{"paper":{"title":"Quantum Divide-and-Conquer Anchoring for Separable Non-negative Matrix Factorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dacheng Tao, Runyao Duan, Tongliang Liu, Yinan Li, Yuxuan Du","submitted_at":"2018-02-20T04:03:09Z","abstract_excerpt":"It is NP-complete to find non-negative factors $W$ and $H$ with fixed rank $r$ from a non-negative matrix $X$ by minimizing $\\|X-WH^\\top\\|_F^2$. Although the separability assumption (all data points are in the conical hull of the extreme rows) enables polynomial-time algorithms, the computational cost is not affordable for big data. This paper investigates how the power of quantum computation can be capitalized to solve the non-negative matrix factorization with the separability assumption (SNMF) by devising a quantum algorithm based on the divide-and-conquer anchoring (DCA) scheme. The design"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07828","kind":"arxiv","version":1},"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"}