{"paper":{"title":"The Projected Power Method: An Efficient Algorithm for Joint Alignment from Pairwise Differences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","cs.LG","math.IT","math.OC","stat.ML"],"primary_cat":"cs.IT","authors_text":"Emmanuel Candes, Yuxin Chen","submitted_at":"2016-09-19T16:29:46Z","abstract_excerpt":"Various applications involve assigning discrete label values to a collection of objects based on some pairwise noisy data. Due to the discrete---and hence nonconvex---structure of the problem, computing the optimal assignment (e.g.~maximum likelihood assignment) becomes intractable at first sight. This paper makes progress towards efficient computation by focusing on a concrete joint alignment problem---that is, the problem of recovering $n$ discrete variables $x_i \\in \\{1,\\cdots, m\\}$, $1\\leq i\\leq n$ given noisy observations of their modulo differences $\\{x_i - x_j~\\mathsf{mod}~m\\}$. We prop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05820","kind":"arxiv","version":3},"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"}