{"paper":{"title":"Deterministic and Probabilistic Conditions for Finite Completability of Low-rank Multi-View Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.AG","math.IT"],"primary_cat":"cs.IT","authors_text":"Morteza Ashraphijuo, Vaneet Aggarwal, Xiaodong Wang","submitted_at":"2017-01-03T16:23:48Z","abstract_excerpt":"We consider the multi-view data completion problem, i.e., to complete a matrix $\\mathbf{U}=[\\mathbf{U}_1|\\mathbf{U}_2]$ where the ranks of $\\mathbf{U},\\mathbf{U}_1$, and $\\mathbf{U}_2$ are given. In particular, we investigate the fundamental conditions on the sampling pattern, i.e., locations of the sampled entries for finite completability of such a multi-view data given the corresponding rank constraints. In contrast with the existing analysis on Grassmannian manifold for a single-view matrix, i.e., conventional matrix completion, we propose a geometric analysis on the manifold structure for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00737","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"}