{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:WQNHONVZYW6M3IXPBFJH534S5O","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":"eefc0766030b3bc63160212f68c1ecce96e7ae0cc86264f081c7ab29f68933fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-10-31T10:39:40Z","title_canon_sha256":"7d7f4a8389def96eb0c1c1554548e83ebdf01712bbcf984130c60e6f49f0f7ca"},"schema_version":"1.0","source":{"id":"1210.8290","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.8290","created_at":"2026-05-18T03:07:34Z"},{"alias_kind":"arxiv_version","alias_value":"1210.8290v2","created_at":"2026-05-18T03:07:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.8290","created_at":"2026-05-18T03:07:34Z"},{"alias_kind":"pith_short_12","alias_value":"WQNHONVZYW6M","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"WQNHONVZYW6M3IXP","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"WQNHONVZ","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:f341f926098c6d0c845774340662203ddffc645c7fd49c316f4d5d1bec7287e8","target":"graph","created_at":"2026-05-18T03:07:34Z","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 extend the Beta divergence family to multivariate power spectral densities. Similarly to the scalar case, we show that it smoothly connects the multivariate Kullback-Leibler divergence with the multivariate Itakura-Saito distance. We successively study a spectrum approximation problem, based on the Beta divergence family, which is related to a multivariate extension of the THREE spectral estimation technique. It is then possible to characterize a family of solutions to the problem. An upper bound on the complexity of these solutions will also be provided. Simulations suggest ","authors_text":"Mattia Zorzi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-10-31T10:39:40Z","title":"A new family of high-resolution multivariate spectral estimators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.8290","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":"sha256:5079f6e7ee6e72861cae3bbc70565af137cf4974054e2d79e79f7534060003bb","target":"record","created_at":"2026-05-18T03:07:34Z","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":"eefc0766030b3bc63160212f68c1ecce96e7ae0cc86264f081c7ab29f68933fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-10-31T10:39:40Z","title_canon_sha256":"7d7f4a8389def96eb0c1c1554548e83ebdf01712bbcf984130c60e6f49f0f7ca"},"schema_version":"1.0","source":{"id":"1210.8290","kind":"arxiv","version":2}},"canonical_sha256":"b41a7736b9c5bccda2ef09527eef92eba566cc100a3f09cf7672e0a1f6eeedd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b41a7736b9c5bccda2ef09527eef92eba566cc100a3f09cf7672e0a1f6eeedd5","first_computed_at":"2026-05-18T03:07:34.636979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:34.636979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3+3rHX5j3sgRyIm4Twko7XcSBE0ExH4QvJeWLF+vRbrHRcA4paAvP63O/OTvRwKKTxOnieVS3tLyahL7WR3gDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:34.637443Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.8290","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5079f6e7ee6e72861cae3bbc70565af137cf4974054e2d79e79f7534060003bb","sha256:f341f926098c6d0c845774340662203ddffc645c7fd49c316f4d5d1bec7287e8"],"state_sha256":"02ec7041b3eac7406749aee0914edef25c7d030dc6f02c6cfcccabff7f3dd78c"}