{"paper":{"title":"Guaranteed Non-Orthogonal Tensor Decomposition via Alternating Rank-$1$ Updates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","stat.ML"],"primary_cat":"cs.LG","authors_text":"Animashree Anandkumar, Majid Janzamin, Rong Ge","submitted_at":"2014-02-21T01:37:02Z","abstract_excerpt":"In this paper, we provide local and global convergence guarantees for recovering CP (Candecomp/Parafac) tensor decomposition. The main step of the proposed algorithm is a simple alternating rank-$1$ update which is the alternating version of the tensor power iteration adapted for asymmetric tensors. Local convergence guarantees are established for third order tensors of rank $k$ in $d$ dimensions, when $k=o \\bigl( d^{1.5} \\bigr)$ and the tensor components are incoherent. Thus, we can recover overcomplete tensor decomposition. We also strengthen the results to global convergence guarantees unde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5180","kind":"arxiv","version":4},"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"}