSV24MZCMSAEAMPAJA/events.json","paper":"https://pith.science/paper/7TYEKQC5"},"agent_actions":{"view_html":"https://pith.science/pith/7TYEKQC5XSV24MZCMSAEAMPAJA","download_json":"https://pith.science/pith/7TYEKQC5XSV24MZCMSAEAMPAJA.json","view_paper":"https://pith.science/paper/7TYEKQC5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.2646&json=true","fetch_graph":"https://pith.science/api/pith-number/7TYEKQC5XSV24MZCMSAEAMPAJA/graph.json","fetch_events":"https://pith.science/api/pith-number/7TYEKQC5XSV24MZCMSAEAMPAJA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7TYEKQC5XSV24MZCMSAEAMPAJA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7TYEKQC5XSV24MZCMSAEAMPAJA/action/storage_attestation","attest_author":"https://pith.science/pith/7TYEKQC5XSV24MZCMSAEAMPAJA/action/author_attestation","sign_citation":"https://pith.science/pith/7TYEKQC5XSV24MZCMSAEAMPAJA/action/citation_signature","submit_replication":"https://pith.science/pith/7TYEKQC5XSV24MZCMSAEAMPAJA/action/replication_record"}},"created_at":"2026-05-18T02:50:01.240018+00:00","updated_at":"2026-05-18T02:50:01.240018+00:00"}