{"paper":{"title":"Exact Reconstruction of Euclidean Distance Geometry Problem Using Low-rank Matrix Completion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.IT","math.NA","math.OC"],"primary_cat":"cs.IT","authors_text":"Abiy Tasissa, Rongjie Lai","submitted_at":"2018-04-12T04:28:06Z","abstract_excerpt":"The Euclidean distance geometry problem arises in a wide variety of applications, from determining molecular conformations in computational chemistry to localization in sensor networks. When the distance information is incomplete, the problem can be formulated as a nuclear norm minimization problem. In this paper, this minimization program is recast as a matrix completion problem of a low-rank $r$ Gram matrix with respect to a suitable basis. The well known restricted isometry property can not be satisfied in this scenario. Instead, a dual basis approach is introduced to theoretically analyze "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04310","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"}